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| author | Chanho Park <chanho61.park@samsung.com> | 2014-12-11 18:55:56 +0900 |
|---|---|---|
| committer | Chanho Park <chanho61.park@samsung.com> | 2014-12-11 18:55:56 +0900 |
| commit | 08c1e93fa36a49f49325a07fe91ff92c964c2b6c (patch) | |
| tree | 7a7053ceb8874b28ec4b868d4c49b500008a102e /libs/multiprecision | |
| parent | bb4dd8289b351fae6b55e303f189127a394a1edd (diff) | |
| download | boost-08c1e93fa36a49f49325a07fe91ff92c964c2b6c.tar.gz boost-08c1e93fa36a49f49325a07fe91ff92c964c2b6c.tar.bz2 boost-08c1e93fa36a49f49325a07fe91ff92c964c2b6c.zip | |
Imported Upstream version 1.57.0upstream/1.57.0
Diffstat (limited to 'libs/multiprecision')
419 files changed, 77678 insertions, 0 deletions
diff --git a/libs/multiprecision/config/Jamfile.v2 b/libs/multiprecision/config/Jamfile.v2 new file mode 100644 index 0000000000..563671f25f --- /dev/null +++ b/libs/multiprecision/config/Jamfile.v2 @@ -0,0 +1,64 @@ +# copyright John Maddock 2008 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local mpfi_path = [ modules.peek : MPFI_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project : requirements + <include>$(gmp_path) + <include>$(gmp_path)/mpfr + <include>$(gmp_path)/gmpfrxx + <include>$(mpfr_path) + <include>$(mpfi_path) + <include>$(mpfi_path)/src + <include>$(tommath_path) + <include>../../.. + <search>$(gmp_path) + <search>$(mpfr_path) + <search>$(mpfr_path)/build.vc10/lib/Win32/Debug + <search>$(tommath_path) + <search>$(mpfi_path) + <search>$(mpfi_path)/src + # We set these to make it easier to set up and test GMP and MPFR under Win32: + <toolset>msvc:<runtime-link>static + <toolset>msvc:<link>static + <toolset>intel-win:<runtime-link>static + <toolset>intel-win:<link>static + <toolset>msvc:<warnings>all + <toolset>gcc:<cxxflags>-Wall + <toolset>gcc:<cxxflags>-Wextra + ; + +lib gmp ; +lib mpfr ; +lib mpfi ; +lib quadmath ; + +exe has_gmp : has_gmp.cpp gmp : + <include>$(gmp_path) <include>$(gmp_path)/mpfr <include>$(gmp_path)/gmpfrxx ; +exe has_mpfr : has_mpfr.cpp mpfr gmp : + <include>$(mpfr_path) <include>$(gmp_path)/mpfr <include>$(gmp_path)/gmpfrxx <include>$(gmp_path) ; +exe has_mpfi : has_mpfi.cpp mpfi mpfr gmp : + <include>$(mpfr_path) <include>$(gmp_path)/mpfr <include>$(gmp_path)/gmpfrxx <include>$(gmp_path) ; +obj has_tommath : has_tommath.cpp : + <include>$(tommath_path) ; +run has_float128.cpp quadmath : : : : has_float128 ; +exe has_intel_quad : has_intel_quad.cpp : <cxxflags>-Qoption,cpp,--extended_float_type ; + +explicit has_gmp ; +explicit has_mpfr ; +explicit has_mpfi ; +explicit has_tommath ; +explicit has_float128 ; +explicit has_intel_quad ; + + + + diff --git a/libs/multiprecision/config/has_float128.cpp b/libs/multiprecision/config/has_float128.cpp new file mode 100644 index 0000000000..38a9fee283 --- /dev/null +++ b/libs/multiprecision/config/has_float128.cpp @@ -0,0 +1,18 @@ +// Copyright John Maddock 2013. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +extern "C" { +#include <quadmath.h> +} + +int main() +{ + __float128 f = -2.0Q; + f = fabsq(f); + f = expq(f); + + return 0; +} + diff --git a/libs/multiprecision/config/has_gmp.cpp b/libs/multiprecision/config/has_gmp.cpp new file mode 100644 index 0000000000..8bb1fe7dc7 --- /dev/null +++ b/libs/multiprecision/config/has_gmp.cpp @@ -0,0 +1,32 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <gmp.h> +#include <boost/config.hpp> + +#ifdef __GNUC__ +#pragma message "__GNU_MP_VERSION=" BOOST_STRINGIZE(__GNU_MP_VERSION) +#pragma message "__GNU_MP_VERSION_MINOR=" BOOST_STRINGIZE(__GNU_MP_VERSION_MINOR) +#endif + +#if (__GNU_MP_VERSION < 4) || ((__GNU_MP_VERSION == 4) && (__GNU_MP_VERSION_MINOR < 2)) +#error "Incompatible GMP version" +#endif + +int main() +{ + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + + mpz_t integ; + mpz_init (integ); + mpz_clear (integ); + + return 0; +} + diff --git a/libs/multiprecision/config/has_intel_quad.cpp b/libs/multiprecision/config/has_intel_quad.cpp new file mode 100644 index 0000000000..a2db80cc50 --- /dev/null +++ b/libs/multiprecision/config/has_intel_quad.cpp @@ -0,0 +1,16 @@ +// Copyright John Maddock 2013. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +extern "C" _Quad __fabs(_Quad); + +int main() +{ + _Quad f = -2.0Q; + f = __fabsq(f); + + return 0; +} + + diff --git a/libs/multiprecision/config/has_mpfi.cpp b/libs/multiprecision/config/has_mpfi.cpp new file mode 100644 index 0000000000..b0e93e50d7 --- /dev/null +++ b/libs/multiprecision/config/has_mpfi.cpp @@ -0,0 +1,55 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <mpfi.h> +#include <boost/config.hpp> + +#ifdef __GNUC__ +#pragma message "MPFR_VERSION_STRING=" MPFR_VERSION_STRING +#endif + +#if (__GNU_MP_VERSION < 4) || ((__GNU_MP_VERSION == 4) && (__GNU_MP_VERSION_MINOR < 2)) +#error "Incompatible GMP version" +#endif + +#if (MPFR_VERSION < 3) +#error "Incompatible MPFR version" +#endif + +#ifdef __GNUC__ +#pragma message "__GNU_MP_VERSION=" BOOST_STRINGIZE(__GNU_MP_VERSION) +#pragma message "__GNU_MP_VERSION_MINOR=" BOOST_STRINGIZE(__GNU_MP_VERSION_MINOR) +#endif + +#if (__GNU_MP_VERSION < 4) || ((__GNU_MP_VERSION == 4) && (__GNU_MP_VERSION_MINOR < 2)) +#error "Incompatible GMP version" +#endif + +/* +#ifdef __GNUC__ +#pragma message "MPFI_VERSION_MAJOR=" BOOST_STRINGIZE(MPFI_VERSION_MAJOR) +#pragma message "MPFI_VERSION_MAJOR=" BOOST_STRINGIZE(MPFI_VERSION_MAJOR) +#endif + +#if MPFI_VERSION_MAJOR < 1 +#error "Incompatible MPFI version" +#endif +#if (MPFI_VERSION_MAJOR == 1) && (MPFI_VERSION_MINOR < 5) +#error "Incompatible MPFI version" +#endif +*/ +int main() +{ + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + + mpfr_buildopt_tls_p(); + + return 0; +} + diff --git a/libs/multiprecision/config/has_mpfr.cpp b/libs/multiprecision/config/has_mpfr.cpp new file mode 100644 index 0000000000..86101a3804 --- /dev/null +++ b/libs/multiprecision/config/has_mpfr.cpp @@ -0,0 +1,42 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <mpfr.h> +#include <boost/config.hpp> + +#ifdef __GNUC__ +#pragma message "MPFR_VERSION_STRING=" MPFR_VERSION_STRING +#endif + +#if (__GNU_MP_VERSION < 4) || ((__GNU_MP_VERSION == 4) && (__GNU_MP_VERSION_MINOR < 2)) +#error "Incompatible GMP version" +#endif + +#if (MPFR_VERSION < 3) +#error "Incompatible MPFR version" +#endif + +#ifdef __GNUC__ +#pragma message "__GNU_MP_VERSION=" BOOST_STRINGIZE(__GNU_MP_VERSION) +#pragma message "__GNU_MP_VERSION_MINOR=" BOOST_STRINGIZE(__GNU_MP_VERSION_MINOR) +#endif + +#if (__GNU_MP_VERSION < 4) || ((__GNU_MP_VERSION == 4) && (__GNU_MP_VERSION_MINOR < 2)) +#error "Incompatible GMP version" +#endif + +int main() +{ + void *(*alloc_func_ptr) (size_t); + void *(*realloc_func_ptr) (void *, size_t, size_t); + void (*free_func_ptr) (void *, size_t); + + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + + mpfr_buildopt_tls_p(); + + return 0; +} + diff --git a/libs/multiprecision/config/has_tommath.cpp b/libs/multiprecision/config/has_tommath.cpp new file mode 100644 index 0000000000..19f1d80115 --- /dev/null +++ b/libs/multiprecision/config/has_tommath.cpp @@ -0,0 +1,15 @@ +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <tommath.h> + +int main() +{ + mp_int v; + mp_init(&v); + mp_clear(&v); + return 0; +} + diff --git a/libs/multiprecision/doc/Jamfile.v2 b/libs/multiprecision/doc/Jamfile.v2 new file mode 100644 index 0000000000..c9479e570e --- /dev/null +++ b/libs/multiprecision/doc/Jamfile.v2 @@ -0,0 +1,82 @@ + +# Copyright John Maddock 2011. Use, modification, and distribution are +# subject to the Boost Software License, Version 1.0. (See accompanying +# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +using quickbook ; +using auto-index ; + +path-constant images_location : html ; +path-constant here : . ; + +xml multiprecision : multiprecision.qbk ; +boostbook standalone + : + multiprecision + : + # Path for links to Boost: + <xsl:param>boost.root=../../../.. + + # Some general style settings: + <xsl:param>table.footnote.number.format=1 + <xsl:param>footnote.number.format=1 + #<xsl:param>html.stylesheet=../../../../doc/src/boostbook.css + + # HTML options first: + # Use graphics not text for navigation: + <xsl:param>navig.graphics=1 + # How far down we chunk nested sections, basically all of them: + <xsl:param>chunk.section.depth=10 + # Don't put the first section on the same page as the TOC: + <xsl:param>chunk.first.sections=10 + # How far down sections get TOC's + <xsl:param>toc.section.depth=10 + # Max depth in each TOC: + <xsl:param>toc.max.depth=4 + # How far down we go with TOC's + #<xsl:param>generate.section.toc.level=10 + # Index on type: + <xsl:param>index.on.type=1 + + # PDF Options: + # TOC Generation: this is needed for FOP-0.9 and later: + <xsl:param>fop1.extensions=0 + <format>pdf:<xsl:param>xep.extensions=1 + # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9! + <format>pdf:<xsl:param>fop.extensions=0 + <format>pdf:<xsl:param>fop1.extensions=0 + # No indent on body text: + <format>pdf:<xsl:param>body.start.indent=0pt + # Margin size: + <format>pdf:<xsl:param>page.margin.inner=0.5in + # Margin size: + <format>pdf:<xsl:param>page.margin.outer=0.5in + # Paper type = A4 + <format>pdf:<xsl:param>paper.type=A4 + # Yes, we want graphics for admonishments: + <xsl:param>admon.graphics=1 + # Set this one for PDF generation *only*: + # default pnd graphics are awful in PDF form, + # better use SVG's instead: + <format>pdf:<xsl:param>admon.graphics.extension=".svg" + <format>pdf:<xsl:param>use.role.for.mediaobject=1 + <format>pdf:<xsl:param>preferred.mediaobject.role=print + <format>pdf:<xsl:param>img.src.path=$(images_location)/ + <format>pdf:<xsl:param>draft.mode="no" + <format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html + # Index generation: + <auto-index>on + <auto-index-script>$(here)/index.idx + <auto-index-prefix>$(here)/../../.. + <auto-index-verbose>on + <format>html:<auto-index-internal>on + <quickbook-define>enable_index + <format>pdf:<xsl:param>index.on.type=1 + ; + +install pdfinstall : standalone : <location>. <install-type>PDF <name>multiprecision.pdf ; + + + + + diff --git a/libs/multiprecision/doc/debugger1.png b/libs/multiprecision/doc/debugger1.png Binary files differnew file mode 100644 index 0000000000..2b19569772 --- /dev/null +++ b/libs/multiprecision/doc/debugger1.png diff --git a/libs/multiprecision/doc/debugger2.png b/libs/multiprecision/doc/debugger2.png Binary files differnew file mode 100644 index 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width="1em"/> + <mtable> + <mtr> + <mtd> + <mi>f</mi> + <mo>′</mo> + <mfenced> + <mrow> + <mi>x</mi> + </mrow> + </mfenced> + </mtd> + <mtd> + <mo>≈</mo> + </mtd> + <mtd> + <msub> + <mi>m</mi> + <mn>1</mn> + </msub> + <mo>+</mo> + <mi>O</mi> + <mfenced> + <mrow> + <mi>d</mi> + <msup> + <mi>x</mi> + <mn>2</mn> + </msup> + </mrow> + </mfenced> + </mtd> + </mtr> + <mtr> + <mtd> + <mi>f</mi> + <mo>′</mo> + <mfenced> + <mrow> + <mi>x</mi> + </mrow> + </mfenced> + </mtd> + <mtd> + <mo>≈</mo> + </mtd> + <mtd> + <mfrac> + <mn>4</mn> + <mn>3</mn> + </mfrac> + <msub> + <mi>m</mi> + <mn>1</mn> + </msub> + <mo>−</mo> + <mfrac> + <mn>1</mn> + <mn>3</mn> + </mfrac> + <msub> + <mi>m</mi> + <mn>2</mn> + </msub> + <mo>+</mo> + <mi>O</mi> + <mfenced> + <mrow> + <mi>d</mi> + <msup> + <mi>x</mi> + <mn>4</mn> + </msup> + </mrow> + </mfenced> + </mtd> + </mtr> + <mtr> + <mtd> + <mi>f</mi> + <mo>′</mo> + <mfenced> + <mrow> + <mi>x</mi> + </mrow> + </mfenced> + </mtd> + <mtd> + <mo>≈</mo> + </mtd> + <mtd> + 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\ No newline at end of file diff --git a/libs/multiprecision/doc/generate.sh b/libs/multiprecision/doc/generate.sh new file mode 100755 index 0000000000..27d1d5eff1 --- /dev/null +++ b/libs/multiprecision/doc/generate.sh @@ -0,0 +1,33 @@ +# Copyright John Maddock 2008. +# Use, modification and distribution are subject to the +# Boost Software License, Version 1.0. (See accompanying file +# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +# +# Generates SVG and PNG files from the MML masters. +# +# Paths to tools come first, change these to match your system: +# +math2svg='m:\download\open\SVGMath-0.3.1\math2svg.py' +python=/cygdrive/c/Python26/python.exe +inkscape=/cygdrive/c/progra~1/Inkscape/inkscape +# Image DPI: +dpi=120 + +for mmlfile in $*; do + svgfile=$(basename $mmlfile .mml).svg + pngfile=$(basename $svgfile .svg).png + tempfile=temp.mml + # strip html wrappers put in by MathCast: + cat $mmlfile | tr -d "\r\n" | sed -e 's/.*\(<math[^>]*>.*<\/math>\).*/\1/' > $tempfile + + echo Generating $svgfile + $python $math2svg $tempfile > $svgfile + echo Generating $pngfile + $inkscape -d $dpi -e $(cygpath -a -w $pngfile) $(cygpath -a -w $svgfile) + rm $tempfile +done + + + + + diff --git a/libs/multiprecision/doc/html/boost_multiprecision/indexes.html b/libs/multiprecision/doc/html/boost_multiprecision/indexes.html new file mode 100644 index 0000000000..4e16e2c321 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/indexes.html @@ -0,0 +1,49 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Indexes</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="prev" href="map/ack.html" title="Acknowledgements"> +<link rel="next" href="indexes/s01.html" title="Function Index"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="map/ack.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="indexes/s01.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="boost_multiprecision.indexes"></a><a class="link" href="indexes.html" title="Indexes">Indexes</a> +</h2></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="indexes/s01.html">Function Index</a></span></dt> +<dt><span class="section"><a href="indexes/s02.html">Class Index</a></span></dt> +<dt><span class="section"><a href="indexes/s03.html">Typedef Index</a></span></dt> +<dt><span class="section"><a href="indexes/s04.html">Index</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. 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"> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">abs</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/todo.html" title="TODO"><span class="index-entry-level-1">TODO</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">assign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">assign_components</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_1"></a><span class="term">B</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bits</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/random.html" title="Generating Random Numbers"><span class="index-entry-level-1">Generating Random Numbers</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/input_output.html" title="Input Output"><span class="index-entry-level-1">Input Output</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rounding.html" title="Rounding Rules for Conversions"><span class="index-entry-level-1">Rounding Rules for Conversions</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_flip</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_set</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_unset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_2"></a><span class="term">C</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">compare</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_3"></a><span class="term">D</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">data</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">default_precision</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">divide_qr</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_4"></a><span class="term">E</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">empty</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_acos</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_asin</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_atan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_atan2</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_and</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_or</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_xor</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_flip</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_set</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_unset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_ceil</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_complement</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_convert_to</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_cos</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_cosh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_decrement</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_divide</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_eq</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_exp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_fabs</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_floor</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_fmod</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_frexp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_gcd</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_get_sign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_gt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_increment</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_integer_sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_is_zero</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_lcm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_ldexp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_left_shift</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_log</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_log10</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_lt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_modulus</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_msb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply_add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply_subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_pow</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_powm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_qr</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_right_shift</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_round</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_scalbn</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sin</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sinh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_tan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_tanh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_trunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_5"></a><span class="term">F</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">fpclassify</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_7"></a><span class="term">I</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">if</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">Primality Testing</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">ilogb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">in</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">infinity</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">integer_modulus</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">iround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isfinite</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isinf</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isnan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isnormal</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">itrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_8"></a><span class="term">L</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">llround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lltrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">log_postfix_event</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">logged_adaptor</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">log_prefix_event</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">logged_adaptor</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lsb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">ltrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_9"></a><span class="term">M</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">max</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">miller_rabin_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">Primality Testing</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">min</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">msb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">multiply</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_11"></a><span class="term">O</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">overlap</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_12"></a><span class="term">P</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">powm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">precision</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/faq.html" title="FAQ"><span class="index-entry-level-1">FAQ</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../intro.html" title="Introduction"><span class="index-entry-level-1">Introduction</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">proper_subset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_13"></a><span class="term">R</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">r</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/egs/bitops.html" title="Bit Operations"><span class="index-entry-level-1">Bit Operations</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">round</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_14"></a><span class="term">S</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">sign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">singleton</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">str</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">subset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">swap</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_15"></a><span class="term">T</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">trunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">two</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_17"></a><span class="term">V</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">value</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/cpp_bin_float_ref.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_18"></a><span class="term">Z</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">zero</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tommath_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tom_int</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">zero_in</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../indexes.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../indexes.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s02.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/indexes/s02.html b/libs/multiprecision/doc/html/boost_multiprecision/indexes/s02.html new file mode 100644 index 0000000000..4833265295 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/indexes/s02.html @@ -0,0 +1,156 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Class Index</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../indexes.html" title="Indexes"> +<link rel="prev" href="s01.html" title="Function Index"> +<link rel="next" href="s03.html" title="Typedef Index"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="s01.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../indexes.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s03.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="idm1549437632"></a>Class Index</h3></div></div></div> +<p><a class="link" href="s02.html#idx_id_21">C</a> <a class="link" href="s02.html#idx_id_22">D</a> <a class="link" href="s02.html#idx_id_23">E</a> <a class="link" href="s02.html#idx_id_24">F</a> <a class="link" href="s02.html#idx_id_25">G</a> <a class="link" href="s02.html#idx_id_26">I</a> <a class="link" href="s02.html#idx_id_27">L</a> <a class="link" href="s02.html#idx_id_28">M</a> <a class="link" href="s02.html#idx_id_29">N</a> <a class="link" href="s02.html#idx_id_34">T</a></p> +<div class="variablelist"><dl class="variablelist"> +<dt> +<a name="idx_id_21"></a><span class="term">C</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">component_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-0">cpp_bin_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_dec_float.html" title="cpp_dec_float"><span class="index-entry-level-0">cpp_dec_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_int_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_22"></a><span class="term">D</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/debug_adaptor.html" title="debug_adaptor"><span class="index-entry-level-0">debug_adaptor</span></a></p></li></ul></div></dd> +<dt> +<a name="idx_id_23"></a><span class="term">E</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">expression_template_default</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_24"></a><span class="term">F</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">float128_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li></ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_25"></a><span class="term">G</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-0">gmp_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-0">gmp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-0">gmp_rational</span></a></p></li> +</ul></div></dd> +<dt> +<a name="idx_id_26"></a><span class="term">I</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_explicitly_convertible</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_lossy_conversion</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_number_expression</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_restricted_conversion</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_signed_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_unsigned_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_27"></a><span class="term">L</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-0">logged_adaptor</span></a></p></li></ul></div></dd> +<dt> +<a name="idx_id_28"></a><span class="term">M</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfi_float_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></strong></span></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_29"></a><span class="term">N</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-0">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">number_category</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_34"></a><span class="term">T</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tommath_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tom_int</span></a></p></li></ul></div> +</li></ul></div></dd> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. 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"><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">float128</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +</ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_45"></a><span class="term">I</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; 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"> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_1000</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_500</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpq_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpz_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mp_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/gi.html" title="Calculating an Integral"><span class="index-entry-level-1">Calculating an Integral</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/poly_eg.html" title="Polynomial Evaluation"><span class="index-entry-level-1">Polynomial Evaluation</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_52"></a><span class="term">S</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">static_mpfr_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">static_mpfr_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_53"></a><span class="term">T</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-0">tommath_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-0">tom_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tom_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tommath_rational</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_54"></a><span class="term">U</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint128_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint256_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint512_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +</ul></div></dd> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="s02.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../indexes.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s04.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/indexes/s04.html b/libs/multiprecision/doc/html/boost_multiprecision/indexes/s04.html new file mode 100644 index 0000000000..5ed87b4e90 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/indexes/s04.html @@ -0,0 +1,1370 @@ +<html> +<head> +<meta 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class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/todo.html" title="TODO"><span class="index-entry-level-1">TODO</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">assign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">assign_components</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_58"></a><span class="term">B</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Bit Operations</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/egs/bitops.html" title="Bit Operations"><span class="index-entry-level-1">r</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bits</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/random.html" title="Generating Random Numbers"><span class="index-entry-level-1">Generating Random Numbers</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/input_output.html" title="Input Output"><span class="index-entry-level-1">Input Output</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rounding.html" title="Rounding Rules for Conversions"><span class="index-entry-level-1">Rounding Rules for Conversions</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_flip</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_set</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">bit_unset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">BOOST_MP_DEFINE_SIZED_CPP_INT_LITERAL</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/lits.html" title="Literal Types and constexpr Support"><span class="index-entry-level-1">Literal Types and constexpr Support</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">BOOST_MP_MIN_EXPONENT_DIGITS</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/input_output.html" title="Input Output"><span class="index-entry-level-1">Input Output</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">BOOST_MP_USE_FLOAT128</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">BOOST_MP_USE_QUAD</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_59"></a><span class="term">C</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Calculating an Integral</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/gi.html" title="Calculating an Integral"><span class="index-entry-level-1">mp_type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_cpp_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_cpp_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_cpp_rational_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_int1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_int128_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_int256_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_int512_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_uint1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_uint128_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_uint256_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">checked_uint512_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">compare</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">component_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Compulsory Requirements on the Backend type.</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_bitwise_or</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_bitwise_xor</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_ceil</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_complement</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_convert_to</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_divide</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_floor</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_frexp</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_ldexp</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_left_shift</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_modulus</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_multiply</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_right_shift</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_sqrt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">eval_subtract</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_bin_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_100</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_double</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_double_extended</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_quad</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float_single</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/cpp_bin_float_ref.html" title="cpp_bin_float"><span class="index-entry-level-1">value</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_bin_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" 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class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_bin_float_double_extended</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_bin_float_quad</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span 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title="cpp_int"><span class="index-entry-level-1">checked_int512_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">checked_uint1024_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">checked_uint128_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">checked_uint256_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">checked_uint512_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int_backend</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_rational_backend</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">int1024_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">int128_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">int256_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">int512_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">limb_type</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">uint1024_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">uint128_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">uint256_t</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">uint512_t</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_int_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/rational/cpp_rational.html" title="cpp_rational"><span class="index-entry-level-1">cpp_rational</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/cpp_rational.html" title="cpp_rational"><span class="index-entry-level-1">cpp_rational_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">cpp_rational_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/cpp_rational.html" title="cpp_rational"><span class="index-entry-level-1">cpp_rational</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_60"></a><span class="term">D</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">data</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/debug_adaptor.html" title="debug_adaptor"><span class="index-entry-level-0">debug_adaptor</span></a></p></li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">default_precision</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">divide_qr</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_61"></a><span class="term">E</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">empty</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_acos</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_asin</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_atan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_atan2</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_and</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_or</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bitwise_xor</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_flip</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_set</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_bit_unset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_ceil</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_complement</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_convert_to</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_cos</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_cosh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_decrement</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_divide</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_eq</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_exp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_fabs</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_floor</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_fmod</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_frexp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_gcd</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_get_sign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_gt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_increment</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_integer_sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_is_zero</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_lcm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_ldexp</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_left_shift</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_log</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_log10</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_lt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_modulus</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_msb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply_add</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_multiply_subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_pow</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_powm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_qr</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_right_shift</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_round</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_scalbn</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sin</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sinh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b" title="Table 1.8. Compulsory Requirements on the Backend type."><span class="index-entry-level-1">Compulsory Requirements on the Backend type.</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_tan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_tanh</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">eval_trunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">Optional Requirements on the Backend Type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">expression_template_default</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_62"></a><span class="term">F</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">FAQ</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/faq.html" title="FAQ"><span class="index-entry-level-1">precision</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">float128</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">BOOST_MP_USE_FLOAT128</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">BOOST_MP_USE_QUAD</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128_backend</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">float128_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/float128.html" title="float128"><span class="index-entry-level-1">float128</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">fpclassify</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_63"></a><span class="term">G</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Generating Random Numbers</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/random.html" title="Generating Random Numbers"><span class="index-entry-level-1">bits</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Generic Integer Operations</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">bit_flip</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">bit_set</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">bit_test</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">bit_unset</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">divide_qr</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">integer_modulus</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">lsb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">miller_rabin_test</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">msb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">multiply</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">powm</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">precision</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">sqrt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">subtract</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">gmp_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">mpf_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">mpf_float_100</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">mpf_float_1000</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">mpf_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">mpf_float_500</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">gmp_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">mpz_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">gmp_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">mpq_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_64"></a><span class="term">I</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">if</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">Primality Testing</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">ilogb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">in</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">infinity</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Input Output</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/input_output.html" title="Input Output"><span class="index-entry-level-1">bits</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/input_output.html" title="Input Output"><span class="index-entry-level-1">BOOST_MP_MIN_EXPONENT_DIGITS</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int128_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int256_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int512_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">integer_modulus</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Internal Support Code</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">is_explicitly_convertible</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">is_lossy_conversion</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">is_restricted_conversion</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">is_signed_number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">is_unsigned_number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Introduction</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../intro.html" title="Introduction"><span class="index-entry-level-1">precision</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">int_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">Primality Testing</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">iround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isfinite</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isinf</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isnan</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">isnormal</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_explicitly_convertible</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_lossy_conversion</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_number_expression</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_restricted_conversion</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_signed_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">is_unsigned_number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/internals.html" title="Internal Support Code"><span class="index-entry-level-1">Internal Support Code</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">itrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_65"></a><span class="term">L</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">limb_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Literal Types and constexpr Support</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/lits.html" title="Literal Types and constexpr Support"><span class="index-entry-level-1">BOOST_MP_DEFINE_SIZED_CPP_INT_LITERAL</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">llround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lltrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">logged_adaptor</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">logged_adaptor</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">log_postfix_event</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">log_prefix_event</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">log_postfix_event</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">logged_adaptor</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">log_prefix_event</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/misc/logged_adaptor.html" title="logged_adaptor"><span class="index-entry-level-1">logged_adaptor</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lround</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">lsb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">ltrunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_66"></a><span class="term">M</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">max</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">miller_rabin_test</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">Primality Testing</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">min</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Mixed Precision Arithmetic</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">multiply</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">subtract</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfi_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">empty</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">in</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float_1000</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float_backend</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">overlap</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">proper_subset</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">singleton</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">subset</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">zero_in</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfi_float_1000</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfi_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfi_float_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">data</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float_100</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float_1000</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float_500</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">static_mpfr_float_100</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">static_mpfr_float_50</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_1000</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_500</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpfr_float_backend</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_100</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_1000</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_500</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../ref/mpfr_ref.html" title="mpfr_float_backend"><span class="index-entry-level-1">mpfr_float_backend</span></a></strong></span></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_1000</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpf_float_500</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpq_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mpz_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">mp_type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/gi.html" title="Calculating an Integral"><span class="index-entry-level-1">Calculating an Integral</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/poly_eg.html" title="Polynomial Evaluation"><span class="index-entry-level-1">Polynomial Evaluation</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">msb</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">multiply</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_67"></a><span class="term">N</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">number</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">abs</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">assign</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">bit_flip</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">bit_set</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">bit_test</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">bit_unset</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">compare</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">component_type</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">default_precision</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">divide_qr</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">expression_template_default</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">fpclassify</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">ilogb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">integer_modulus</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">iround</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">isfinite</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">isinf</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">isnan</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">isnormal</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">is_number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">is_number_expression</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">itrunc</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">llround</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">lltrunc</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">lround</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">lsb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">ltrunc</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">miller_rabin_test</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">msb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">multiply</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number_category</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">powm</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">precision</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">round</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">sign</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">sqrt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">str</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">subtract</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">swap</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">trunc</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">value</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">number_category</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_68"></a><span class="term">O</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Optional Requirements on the Backend Type</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">assign_components</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_acos</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_asin</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_atan</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_atan2</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bitwise_and</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bitwise_or</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bitwise_xor</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bit_flip</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bit_set</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bit_test</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_bit_unset</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_cos</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_cosh</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_decrement</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_divide</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_eq</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_exp</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_fabs</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_fmod</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_gcd</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_get_sign</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_gt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_increment</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_integer_sqrt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_is_zero</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_lcm</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_left_shift</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_log</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_log10</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_lt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_modulus</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_msb</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_multiply</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_multiply_add</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_multiply_subtract</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_pow</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_powm</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_qr</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_right_shift</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_round</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_scalbn</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_sin</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_sinh</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_subtract</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_tan</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_tanh</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/backendconc.html#boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac" title="Table 1.9. Optional Requirements on the Backend Type"><span class="index-entry-level-1">eval_trunc</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">overlap</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_69"></a><span class="term">P</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Polynomial Evaluation</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/fp_eg/poly_eg.html" title="Polynomial Evaluation"><span class="index-entry-level-1">mp_type</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">powm</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">precision</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/faq.html" title="FAQ"><span class="index-entry-level-1">FAQ</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../intro.html" title="Introduction"><span class="index-entry-level-1">Introduction</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Primality Testing</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">if</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">int_type</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/primetest.html" title="Primality Testing"><span class="index-entry-level-1">miller_rabin_test</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">proper_subset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_70"></a><span class="term">R</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">r</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/egs/bitops.html" title="Bit Operations"><span class="index-entry-level-1">Bit Operations</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">round</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">Rounding Rules for Conversions</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rounding.html" title="Rounding Rules for Conversions"><span class="index-entry-level-1">bits</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_71"></a><span class="term">S</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">sign</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">singleton</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">sqrt</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">static_mpfr_float_100</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">static_mpfr_float_50</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float"><span class="index-entry-level-1">mpfr_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">std::numeric_limits<> constants</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">bits</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">cpp_dec_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">float128</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">max</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">two</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">std::numeric_limits<> functions</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">cpp_dec_float_50</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">infinity</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">max</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">min</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">sqrt</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">value</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">str</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">subset</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">subtract</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/gen_int.html" title="Generic Integer Operations"><span class="index-entry-level-1">Generic Integer Operations</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/mixed.html" title="Mixed Precision Arithmetic"><span class="index-entry-level-1">Mixed Precision Arithmetic</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">swap</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_72"></a><span class="term">T</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">TODO</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../map/todo.html" title="TODO"><span class="index-entry-level-1">add</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tommath_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tom_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tommath_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tommath_rational</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tom_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tom_int</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tommath_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tom_int</span></a></strong></span></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">zero</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">tom_rational</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tommath_rational</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">trunc</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">two</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_73"></a><span class="term">U</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint1024_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint128_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint256_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">uint512_t</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/cpp_int.html" title="cpp_int"><span class="index-entry-level-1">cpp_int</span></a></p></li></ul></div> +</li> +</ul></div></dd> +<dt> +<a name="idx_id_74"></a><span class="term">V</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">value</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/cpp_bin_float_ref.html" title="cpp_bin_float"><span class="index-entry-level-1">cpp_bin_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../ref/number.html" title="number"><span class="index-entry-level-1">number</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/functions.html" title="std::numeric_limits<> functions"><span class="index-entry-level-1">std::numeric_limits<> functions</span></a></p></li> +</ul></div> +</li></ul></div></dd> +<dt> +<a name="idx_id_75"></a><span class="term">Z</span> +</dt> +<dd><div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">zero</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/floats/gmp_float.html" title="gmp_float"><span class="index-entry-level-1">gmp_float</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/gmp_int.html" title="gmp_int"><span class="index-entry-level-1">gmp_int</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational"><span class="index-entry-level-1">gmp_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/limits/constants.html" title="std::numeric_limits<> constants"><span class="index-entry-level-1">std::numeric_limits<> constants</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/rational/tommath_rational.html" title="tommath_rational"><span class="index-entry-level-1">tommath_rational</span></a></p></li> +<li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/ints/tom_int.html" title="tom_int"><span class="index-entry-level-1">tom_int</span></a></p></li> +</ul></div> +</li> +<li class="listitem" style="list-style-type: none"> +<p><span class="index-entry-level-0">zero_in</span></p> +<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../tut/interval/mpfi.html" title="mpfi_float"><span class="index-entry-level-1">mpfi_float</span></a></p></li></ul></div> +</li> +</ul></div></dd> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="s03.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../indexes.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/intro.html b/libs/multiprecision/doc/html/boost_multiprecision/intro.html new file mode 100644 index 0000000000..d19421baac --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/intro.html @@ -0,0 +1,710 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Introduction</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="prev" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="next" href="tut.html" title="Tutorial"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../index.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tut.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="boost_multiprecision.intro"></a><a class="link" href="intro.html" title="Introduction">Introduction</a> +</h2></div></div></div> +<p> + The Multiprecision Library provides <a class="link" href="tut/ints.html" title="Integer Types">integer</a>, + <a class="link" href="tut/rational.html" title="Rational Number Types">rational</a> and <a class="link" href="tut/floats.html" title="Floating Point Numbers">floating-point</a> types in C++ + that have more range and precision than C++'s ordinary built-in types. The + big number types in Multiprecision can be used with a wide selection of basic + mathematical operations, elementary transcendental functions as well as the + functions in Boost.Math. The Multiprecision types can also interoperate with + the built-in types in C++ using clearly defined conversion rules. This allows + Boost.Multiprecision to be used for all kinds of mathematical calculations + involving integer, rational and floating-point types requiring extended range + and precision. + </p> +<p> + Multiprecision consists of a generic interface to the mathematics of large + numbers as well as a selection of big number back ends, with support for integer, + rational and floating-point types. Boost.Multiprecision provides a selection + of back ends provided off-the-rack in including interfaces to GMP, MPFR, MPIR, + TomMath as well as its own collection of Boost-licensed, header-only back ends + for integers, rationals and floats. In addition, user-defined back ends can + be created and used with the interface of Multiprecision, provided the class + implementation adheres to the necessary <a class="link" href="ref/backendconc.html" title="Backend Requirements">concepts</a>. + </p> +<p> + Depending upon the number type, precision may be arbitrarily large (limited + only by available memory), fixed at compile time (for example 50 or 100 decimal + digits), or a variable controlled at run-time by member functions. The types + are expression-template-enabled for better performance than naive user-defined + types. + </p> +<p> + The Multiprecision library comes in two distinct parts: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + An expression-template-enabled front-end <code class="computeroutput"><span class="identifier">number</span></code> + that handles all the operator overloading, expression evaluation optimization, + and code reduction. + </li> +<li class="listitem"> + A selection of back-ends that implement the actual arithmetic operations, + and need conform only to the reduced interface requirements of the front-end. + </li> +</ul></div> +<p> + Separation of front-end and back-end allows use of highly refined, but restricted + license libraries where possible, but provides Boost license alternatives for + users who must have a portable unconstrained license. Which is to say some + back-ends rely on 3rd party libraries, but a header-only Boost license version + is always available (if somewhat slower). + </p> +<p> + Should you just wish to cut to the chase and use a fully Boost-licensed number + type, then skip to <a class="link" href="tut/ints/cpp_int.html" title="cpp_int">cpp_int</a> + for multiprecision integers, <a class="link" href="tut/floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> + for multiprecision floating point types and <a class="link" href="tut/rational/cpp_rational.html" title="cpp_rational">cpp_rational</a> + for rational types. + </p> +<p> + The library is often used via one of the predefined typedefs: for example if + you wanted an <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> integer type using <a href="http://gmplib.org" target="_top">GMP</a> + as the underlying implementation then you could use: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// Defines the wrappers around the GMP library's types</span> + +<span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">mpz_int</span> <span class="identifier">myint</span><span class="special">;</span> <span class="comment">// Arbitrary precision integer type.</span> +</pre> +<p> + Alternatively, you can compose your own multiprecision type, by combining + <code class="computeroutput"><span class="identifier">number</span></code> with one of the predefined + back-end types. For example, suppose you wanted a 300 decimal digit floating-point + type based on the <a href="http://www.mpfr.org" target="_top">MPFR</a> library. In + this case, there's no predefined typedef with that level of precision, so instead + we compose our own: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// Defines the Backend type that wraps MPFR</span> + +<span class="keyword">namespace</span> <span class="identifier">mp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> <span class="comment">// Reduce the typing a bit later...</span> + +<span class="keyword">typedef</span> <span class="identifier">mp</span><span class="special">::</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">mp</span><span class="special">::</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">300</span><span class="special">></span> <span class="special">></span> <span class="identifier">my_float</span><span class="special">;</span> + +<span class="identifier">my_float</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</span><span class="special">;</span> <span class="comment">// These variables have 300 decimal digits precision</span> +</pre> +<p> + We can repeat the above example, but with the expression templates disabled + (for faster compile times, but slower runtimes) by passing a second template + argument to <code class="computeroutput"><span class="identifier">number</span></code>: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// Defines the Backend type that wraps MPFR</span> + +<span class="keyword">namespace</span> <span class="identifier">mp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> <span class="comment">// Reduce the typing a bit later...</span> + +<span class="keyword">typedef</span> <span class="identifier">mp</span><span class="special">::</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">mp</span><span class="special">::</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">300</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">my_float</span><span class="special">;</span> + +<span class="identifier">my_float</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</span><span class="special">;</span> <span class="comment">// These variables have 300 decimal digits precision</span> +</pre> +<p> + We can also mix arithmetic operations between different types, provided there + is an unambiguous implicit conversion from one type to the other: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">namespace</span> <span class="identifier">mp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> <span class="comment">// Reduce the typing a bit later...</span> + +<span class="identifier">mp</span><span class="special">::</span><span class="identifier">int128_t</span> <span class="identifier">a</span><span class="special">(</span><span class="number">3</span><span class="special">),</span> <span class="identifier">b</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> +<span class="identifier">mp</span><span class="special">::</span><span class="identifier">int512_t</span> <span class="identifier">c</span><span class="special">(</span><span class="number">50</span><span class="special">),</span> <span class="identifier">d</span><span class="special">;</span> + +<span class="identifier">d</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">*</span> <span class="identifier">a</span><span class="special">;</span> <span class="comment">// OK, result of mixed arithmetic is an int512_t</span> +</pre> +<p> + Conversions are also allowed: + </p> +<pre class="programlisting"><span class="identifier">d</span> <span class="special">=</span> <span class="identifier">a</span><span class="special">;</span> <span class="comment">// OK, widening conversion.</span> +<span class="identifier">d</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">;</span> <span class="comment">// OK, can convert from an expression template too.</span> +</pre> +<p> + However conversions that are inherently lossy are either declared explicit + or else forbidden altogether: + </p> +<pre class="programlisting"><span class="identifier">d</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error implicit conversion from float not allowed.</span> +<span class="identifier">d</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">mp</span><span class="special">::</span><span class="identifier">int512_t</span><span class="special">>(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK explicit construction is allowed</span> +</pre> +<p> + Mixed arithmetic will fail if the conversion is either ambiguous or explicit: + </p> +<pre class="programlisting"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">a</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><>,</span> <span class="identifier">et_on</span><span class="special">></span> <span class="identifier">b</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> + +<span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">;</span> <span class="comment">// Error, implicit conversion could go either way.</span> +<span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no operator overload if the conversion would be explicit.</span> +</pre> +<h5> +<a name="boost_multiprecision.intro.h0"></a> + <span class="phrase"><a name="boost_multiprecision.intro.move_semantics"></a></span><a class="link" href="intro.html#boost_multiprecision.intro.move_semantics">Move + Semantics</a> + </h5> +<p> + On compilers that support rvalue-references, class <code class="computeroutput"><span class="identifier">number</span></code> + is move-enabled if the underlying backend is. + </p> +<p> + In addition the non-expression template operator overloads (see below) are + move aware and have overloads that look something like: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">B</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">>&&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">a</span> <span class="special">+=</span> <span class="identifier">b</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + These operator overloads ensure that many expressions can be evaluated without + actually generating any temporaries. However, there are still many simple expressions + such as: + </p> +<pre class="programlisting"><span class="identifier">a</span> <span class="special">=</span> <span class="identifier">b</span> <span class="special">*</span> <span class="identifier">c</span><span class="special">;</span> +</pre> +<p> + Which don't noticeably benefit from move support. Therefore, optimal performance + comes from having both move-support, and expression templates enabled. + </p> +<p> + Note that while "moved-from" objects are left in a sane state, they + have an unspecified value, and the only permitted operations on them are destruction + or the assignment of a new value. Any other operation should be considered + a programming error and all of our backends will trigger an assertion if any + other operation is attempted. This behavior allows for optimal performance + on move-construction (i.e. no allocation required, we just take ownership of + the existing object's internal state), while maintaining usability in the standard + library containers. + </p> +<h5> +<a name="boost_multiprecision.intro.h1"></a> + <span class="phrase"><a name="boost_multiprecision.intro.expression_templates"></a></span><a class="link" href="intro.html#boost_multiprecision.intro.expression_templates">Expression + Templates</a> + </h5> +<p> + Class <code class="computeroutput"><span class="identifier">number</span></code> is expression-template-enabled: + that means that rather than having a multiplication operator that looks like + this: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">></span> <span class="identifier">result</span><span class="special">(</span><span class="identifier">a</span><span class="special">);</span> + <span class="identifier">result</span> <span class="special">*=</span> <span class="identifier">b</span><span class="special">;</span> + <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Instead the operator looks more like this: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="emphasis"><em>unmentionable-type</em></span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Where the "unmentionable" return type is an implementation detail + that, rather than containing the result of the multiplication, contains instructions + on how to compute the result. In effect it's just a pair of references to the + arguments of the function, plus some compile-time information that stores what + the operation is. + </p> +<p> + The great advantage of this method is the <span class="emphasis"><em>elimination of temporaries</em></span>: + for example the "naive" implementation of <code class="computeroutput"><span class="keyword">operator</span><span class="special">*</span></code> above, requires one temporary for computing + the result, and at least another one to return it. It's true that sometimes + this overhead can be reduced by using move-semantics, but it can't be eliminated + completely. For example, lets suppose we're evaluating a polynomial via Horner's + method, something like this: + </p> +<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">a</span><span class="special">[</span><span class="number">7</span><span class="special">]</span> <span class="special">=</span> <span class="special">{</span> <span class="comment">/* some values */</span> <span class="special">};</span> +<span class="comment">//....</span> +<span class="identifier">y</span> <span class="special">=</span> <span class="special">(((((</span><span class="identifier">a</span><span class="special">[</span><span class="number">6</span><span class="special">]</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">5</span><span class="special">])</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">4</span><span class="special">])</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">3</span><span class="special">])</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">2</span><span class="special">])</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">1</span><span class="special">])</span> <span class="special">*</span> <span class="identifier">x</span> <span class="special">+</span> <span class="identifier">a</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> +</pre> +<p> + If type <code class="computeroutput"><span class="identifier">T</span></code> is a <code class="computeroutput"><span class="identifier">number</span></code>, then this expression is evaluated + <span class="emphasis"><em>without creating a single temporary value</em></span>. In contrast, + if we were using the <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + C++ wrapper for <a href="http://www.mpfr.org" target="_top">MPFR</a> - then this expression + would result in no less than 11 temporaries (this is true even though <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> does + use expression templates to reduce the number of temporaries somewhat). Had + we used an even simpler wrapper around <a href="http://www.mpfr.org" target="_top">MPFR</a> + like <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> things + would have been even worse and no less that 24 temporaries are created for + this simple expression (note - we actually measure the number of memory allocations + performed rather than the number of temporaries directly, note also that the + <a href="http://gmplib.org/manual/C_002b_002b-Interface-Floats.html#C_002b_002b-Interface-Floats" target="_top">mpf_class</a> + wrapper that will be supplied with GMP-5.1 reduces the number of temporaries + to pretty much zero). Note that if we compile with expression templates disabled + and rvalue-reference support on, then actually still have no wasted memory + allocations as even though temporaries are created, their contents are moved + rather than copied. <a href="#ftn.boost_multiprecision.intro.f0" class="footnote" name="boost_multiprecision.intro.f0"><sup class="footnote">[1]</sup></a> + </p> +<div class="important"><table border="0" summary="Important"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../doc/src/images/important.png"></td> +<th align="left">Important</th> +</tr> +<tr><td align="left" valign="top"> +<p> + Expression templates can radically reorder the operations in an expression, + for example: + </p> +<p> + a = (b * c) * a; + </p> +<p> + Will get transformed into: + </p> +<p> + a *= c; a *= b; + </p> +<p> + If this is likely to be an issue for a particular application, then they + should be disabled. + </p> +</td></tr> +</table></div> +<p> + This library also extends expression template support to standard library functions + like <code class="computeroutput"><span class="identifier">abs</span></code> or <code class="computeroutput"><span class="identifier">sin</span></code> + with <code class="computeroutput"><span class="identifier">number</span></code> arguments. This + means that an expression such as: + </p> +<pre class="programlisting"><span class="identifier">y</span> <span class="special">=</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + can be evaluated without a single temporary being calculated. Even expressions + like: + </p> +<pre class="programlisting"><span class="identifier">y</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + get this treatment, so that variable 'y' is used as "working storage" + within the implementation of <code class="computeroutput"><span class="identifier">sin</span></code>, + thus reducing the number of temporaries used by one. Of course, should you + write: + </p> +<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + Then we clearly can't use <code class="computeroutput"><span class="identifier">x</span></code> + as working storage during the calculation, so then a temporary variable is + created in this case. + </p> +<p> + Given the comments above, you might be forgiven for thinking that expression-templates + are some kind of universal-panacea: sadly though, all tricks like this have + their downsides. For one thing, expression template libraries like this one, + tend to be slower to compile than their simpler cousins, they're also harder + to debug (should you actually want to step through our code!), and rely on + compiler optimizations being turned on to give really good performance. Also, + since the return type from expressions involving <code class="computeroutput"><span class="identifier">number</span></code>s + is an "unmentionable implementation detail", you have to be careful + to cast the result of an expression to the actual number type when passing + an expression to a template function. For example, given: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">my_proc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&);</span> +</pre> +<p> + Then calling: + </p> +<pre class="programlisting"><span class="identifier">my_proc</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Will very likely result in obscure error messages inside the body of <code class="computeroutput"><span class="identifier">my_proc</span></code> - since we've passed it an expression + template type, and not a number type. Instead we probably need: + </p> +<pre class="programlisting"><span class="identifier">my_proc</span><span class="special">(</span><span class="identifier">my_number_type</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">));</span> +</pre> +<p> + Having said that, these situations don't occur that often - or indeed not at + all for non-template functions. In addition, all the functions in the Boost.Math + library will automatically convert expression-template arguments to the underlying + number type without you having to do anything, so: + </p> +<pre class="programlisting"><span class="identifier">mpfr_float_100</span> <span class="identifier">a</span><span class="special">(</span><span class="number">20</span><span class="special">),</span> <span class="identifier">delta</span><span class="special">(</span><span class="number">0.125</span><span class="special">);</span> +<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span> <span class="special">+</span> <span class="identifier">delta</span><span class="special">);</span> +</pre> +<p> + Will work just fine, with the <code class="computeroutput"><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">delta</span></code> expression + template argument getting converted to an <code class="computeroutput"><span class="identifier">mpfr_float_100</span></code> + internally by the Boost.Math library. + </p> +<p> + One other potential pitfall that's only possible in C++11: you should never + store an expression template using: + </p> +<pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">my_expression</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">-</span> <span class="identifier">c</span><span class="special">;</span> +</pre> +<p> + unless you're absolutely sure that the lifetimes of <code class="computeroutput"><span class="identifier">a</span></code>, + <code class="computeroutput"><span class="identifier">b</span></code> and <code class="computeroutput"><span class="identifier">c</span></code> + will outlive that of <code class="computeroutput"><span class="identifier">my_expression</span></code>. + </p> +<p> + And finally... the performance improvements from an expression template library + like this are often not as dramatic as the reduction in number of temporaries + would suggest. For example if we compare this library with <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + and <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a>, with + all three using the underlying <a href="http://www.mpfr.org" target="_top">MPFR</a> + library at 50 decimal digits precision then we see the following typical results + for polynomial execution: + </p> +<div class="table"> +<a name="boost_multiprecision.intro.evaluation_of_order_6_polynomial"></a><p class="title"><b>Table 1.1. Evaluation of Order 6 Polynomial.</b></p> +<div class="table-contents"><table class="table" summary="Evaluation of Order 6 Polynomial."> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Library + </p> + </th> +<th> + <p> + Relative Time + </p> + </th> +<th> + <p> + Relative number of memory allocations + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + number + </p> + </td> +<td> + <p> + 1.0 (0.00957s) + </p> + </td> +<td> + <p> + 1.0 (2996 total) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + </p> + </td> +<td> + <p> + 1.1 (0.0102s) + </p> + </td> +<td> + <p> + 4.3 (12976 total) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> + </p> + </td> +<td> + <p> + 1.6 (0.0151s) + </p> + </td> +<td> + <p> + 9.3 (27947 total) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + As you can see, the execution time increases a lot more slowly than the number + of memory allocations. There are a number of reasons for this: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The cost of extended-precision multiplication and division is so great, + that the times taken for these tend to swamp everything else. + </li> +<li class="listitem"> + The cost of an in-place multiplication (using <code class="computeroutput"><span class="keyword">operator</span><span class="special">*=</span></code>) tends to be more than an out-of-place + <code class="computeroutput"><span class="keyword">operator</span><span class="special">*</span></code> + (typically <code class="computeroutput"><span class="keyword">operator</span> <span class="special">*=</span></code> + has to create a temporary workspace to carry out the multiplication, where + as <code class="computeroutput"><span class="keyword">operator</span><span class="special">*</span></code> + can use the target variable as workspace). Since the expression templates + carry out their magic by converting out-of-place operators to in-place + ones, we necessarily take this hit. Even so the transformation is more + efficient than creating the extra temporary variable, just not by as much + as one would hope. + </li> +</ul></div> +<p> + Finally, note that <code class="computeroutput"><span class="identifier">number</span></code> takes + a second template argument, which, when set to <code class="computeroutput"><span class="identifier">et_off</span></code> + disables all the expression template machinery. The result is much faster to + compile, but slower at runtime. + </p> +<p> + We'll conclude this section by providing some more performance comparisons + between these three libraries, again, all are using <a href="http://www.mpfr.org" target="_top">MPFR</a> + to carry out the underlying arithmetic, and all are operating at the same precision + (50 decimal digits): + </p> +<div class="table"> +<a name="boost_multiprecision.intro.evaluation_of_boost_math_s_besse"></a><p class="title"><b>Table 1.2. Evaluation of Boost.Math's Bessel function test data</b></p> +<div class="table-contents"><table class="table" summary="Evaluation of Boost.Math's Bessel function test data"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Library + </p> + </th> +<th> + <p> + Relative Time + </p> + </th> +<th> + <p> + Relative Number of Memory Allocations + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + mpfr_float_50 + </p> + </td> +<td> + <p> + 1.0 (5.78s) + </p> + </td> +<td> + <p> + 1.0 (1611963) + </p> + </td> +</tr> +<tr> +<td> + <p> + number<mpfr_float_backend<50>, et_off><br> (but with + rvalue reference support) + </p> + </td> +<td> + <p> + 1.1 (6.29s) + </p> + </td> +<td> + <p> + 2.64 (4260868) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + </p> + </td> +<td> + <p> + 1.1 (6.28s) + </p> + </td> +<td> + <p> + 2.45 (3948316) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> + </p> + </td> +<td> + <p> + 1.65 (9.54s) + </p> + </td> +<td> + <p> + 8.21 (13226029) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.intro.evaluation_of_boost_math_s_non_c"></a><p class="title"><b>Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data</b></p> +<div class="table-contents"><table class="table" summary="Evaluation of Boost.Math's Non-Central T distribution test data"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Library + </p> + </th> +<th> + <p> + Relative Time + </p> + </th> +<th> + <p> + Relative Number of Memory Allocations + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + number + </p> + </td> +<td> + <p> + 1.0 (263s) + </p> + </td> +<td> + <p> + 1.0 (127710873) + </p> + </td> +</tr> +<tr> +<td> + <p> + number<mpfr_float_backend<50>, et_off><br> (but with + rvalue reference support) + </p> + </td> +<td> + <p> + 1.0 (260s) + </p> + </td> +<td> + <p> + 1.2 (156797871) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + </p> + </td> +<td> + <p> + 1.1 (287s) + </p> + </td> +<td> + <p> + 2.1 (268336640) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> + </p> + </td> +<td> + <p> + 1.5 (389s) + </p> + </td> +<td> + <p> + 3.6 (466960653) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + The above results were generated on Win32 compiling with Visual C++ 2010, all + optimizations on (/Ox), with MPFR 3.0 and MPIR 2.3.0. + </p> +<div class="footnotes"> +<br><hr style="width:100; text-align:left;margin-left: 0"> +<div id="ftn.boost_multiprecision.intro.f0" class="footnote"><p><a href="#boost_multiprecision.intro.f0" class="para"><sup class="para">[1] </sup></a> + The actual number generated will depend on the compiler, how well it optimises + the code, and whether it supports rvalue references. The number of 11 temporaries + was generated with Visual C++ 10 + </p></div> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. 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(See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="perf/rational_performance.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="map/hist.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/map/ack.html b/libs/multiprecision/doc/html/boost_multiprecision/map/ack.html new file mode 100644 index 0000000000..23a4f32240 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/map/ack.html @@ -0,0 +1,64 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Acknowledgements</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../map.html" title="Roadmap"> +<link rel="prev" href="faq.html" title="FAQ"> +<link rel="next" href="../indexes.html" title="Indexes"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="faq.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../indexes.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.map.ack"></a><a class="link" href="ack.html" title="Acknowledgements">Acknowledgements</a> +</h3></div></div></div> +<p> + This library would not have happened without: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Christopher Kormanyos' C++ decimal number code. + </li> +<li class="listitem"> + Paul Bristow for patiently testing, and commenting on the library. + </li> +<li class="listitem"> + All the folks at GMP, MPFR and libtommath, for providing the "guts" + that makes this library work. + </li> +<li class="listitem"> + <a href="http://www-cs-faculty.stanford.edu/~uno/taocp.html" target="_top">"The + Art Of Computer Programming"</a>, Donald E. Knuth, Volume 2: + Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, + 1997), xiv+762pp. ISBN 0-201-89684-2 + </li> +</ul></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="faq.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../indexes.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/map/faq.html b/libs/multiprecision/doc/html/boost_multiprecision/map/faq.html new file mode 100644 index 0000000000..3eb2ac3528 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/map/faq.html @@ -0,0 +1,120 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>FAQ</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../map.html" title="Roadmap"> +<link rel="prev" href="todo.html" title="TODO"> +<link rel="next" href="ack.html" title="Acknowledgements"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="todo.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ack.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.map.faq"></a><a class="link" href="faq.html" title="FAQ">FAQ</a> +</h3></div></div></div> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">Why do I get compiler errors when passing a <code class="computeroutput"><span class="identifier">number</span></code> + to a template function?</span></dt> +<dd><p> + Most likely you are actually passing an expression template type to + the function and template-argument-deduction deduces the "wrong" + type. Try casting the arguments involving expressions to the actual + number type, or as a last resort turning off expression template support + in the number type you are using. + </p></dd> +<dt><span class="term">When is expression template support a performance gain?</span></dt> +<dd><p> + As a general rule, expression template support adds a small runtime + overhead creating and unpacking the expression templates, but greatly + reduces the number of temporaries created. So it's most effective in + improving performance when the cost of creating a temporary is high: + for example when creating a temporary involves a memory allocation. + It is least effective (and may even be a dis-optimisation) when temporaries + are cheap: for example if the number type is basically a thin wrapper + around a native arithmetic type. In addition, since the library makes + extensive use of thin inline wrapper functions, turning on compiler + optimization is essential to achieving high performance. + </p></dd> +<dt><span class="term">Do expression templates reorder operations?</span></dt> +<dd><p> + Yes they do, sometimes quite radically so, if this is a concern then + they should be turned off for the number type you are using. + </p></dd> +<dt><span class="term">I can't construct my number type from <span class="emphasis"><em>some other type</em></span>, + but the docs indicate that the conversion should be allowed, what's up?</span></dt> +<dd><p> + Some conversions are <span class="emphasis"><em>explicit</em></span>, that includes construction + from a string, or constructing from any type that may result in loss + of precision (for example constructing an integer type from a float). + </p></dd> +<dt><span class="term">Why do I get an exception thrown (or the program crash due to an + uncaught exception) when using the bitwise operators on a checked <code class="computeroutput"><span class="identifier">cpp_int</span></code>?</span></dt> +<dd><p> + Bitwise operations on negative values (or indeed any signed integer + type) are unspecified by the standard. As a result any attempt to carry + out a bitwise operation on a negative checked-integer will result in + a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> being thrown. + </p></dd> +<dt><span class="term">Why do I get compiler errors when trying to use the complement operator?</span></dt> +<dd><p> + Use of the complement operator on signed types is problematic as the + result is unspecified by the standard, and is further complicated by + the fact that most extended precision integer types use a sign-magnitude + representation rather than the 2's complement one favored by most native + integer types. As a result the complement operator is deliberately + disabled for checked <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s. + Unchecked <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s + give the same valued result as a 2's complement type would, but not + the same bit-pattern. + </p></dd> +<dt><span class="term">Why can't I negate an unsigned type?</span></dt> +<dd><p> + The unary negation operator is deliberately disabled for unsigned integer + types as its use would almost always be a programming error. + </p></dd> +<dt><span class="term">Why doesn't the library use proto?</span></dt> +<dd><p> + A very early version of the library did use proto, but compile times + became too slow for the library to be usable. Since the library only + required a tiny fraction of what proto has to offer anyway, a lightweight + expression template mechanism was used instead. Compile times are still + too slow... + </p></dd> +<dt><span class="term">Why not abstract out addition/multiplication algorithms?</span></dt> +<dd><p> + This was deemed not to be practical: these algorithms are intimately + tied to the actual data representation used. + </p></dd> +</dl> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="todo.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ack.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/map/hist.html b/libs/multiprecision/doc/html/boost_multiprecision/map/hist.html new file mode 100644 index 0000000000..c8469f448b --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/map/hist.html @@ -0,0 +1,295 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>History</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../map.html" title="Roadmap"> +<link rel="prev" href="../map.html" title="Roadmap"> +<link rel="next" href="todo.html" title="TODO"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../map.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="todo.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.map.hist"></a><a class="link" href="hist.html" title="History">History</a> +</h3></div></div></div> +<h5> +<a name="boost_multiprecision.map.hist.h0"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.multiprecision_2_2_3_boost_1_57"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.multiprecision_2_2_3_boost_1_57">Multiprecision-2.2.3 + (Boost-1.57)</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Changed rational to float conversions to exactly round to nearest, see + [https://svn.boost.org/trac/boost/ticket/10085 10085]. + </li> +<li class="listitem"> + Added improved generic float to rational conversions. + </li> +<li class="listitem"> + Fixed rare bug in exponent function for <a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a>. + </li> +<li class="listitem"> + Fixed various minor documentation issues. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h1"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.multiprecision_2_2_2_boost_1_56"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.multiprecision_2_2_2_boost_1_56">Multiprecision-2.2.2 + (Boost-1.56)</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Change floating point to rational conversions to be implicit, see <a href="https://svn.boost.org/trac/boost/ticket/10082" target="_top">10082</a>. + </li> +<li class="listitem"> + Fix definition of checked_cpp_rational typedef. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h2"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.multiprecision_2_2_1"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.multiprecision_2_2_1">Multiprecision-2.2.1</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"> + Fix bug in assignment from string in cpp_int, see <a href="https://svn.boost.org/trac/boost/ticket/9936" target="_top">9936</a>. + </li></ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h3"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.multiprecision_2_2_0"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.multiprecision_2_2_0">Multiprecision-2.2.0</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Moved to Boost.Multiprecision specific version number - we have one breaking + change in Boost-1.54 which makes this major version 2, plus two releases + with new features since then. + </li> +<li class="listitem"> + Added new <a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a> + backend for binary floating point. + </li> +<li class="listitem"> + Added MSVC-specific #include for compiler intrinsics, see <a href="https://svn.boost.org/trac/boost/ticket/9336" target="_top">9336</a>. + </li> +<li class="listitem"> + Fixed various typos in docs, see <a href="https://svn.boost.org/trac/boost/ticket/9432" target="_top">9432</a>. + </li> +<li class="listitem"> + Fixed <a class="link" href="../tut/rational/gmp_rational.html" title="gmp_rational">gmp_rational</a> + to allow move-copy from an already copied-from object, see <a href="https://svn.boost.org/trac/boost/ticket/9497" target="_top">9497</a>. + </li> +<li class="listitem"> + Added list of values for numeric_limits. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h4"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.boost_1_55"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.boost_1_55">Boost-1.55</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Added support for Boost.Serialization. + </li> +<li class="listitem"> + Suppressed some GCC warnings. See <a href="https://svn.boost.org/trac/boost/ticket/8872" target="_top">8872</a>. + </li> +<li class="listitem"> + Fixed bug in pow for large integer arguments. See <a href="https://svn.boost.org/trac/boost/ticket/8809" target="_top">8809</a>. + </li> +<li class="listitem"> + Fixed bug in pow for calculation of 0<sup>N</sup>. See <a href="https://svn.boost.org/trac/boost/ticket/8798" target="_top">8798</a>. + </li> +<li class="listitem"> + Fixed bug in fixed precision cpp_int IO code that causes conversion to + string to fail when the bit count is very small (less than CHAR_BIT). + See <a href="https://svn.boost.org/trac/boost/ticket/8745" target="_top">8745</a>. + </li> +<li class="listitem"> + Fixed bug in cpp_int that causes left shift to fail when a fixed precision + type would overflow. See <a href="https://svn.boost.org/trac/boost/ticket/8741" target="_top">8741</a>. + </li> +<li class="listitem"> + Fixed some cosmetic warnings from cpp_int. See <a href="https://svn.boost.org/trac/boost/ticket/8748" target="_top">8748</a>. + </li> +<li class="listitem"> + Fixed calls to functions which are required to be macros in C99. See + <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">8732</a>. + </li> +<li class="listitem"> + Fixed bug that causes construction from INT_MIN, LONG_MIN etc to fail + in cpp_int. See <a href="https://svn.boost.org/trac/boost/ticket/8711" target="_top">8711</a>. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h5"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.1_54"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.1_54">1.54</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + <span class="bold"><strong>Breaking change</strong></span> renamed <code class="computeroutput"><span class="identifier">rational_adapter</span></code> to <code class="computeroutput"><span class="identifier">rational_adaptor</span></code>. + </li> +<li class="listitem"> + Add support for <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>. + </li> +<li class="listitem"> + Add logged_adaptor. + </li> +<li class="listitem"> + Add support for 128-bit floats via GCC's <code class="computeroutput"><a class="link" href="../tut/floats/float128.html" title="float128">float128</a></code> + or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data + types. + </li> +<li class="listitem"> + Add support for user-defined literals in cpp_int, improve <code class="computeroutput"><span class="keyword">constexpr</span></code> support. + </li> +<li class="listitem"> + Fixed bug in integer division of <code class="computeroutput"><span class="identifier">cpp_int</span></code> + that results in incorrect sign of <code class="computeroutput"><span class="identifier">cpp_int</span></code> + when both arguments are small enough to fit in a <code class="computeroutput"><span class="identifier">double_limb_type</span></code>. + See <a href="https://svn.boost.org/trac/boost/ticket/8126" target="_top">8126</a>. + </li> +<li class="listitem"> + Fixed bug in subtraction of a single limb in <code class="computeroutput"><span class="identifier">cpp_int</span></code> + that results in incorrect value when the result should have a 0 in the + last limb: <a href="https://svn.boost.org/trac/boost/ticket/8133" target="_top">8133</a>. + </li> +<li class="listitem"> + Fixed bug in <code class="computeroutput"><span class="identifier">cpp_int</span></code> + where division of 0 by something doesn't get zero in the result: <a href="https://svn.boost.org/trac/boost/ticket/8160" target="_top">8160</a>. + </li> +<li class="listitem"> + Fixed bug in some transcendental functions that caused incorrect return + values when variables are reused, for example with <code class="computeroutput"><span class="identifier">a</span> + <span class="special">=</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">)</span></code>. See <a href="https://svn.boost.org/trac/boost/ticket/8326" target="_top">8326</a>. + </li> +<li class="listitem"> + Fixed some assignment operations in the mpfr and gmp backends to be safe + if the target has been moved from: <a href="https://svn.boost.org/trac/boost/ticket/8326" target="_top">8667</a>. + </li> +<li class="listitem"> + Fixed bug in <code class="computeroutput"><span class="identifier">cpp_int</span></code> + that gives incorrect answer for 0%N for large N: <a href="https://svn.boost.org/trac/boost/ticket/8670" target="_top">8670</a>. + </li> +<li class="listitem"> + Fixed set_precision in mpfr backend so it doesn't trample over an existing + value: <a href="https://svn.boost.org/trac/boost/ticket/8692" target="_top">8692</a>. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h6"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.1_53"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.1_53">1.53</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + First Release. + </li> +<li class="listitem"> + Fix bug in <a href="https://svn.boost.org/trac/boost/ticket/7878" target="_top">cpp_int + division</a>. + </li> +<li class="listitem"> + Fix issue <a href="https://svn.boost.org/trac/boost/ticket/7806" target="_top">#7806</a>. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h7"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.post_review_changes"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.post_review_changes">Post + review changes</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Non-expression template operators further optimised with rvalue reference + support. + </li> +<li class="listitem"> + Many functions made <code class="computeroutput"><span class="identifier">constexp</span></code>. + </li> +<li class="listitem"> + Differentiate between explicit and implicit conversions in the number + constructor. + </li> +<li class="listitem"> + Removed "mp_" prefix from types. + </li> +<li class="listitem"> + Allowed mixed precision arithmetic. + </li> +<li class="listitem"> + Changed ExpressionTemplates parameter to class <code class="computeroutput"><span class="identifier">number</span></code> + to use enumerated values rather than true/false. + </li> +<li class="listitem"> + Changed ExpressionTemplate parameter default value to use a traits class + so that the default value depends on the backend used. + </li> +<li class="listitem"> + Added support for fused-multiply-add/subtract with GMP support. + </li> +<li class="listitem"> + Tweaked expression template unpacking to use fewer temporaries when the + LHS also appears in the RHS. + </li> +<li class="listitem"> + Refactored <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> + based on review comments with new template parameter structure. + </li> +<li class="listitem"> + Added additional template parameter to <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> + to allow stack-based allocation. + </li> +<li class="listitem"> + Added section on mixed precision arithmetic, and added support for operations + yielding a higher precision result than either of the arguments. + </li> +<li class="listitem"> + Added overloads of integer-specific functions for built in integer types. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.hist.h8"></a> + <span class="phrase"><a name="boost_multiprecision.map.hist.pre_review_history"></a></span><a class="link" href="hist.html#boost_multiprecision.map.hist.pre_review_history">Pre-review + history</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + 2011-2012, John Maddock adds an expression template enabled front end + to Christopher's code, and adds support for other backends. + </li> +<li class="listitem"> + 2011, Christopher Kormanyos publishes the decimal floating point code + under the Boost Software Licence. The code is published as: <a href="http://doi.acm.org/10.1145/1916461.1916469" target="_top">"Algorithm + 910: A Portable C++ Multiple-Precision System for Special-Function Calculations"</a>, + in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. + </li> +<li class="listitem"> + 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic + floating point code. + </li> +</ul></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../map.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="todo.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/map/todo.html b/libs/multiprecision/doc/html/boost_multiprecision/map/todo.html new file mode 100644 index 0000000000..067af586b0 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/map/todo.html @@ -0,0 +1,229 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>TODO</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../map.html" title="Roadmap"> +<link rel="prev" href="hist.html" title="History"> +<link rel="next" href="faq.html" title="FAQ"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="hist.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="faq.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.map.todo"></a><a class="link" href="todo.html" title="TODO">TODO</a> +</h3></div></div></div> +<p> + More a list of what <span class="emphasis"><em>could</em></span> be done, rather than what + <span class="emphasis"><em>should</em></span> be done (which may be a much smaller list!). + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Add back-end support for libdecNumber. + </li> +<li class="listitem"> + Add an adaptor back-end for complex number types. + </li> +<li class="listitem"> + Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. + </li> +<li class="listitem"> + Add assembly level routines to cpp_int_backend. + </li> +<li class="listitem"> + Can ring types (exact floating point types) be supported? The answer + should be yes, but someone needs to write it, the hard part is IO and + binary-decimal conversion. + </li> +<li class="listitem"> + Should there be a choice of rounding mode (probably MPFR specific)? + </li> +<li class="listitem"> + We can reuse temporaries in multiple subtrees (temporary caching). + </li> +<li class="listitem"> + cpp_dec_float should round to nearest. + </li> +<li class="listitem"> + A 2's complement fixed precision int that uses exactly N bits and no + more. + </li> +</ul></div> +<p> + Things requested in review: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The performances of mp_number<a_trivial_adaptor<float>, false>respect + to float and mp_number<a_trivial_adaptor<int>, false> and + int should be given to show the cost of using the generic interface (Mostly + done, just need to update docs to the latest results). + </li> +<li class="listitem"> + Should we provide min/max overloads for expression templates? (Not done + - we can't overload functions declared in the std namespace :-( ). + </li> +<li class="listitem"> + The rounding applied when converting must be documented (Done). + </li> +<li class="listitem"> + Document why we don't abstract out addition/multiplication algorithms + etc. (done - FAQ) + </li> +<li class="listitem"> + Document why we don't use proto (compile times) (Done). + </li> +<li class="listitem"> + We can reuse temporaries in multiple subtrees (temporary caching) Moved + to TODO list. + </li> +<li class="listitem"> + Emphasise in the docs that ET's may reorder operations (done 2012/10/31). + </li> +<li class="listitem"> + Document what happens to small fixed precision cpp_int's (done 2012/10/31). + </li> +<li class="listitem"> + The use of bool in template parameters could be improved by the use of + an enum class which will be more explicit. E.g <code class="computeroutput"><span class="keyword">enum</span> + <span class="keyword">class</span> <span class="identifier">expression_template</span> + <span class="special">{</span><span class="identifier">disabled</span><span class="special">,</span> <span class="identifier">enabled</span><span class="special">};</span> <span class="keyword">enum</span> <span class="keyword">class</span> <span class="identifier">sign</span> + <span class="special">{</span><span class="keyword">unsigned</span><span class="special">,</span> <span class="keyword">signed</span><span class="special">};</span></code> (Partly done 2012/09/15, done 2012/10/31). + </li> +<li class="listitem"> + Each back-end should document the requirements it satisfies (not currently + scheduled for inclusion: it's deliberately an implementation detail, + and "optional" requirements are optimisations which can't be + detected by the user). Not done: this is an implementation detail, the + exact list of requirements satisfied is purely an optimization, not something + the user can detect. + </li> +<li class="listitem"> + A backend for an overflow aware integers (done 2012/10/31). + </li> +<li class="listitem"> + IIUC convert_to is used to emulate in c++98 compilers C++11 explicit + conversions. Could the explicit conversion operator be added on compilers + supporting it? (Done 2012/09/15). + </li> +<li class="listitem"> + The front-end should make the differences between implicit and explicit + construction (Done 2012/09/15). + </li> +<li class="listitem"> + The tutorial should add more examples concerning implicit or explicit + conversions. (Done 2012/09/15). + </li> +<li class="listitem"> + The documentation must explain how move semantics helps in this domain + and what the backend needs to do to profit from this optimization. (Done + 2012/09/15). + </li> +<li class="listitem"> + The documentation should contain Throws specification on the mp_number + and backend requirements operations. (Done 2012/09/15). + </li> +<li class="listitem"> + The library interface should use the noexcept (BOOST_NOEXCEPT, ...) facilities + (Done 2012/09/15). + </li> +<li class="listitem"> + It is unfortunate that the generic mp_number front end can not make use + constexpr as not all the backends can ensure this (done - we can go quite + a way). + </li> +<li class="listitem"> + literals: The library doesn't provide some kind of literals. I think + that the mp_number class should provide a way to create literals if the + backend is able to. (Done 2012/09/15). + </li> +<li class="listitem"> + The ExpresionTemplate parameter could be defaulted to a traits class + for more sensible defaults (done 2012/09/20). + </li> +<li class="listitem"> + In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we + can optimise and eliminate one more temporary (done 2012/09/20). + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.map.todo.h0"></a> + <span class="phrase"><a name="boost_multiprecision.map.todo.pre_review_comments"></a></span><a class="link" href="todo.html#boost_multiprecision.map.todo.pre_review_comments">Pre-Review + Comments</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Make fixed precision orthogonal to Allocator type in cpp_int. Possible + solution - add an additional MaxBits template argument that defaults + to 0 (meaning keep going till no more space/memory). Done. + </li> +<li class="listitem"> + Can ring types (exact floating point types) be supported? The answer + should be yes, but someone needs to write it (Moved to TODO list). + </li> +<li class="listitem"> + Should there be a choice of rounding mode (probably MPFR specific)? Moved + to TODO list. + </li> +<li class="listitem"> + Make the exponent type for cpp_dec_float a template parameter, maybe + include support for big-integer exponents. Open question - what should + be the default - int32_t or int64_t? (done 2012/09/06) + </li> +<li class="listitem"> + Document the size requirements of fixed precision ints (done 2012/09/15). + </li> +<li class="listitem"> + Document std lib function accuracy (done 2012/09/15). + </li> +<li class="listitem"> + Be a bit clearer on the effects of sign-magnitude representation of cpp_int + - min == -max etc - done. + </li> +<li class="listitem"> + Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). + </li> +<li class="listitem"> + Can we be clearer in the docs that mixed arithmetic doesn't work (no + longer applicable as of 2012/09/06)? + </li> +<li class="listitem"> + Document round functions behaviour better (they behave as in C++11) (added + note 2012/09/06). + </li> +<li class="listitem"> + Document limits on size of cpp_dec_float (done 2012/09/06). + </li> +<li class="listitem"> + Add support for fused multiply add (and subtract). GMP mpz_t could use + this (done 2012/09/20). + </li> +</ul></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="hist.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../map.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="faq.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf.html b/libs/multiprecision/doc/html/boost_multiprecision/perf.html new file mode 100644 index 0000000000..f4cd63d2e0 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf.html @@ -0,0 +1,57 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Performance Comparison</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="prev" href="ref/headers.html" title="Header File Structure"> +<link rel="next" href="perf/overhead.html" title="The Overhead in the Number Class Wrapper"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="ref/headers.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="perf/overhead.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="boost_multiprecision.perf"></a><a class="link" href="perf.html" title="Performance Comparison">Performance Comparison</a> +</h2></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="perf/overhead.html">The Overhead in the + Number Class Wrapper</a></span></dt> +<dt><span class="section"><a href="perf/realworld.html">Floating-Point Real + World Tests</a></span></dt> +<dt><span class="section"><a href="perf/int_real_world.html">Integer Real + World Tests</a></span></dt> +<dt><span class="section"><a href="perf/float_performance.html">Float Algorithm + Performance</a></span></dt> +<dt><span class="section"><a href="perf/integer_performance.html">Integer + Algorithm Performance</a></span></dt> +<dt><span class="section"><a href="perf/rational_performance.html">Rational + Type Performance</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="ref/headers.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="perf/overhead.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/float_performance.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/float_performance.html new file mode 100644 index 0000000000..4c0a963759 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/float_performance.html @@ -0,0 +1,2078 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Float Algorithm Performance</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="int_real_world.html" title="Integer Real World Tests"> +<link rel="next" href="integer_performance.html" title="Integer Algorithm Performance"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="int_real_world.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="integer_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.float_performance"></a><a class="link" href="float_performance.html" title="Float Algorithm Performance">Float Algorithm + Performance</a> +</h3></div></div></div> +<p> + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. + </p> +<div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator"></a><p class="title"><b>Table 1.14. Operator +</b></p> +<div class="table-contents"><table class="table" summary="Operator +"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0575156s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0740086s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.219073s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 2.45065 (0.14095s) + </p> + </td> +<td> + <p> + 2.01398 (0.149052s) + </p> + </td> +<td> + <p> + 1.09608 (0.240122s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.6001 (0.149546s) + </p> + </td> +<td> + <p> + 2.12079 (0.156957s) + </p> + </td> +<td> + <p> + 1.09078 (0.23896s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_int"></a><p class="title"><b>Table 1.15. Operator +(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(int)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 1.46115 (0.0855392s) + </p> + </td> +<td> + <p> + 2.60353 (0.114398s) + </p> + </td> +<td> + <p> + 3.62562 (0.264905s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0585424s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0439398s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0730648s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.40441 (0.14076s) + </p> + </td> +<td> + <p> + 3.2877 (0.144461s) + </p> + </td> +<td> + <p> + 2.40379 (0.175632s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long"></a><p class="title"><b>Table 1.16. Operator +(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.118146s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.144714s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.315639s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 4.5555 (0.538213s) + </p> + </td> +<td> + <p> + 3.83096 (0.554395s) + </p> + </td> +<td> + <p> + 1.95079 (0.615745s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 5.74477 (0.678719s) + </p> + </td> +<td> + <p> + 4.85295 (0.702291s) + </p> + </td> +<td> + <p> + 2.70354 (0.853342s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long0"></a><p class="title"><b>Table 1.17. Operator +=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.101188s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.122394s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.251975s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 5.199 (0.526079s) + </p> + </td> +<td> + <p> + 4.39327 (0.537712s) + </p> + </td> +<td> + <p> + 2.42151 (0.610159s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 6.08318 (0.615547s) + </p> + </td> +<td> + <p> + 5.18525 (0.634645s) + </p> + </td> +<td> + <p> + 3.1022 (0.781677s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator0"></a><p class="title"><b>Table 1.18. Operator -</b></p> +<div class="table-contents"><table class="table" summary="Operator -"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0895163s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.129248s) + </p> + </td> +<td> + <p> + 1.5088 (0.374512s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 1.72566 (0.154474s) + </p> + </td> +<td> + <p> + 1.22567 (0.158415s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.248219s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.83764 (0.164499s) + </p> + </td> +<td> + <p> + 1.34284 (0.173559s) + </p> + </td> +<td> + <p> + 1.00226 (0.248781s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_int0"></a><p class="title"><b>Table 1.19. Operator -(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(int)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.105285s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.142741s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.278718s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 2.34437 (0.246828s) + </p> + </td> +<td> + <p> + 1.28814 (0.183871s) + </p> + </td> +<td> + <p> + 1.00731 (0.280754s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.8032 (0.295136s) + </p> + </td> +<td> + <p> + 2.09178 (0.298582s) + </p> + </td> +<td> + <p> + 1.25213 (0.34899s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long1"></a><p class="title"><b>Table 1.20. Operator -(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.13719s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.184428s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.344212s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 4.0804 (0.559791s) + </p> + </td> +<td> + <p> + 3.06776 (0.565781s) + </p> + </td> +<td> + <p> + 2.07736 (0.715053s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 5.10114 (0.699828s) + </p> + </td> +<td> + <p> + 3.88684 (0.716843s) + </p> + </td> +<td> + <p> + 2.50074 (0.860784s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long2"></a><p class="title"><b>Table 1.21. Operator -=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.100984s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.123148s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.246181s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 5.68353 (0.573944s) + </p> + </td> +<td> + <p> + 4.68636 (0.577116s) + </p> + </td> +<td> + <p> + 2.6958 (0.663655s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 6.19738 (0.625834s) + </p> + </td> +<td> + <p> + 5.18544 (0.638577s) + </p> + </td> +<td> + <p> + 3.18738 (0.784673s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator1"></a><p class="title"><b>Table 1.22. Operator *</b></p> +<div class="table-contents"><table class="table" summary="Operator *"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 1.03667 (0.284251s) + </p> + </td> +<td> + <p> + 1.30576 (0.536527s) + </p> + </td> +<td> + <p> + 1.44686 (4.81057s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.274196s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.410891s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (3.32484s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.24537 (0.341477s) + </p> + </td> +<td> + <p> + 1.15785 (0.475749s) + </p> + </td> +<td> + <p> + 1.1796 (3.92199s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_int1"></a><p class="title"><b>Table 1.23. Operator *(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(int)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 3.97453 (0.240262s) + </p> + </td> +<td> + <p> + 9.91222 (0.463473s) + </p> + </td> +<td> + <p> + 50.7926 (4.36527s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0604505s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0467577s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0859431s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.56974 (0.155342s) + </p> + </td> +<td> + <p> + 3.56312 (0.166603s) + </p> + </td> +<td> + <p> + 3.22964 (0.277565s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long3"></a><p class="title"><b>Table 1.24. Operator *(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.331877s) + </p> + </td> +<td> + <p> + 1.01058 (0.586122s) + </p> + </td> +<td> + <p> + 6.688 (4.7931s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 1.72433 (0.572266s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.579987s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.716672s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.5553 (0.848047s) + </p> + </td> +<td> + <p> + 1.74987 (1.0149s) + </p> + </td> +<td> + <p> + 1.80403 (1.2929s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long4"></a><p class="title"><b>Table 1.25. Operator *=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.321397s) + </p> + </td> +<td> + <p> + 1.00772 (0.574887s) + </p> + </td> +<td> + <p> + 6.65946 (4.7468s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 1.77419 (0.570218s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.570482s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.712791s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 2.62172 (0.842611s) + </p> + </td> +<td> + <p> + 1.77691 (1.01369s) + </p> + </td> +<td> + <p> + 1.77511 (1.26528s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator2"></a><p class="title"><b>Table 1.26. Operator /</b></p> +<div class="table-contents"><table class="table" summary="Operator /"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 2.96096 (4.00777s) + </p> + </td> +<td> + <p> + 4.53244 (7.86435s) + </p> + </td> +<td> + <p> + 6.11936 (51.5509s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.35354s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.73512s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (8.42422s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.30002 (1.75963s) + </p> + </td> +<td> + <p> + 1.39045 (2.41261s) + </p> + </td> +<td> + <p> + 1.66762 (14.0484s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_int2"></a><p class="title"><b>Table 1.27. Operator /(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(int)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 8.60726 (1.8181s) + </p> + </td> +<td> + <p> + 15.4122 (3.67479s) + </p> + </td> +<td> + <p> + 34.5119 (24.729s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 1.24394 (0.262756s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.238433s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.716536s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.211229s) + </p> + </td> +<td> + <p> + 1.12178 (0.26747s) + </p> + </td> +<td> + <p> + 1.02237 (0.732562s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long5"></a><p class="title"><b>Table 1.28. Operator /(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 2.10976 (1.97569s) + </p> + </td> +<td> + <p> + 3.73601 (3.9133s) + </p> + </td> +<td> + <p> + 11.3085 (25.4533s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.936452s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.04746s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.25081s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.3423 (1.257s) + </p> + </td> +<td> + <p> + 1.51575 (1.58768s) + </p> + </td> +<td> + <p> + 3.31513 (7.46175s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_unsigned_long_long6"></a><p class="title"><b>Table 1.29. Operator /=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 2.17401 (1.96883s) + </p> + </td> +<td> + <p> + 3.79591 (3.8965s) + </p> + </td> +<td> + <p> + 11.2328 (25.2606s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.905621s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.0265s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.24882s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.37953 (1.24933s) + </p> + </td> +<td> + <p> + 1.53073 (1.57129s) + </p> + </td> +<td> + <p> + 3.30546 (7.43339s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_construct"></a><p class="title"><b>Table 1.30. Operator construct</b></p> +<div class="table-contents"><table class="table" summary="Operator construct"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00929804s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0268321s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0310685s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 30.8781 (0.287106s) + </p> + </td> +<td> + <p> + 7.59969 (0.203916s) + </p> + </td> +<td> + <p> + 6.51873 (0.202527s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 23.5296 (0.218779s) + </p> + </td> +<td> + <p> + 8.11058 (0.217624s) + </p> + </td> +<td> + <p> + 7.16325 (0.222552s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_construct_unsigned"></a><p class="title"><b>Table 1.31. Operator construct(unsigned)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0603971s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0735485s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.116464s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 3.91573 (0.236498s) + </p> + </td> +<td> + <p> + 2.88171 (0.211945s) + </p> + </td> +<td> + <p> + 1.81075 (0.210887s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 4.90052 (0.295977s) + </p> + </td> +<td> + <p> + 4.01118 (0.295017s) + </p> + </td> +<td> + <p> + 2.62005 (0.305141s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_construct_unsigned_long"></a><p class="title"><b>Table 1.32. Operator construct(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0610288s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0759005s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.118511s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + 8.26247 (0.504249s) + </p> + </td> +<td> + <p> + 6.69042 (0.507806s) + </p> + </td> +<td> + <p> + 4.32819 (0.51294s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 10.1593 (0.620013s) + </p> + </td> +<td> + <p> + 8.45884 (0.64203s) + </p> + </td> +<td> + <p> + 5.51472 (0.653557s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.float_performance.operator_str"></a><p class="title"><b>Table 1.33. Operator str</b></p> +<div class="table-contents"><table class="table" summary="Operator str"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 50 Bits + </p> + </th> +<th> + <p> + 100 Bits + </p> + </th> +<th> + <p> + 500 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 2.95848 (0.0223061s) + </p> + </td> +<td> + <p> + 3.33461 (0.033471s) + </p> + </td> +<td> + <p> + 3.0159 (0.132732s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00753971s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0100374s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0440106s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.25424 (0.00945658s) + </p> + </td> +<td> + <p> + 1.24943 (0.012541s) + </p> + </td> +<td> + <p> + 1.09428 (0.0481601s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0. + The tests were run on 32-bit Windows Vista machine. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="int_real_world.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="integer_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/int_real_world.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/int_real_world.html new file mode 100644 index 0000000000..7c8946099c --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/int_real_world.html @@ -0,0 +1,381 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Integer Real World Tests</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="realworld.html" title="Floating-Point Real World Tests"> +<link rel="next" href="float_performance.html" title="Float Algorithm Performance"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="realworld.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.int_real_world"></a><a class="link" href="int_real_world.html" title="Integer Real World Tests">Integer Real + World Tests</a> +</h3></div></div></div> +<p> + The first set of <a href="../../../../performance/voronoi_performance.cpp" target="_top">tests</a> + measure the times taken to execute the multiprecision part of the Voronoi-diagram + builder from Boost.Polygon. The tests mainly create a large number of temporaries + "just in case" multiprecision arithmetic is required, for comparison, + also included in the tests is Boost.Polygon's own partial-multiprecision + integer type which was custom written for this specific task: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Integer Type + </p> + </th> +<th> + <p> + Relative Performance (Actual time in parenthesis) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + polygon::detail::extended_int + </p> + </td> +<td> + <p> + 1(0.138831s) + </p> + </td> +</tr> +<tr> +<td> + <p> + int256_t + </p> + </td> +<td> + <p> + 1.19247(0.165551s) + </p> + </td> +</tr> +<tr> +<td> + <p> + int512_t + </p> + </td> +<td> + <p> + 1.23301(0.17118s) + </p> + </td> +</tr> +<tr> +<td> + <p> + int1024_t + </p> + </td> +<td> + <p> + 1.21463(0.168628s) + </p> + </td> +</tr> +<tr> +<td> + <p> + checked_int256_t + </p> + </td> +<td> + <p> + 1.31711(0.182855s) + </p> + </td> +</tr> +<tr> +<td> + <p> + checked_int512_t + </p> + </td> +<td> + <p> + 1.57413(0.218538s) + </p> + </td> +</tr> +<tr> +<td> + <p> + checked_int1024_t + </p> + </td> +<td> + <p> + 1.36992(0.190187s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.63244(0.226632s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpz_int + </p> + </td> +<td> + <p> + 5.42511(0.753172s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tom_int + </p> + </td> +<td> + <p> + 29.0793(4.03709s) + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + Note how for this use case, any dynamic allocation is a performance killer. + </p> +<p> + The next <a href="../../../../performance/miller_rabin_performance.cpp" target="_top">tests</a> + measure the time taken to generate 1000 128-bit random numbers and test for + primality using the Miller Rabin test. This is primarily a test of modular-exponentiation + since that is the rate limiting step: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Integer Type + </p> + </th> +<th> + <p> + Relative Performance (Actual time in parenthesis) + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 5.25827(0.379597s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int (no Expression templates) + </p> + </td> +<td> + <p> + 5.15675(0.372268s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int (128-bit cache) + </p> + </td> +<td> + <p> + 5.10882(0.368808s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int (256-bit cache) + </p> + </td> +<td> + <p> + 5.50623(0.397497s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int (512-bit cache) + </p> + </td> +<td> + <p> + 4.82257(0.348144s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int (1024-bit cache) + </p> + </td> +<td> + <p> + 5.00053(0.360991s) + </p> + </td> +</tr> +<tr> +<td> + <p> + int1024_t + </p> + </td> +<td> + <p> + 4.37589(0.315897s) + </p> + </td> +</tr> +<tr> +<td> + <p> + checked_int1024_t + </p> + </td> +<td> + <p> + 4.52396(0.326587s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpz_int + </p> + </td> +<td> + <p> + 1(0.0721905s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpz_int (no Expression templates) + </p> + </td> +<td> + <p> + 1.0248(0.0739806s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tom_int + </p> + </td> +<td> + <p> + 2.60673(0.188181s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tom_int (no Expression templates) + </p> + </td> +<td> + <p> + 2.64997(0.191303s) + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + It's interesting to note that expression templates have little effect here + - perhaps because the actual expressions involved are relatively trivial + in this case - so the time taken for multiplication and division tends to + dominate. Also note how increasing the internal cache size used by <code class="computeroutput"><span class="identifier">cpp_int</span></code> is quite effective in this case + in cutting out memory allocations altogether - cutting about a third off + the total runtime. Finally the much quicker times from GMP and tommath are + down to their much better modular-exponentiation algorithms (GMP's is about + 5x faster). That's an issue which needs to be addressed in a future release + for <a class="link" href="../tut/ints/cpp_int.html" title="cpp_int">cpp_int</a>. + </p> +<p> + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0. + The tests were run on 32-bit Windows Vista machine. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="realworld.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/integer_performance.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/integer_performance.html new file mode 100644 index 0000000000..dbc6f2a63a --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/integer_performance.html @@ -0,0 +1,4830 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Integer Algorithm Performance</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="float_performance.html" title="Float Algorithm Performance"> +<link rel="next" href="rational_performance.html" title="Rational Type Performance"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="float_performance.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.integer_performance"></a><a class="link" href="integer_performance.html" title="Integer Algorithm Performance">Integer + Algorithm Performance</a> +</h3></div></div></div> +<p> + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. + </p> +<div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator"></a><p class="title"><b>Table 1.34. Operator +</b></p> +<div class="table-contents"><table class="table" summary="Operator +"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.23704 (0.0274266s) + </p> + </td> +<td> + <p> + 1.09358 (0.0383278s) + </p> + </td> +<td> + <p> + 1.26645 (0.0558828s) + </p> + </td> +<td> + <p> + 1.32188 (0.0916899s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.62044 (0.0359271s) + </p> + </td> +<td> + <p> + 1.5277 (0.053543s) + </p> + </td> +<td> + <p> + 1.73059 (0.076363s) + </p> + </td> +<td> + <p> + 1.71537 (0.118983s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.87515 (0.0415741s) + </p> + </td> +<td> + <p> + 1.21699 (0.042653s) + </p> + </td> +<td> + <p> + 1.15599 (0.0510088s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0693631s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0221711s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.035048s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0441255s) + </p> + </td> +<td> + <p> + 1.04441 (0.0724435s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int"></a><p class="title"><b>Table 1.35. Operator +(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0155377s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0209523s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0306377s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.043125s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.31904 (0.0204948s) + </p> + </td> +<td> + <p> + 1.76211 (0.0369203s) + </p> + </td> +<td> + <p> + 1.52941 (0.0468577s) + </p> + </td> +<td> + <p> + 1.60412 (0.0691778s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.96204 (0.0304855s) + </p> + </td> +<td> + <p> + 2.02569 (0.0424428s) + </p> + </td> +<td> + <p> + 2.11505 (0.0648002s) + </p> + </td> +<td> + <p> + 2.65993 (0.114709s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 14.0654 (0.218543s) + </p> + </td> +<td> + <p> + 10.8239 (0.226786s) + </p> + </td> +<td> + <p> + 7.76691 (0.23796s) + </p> + </td> +<td> + <p> + 6.10039 (0.263079s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long"></a><p class="title"><b>Table 1.36. Operator +(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.026624s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0291407s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0373209s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0464919s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.31378 (0.034978s) + </p> + </td> +<td> + <p> + 1.54897 (0.045138s) + </p> + </td> +<td> + <p> + 1.53649 (0.0573431s) + </p> + </td> +<td> + <p> + 1.27833 (0.0594319s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 25.5775 (0.680974s) + </p> + </td> +<td> + <p> + 24.0117 (0.699717s) + </p> + </td> +<td> + <p> + 19.5633 (0.730121s) + </p> + </td> +<td> + <p> + 16.8939 (0.785432s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 19.4694 (0.518354s) + </p> + </td> +<td> + <p> + 18.4246 (0.536907s) + </p> + </td> +<td> + <p> + 14.7715 (0.551288s) + </p> + </td> +<td> + <p> + 12.3637 (0.574812s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long0"></a><p class="title"><b>Table 1.37. Operator +=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.18405 (0.0196905s) + </p> + </td> +<td> + <p> + 1.22304 (0.0206476s) + </p> + </td> +<td> + <p> + 1.25861 (0.0217397s) + </p> + </td> +<td> + <p> + 1.29525 (0.0220829s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0166298s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0168822s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0172728s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0170492s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 39.9082 (0.663668s) + </p> + </td> +<td> + <p> + 39.4584 (0.666147s) + </p> + </td> +<td> + <p> + 38.5504 (0.665873s) + </p> + </td> +<td> + <p> + 39.2231 (0.668722s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 30.6219 (0.509238s) + </p> + </td> +<td> + <p> + 30.4135 (0.513447s) + </p> + </td> +<td> + <p> + 30.9077 (0.533863s) + </p> + </td> +<td> + <p> + 32.3086 (0.550835s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator0"></a><p class="title"><b>Table 1.38. Operator -</b></p> +<div class="table-contents"><table class="table" summary="Operator -"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.06986 (0.0296064s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0381508s) + </p> + </td> +<td> + <p> + 1.05932 (0.053186s) + </p> + </td> +<td> + <p> + 1.1766 (0.0844721s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.3304 (0.0368163s) + </p> + </td> +<td> + <p> + 1.44506 (0.0551303s) + </p> + </td> +<td> + <p> + 1.4431 (0.0724545s) + </p> + </td> +<td> + <p> + 1.57255 (0.112898s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.48072 (0.0409761s) + </p> + </td> +<td> + <p> + 1.19003 (0.0454007s) + </p> + </td> +<td> + <p> + 1.0794 (0.0541942s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0717934s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0276731s) + </p> + </td> +<td> + <p> + 1.10891 (0.0423057s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0502076s) + </p> + </td> +<td> + <p> + 1.08479 (0.0778811s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int0"></a><p class="title"><b>Table 1.39. Operator -(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0147372s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0170001s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0232882s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0310734s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.4267 (0.0210256s) + </p> + </td> +<td> + <p> + 1.98887 (0.0338109s) + </p> + </td> +<td> + <p> + 1.83788 (0.0428009s) + </p> + </td> +<td> + <p> + 1.81269 (0.0563264s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 2.07504 (0.0305803s) + </p> + </td> +<td> + <p> + 2.40928 (0.0409579s) + </p> + </td> +<td> + <p> + 2.58711 (0.0602493s) + </p> + </td> +<td> + <p> + 3.26438 (0.101435s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 13.5424 (0.199577s) + </p> + </td> +<td> + <p> + 12.1793 (0.207048s) + </p> + </td> +<td> + <p> + 9.28855 (0.216314s) + </p> + </td> +<td> + <p> + 7.49327 (0.232842s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long1"></a><p class="title"><b>Table 1.40. Operator -(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0277377s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0296807s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0372392s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0455855s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.19867 (0.0332484s) + </p> + </td> +<td> + <p> + 1.48639 (0.0441169s) + </p> + </td> +<td> + <p> + 1.43253 (0.0533464s) + </p> + </td> +<td> + <p> + 1.27697 (0.0582111s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 24.1794 (0.670683s) + </p> + </td> +<td> + <p> + 22.9073 (0.679904s) + </p> + </td> +<td> + <p> + 18.8758 (0.702922s) + </p> + </td> +<td> + <p> + 16.5837 (0.755975s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 18.149 (0.503413s) + </p> + </td> +<td> + <p> + 17.4116 (0.516787s) + </p> + </td> +<td> + <p> + 14.0411 (0.52288s) + </p> + </td> +<td> + <p> + 11.8237 (0.538987s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long2"></a><p class="title"><b>Table 1.41. Operator -=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.26896 (0.0203467s) + </p> + </td> +<td> + <p> + 1.25722 (0.0206147s) + </p> + </td> +<td> + <p> + 1.36108 (0.0225485s) + </p> + </td> +<td> + <p> + 1.18351 (0.0226161s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0160342s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0163971s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0165667s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0191094s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 41.1339 (0.659547s) + </p> + </td> +<td> + <p> + 40.3982 (0.662411s) + </p> + </td> +<td> + <p> + 39.925 (0.661425s) + </p> + </td> +<td> + <p> + 34.636 (0.661874s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 31.1543 (0.499533s) + </p> + </td> +<td> + <p> + 31.0303 (0.508806s) + </p> + </td> +<td> + <p> + 30.7699 (0.509756s) + </p> + </td> +<td> + <p> + 27.7054 (0.529434s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator1"></a><p class="title"><b>Table 1.42. Operator *</b></p> +<div class="table-contents"><table class="table" summary="Operator *"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.11839 (0.0757577s) + </p> + </td> +<td> + <p> + 1.61061 (0.207951s) + </p> + </td> +<td> + <p> + 1.4501 (0.696912s) + </p> + </td> +<td> + <p> + 1.72796 (2.64108s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.01115 (0.0684934s) + </p> + </td> +<td> + <p> + 1.28687 (0.166152s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.480595s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.52844s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0677384s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.129113s) + </p> + </td> +<td> + <p> + 1.09011 (0.523902s) + </p> + </td> +<td> + <p> + 1.03374 (1.58s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 1.6322 (0.110562s) + </p> + </td> +<td> + <p> + 2.71751 (0.350866s) + </p> + </td> +<td> + <p> + 2.05222 (0.986288s) + </p> + </td> +<td> + <p> + 2.0644 (3.15531s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int1"></a><p class="title"><b>Table 1.43. Operator *(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.01611 (0.0229536s) + </p> + </td> +<td> + <p> + 1.12175 (0.0298152s) + </p> + </td> +<td> + <p> + 1.16413 (0.0416439s) + </p> + </td> +<td> + <p> + 1.31747 (0.0666043s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.30215 (0.0294152s) + </p> + </td> +<td> + <p> + 1.669 (0.0443606s) + </p> + </td> +<td> + <p> + 1.72395 (0.0616701s) + </p> + </td> +<td> + <p> + 1.88315 (0.095202s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0225897s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0265791s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0357725s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0505547s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 10.8281 (0.244603s) + </p> + </td> +<td> + <p> + 10.1516 (0.26982s) + </p> + </td> +<td> + <p> + 8.76424 (0.313519s) + </p> + </td> +<td> + <p> + 8.04364 (0.406644s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long3"></a><p class="title"><b>Table 1.44. Operator *(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0570721s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0856141s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.143279s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.252785s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.10857 (0.0632686s) + </p> + </td> +<td> + <p> + 1.2951 (0.110878s) + </p> + </td> +<td> + <p> + 1.20827 (0.173121s) + </p> + </td> +<td> + <p> + 1.18463 (0.299456s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 12.0605 (0.68832s) + </p> + </td> +<td> + <p> + 8.13434 (0.696415s) + </p> + </td> +<td> + <p> + 5.21762 (0.747577s) + </p> + </td> +<td> + <p> + 3.11601 (0.787681s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 10.0524 (0.57371s) + </p> + </td> +<td> + <p> + 7.33116 (0.627651s) + </p> + </td> +<td> + <p> + 4.85202 (0.695193s) + </p> + </td> +<td> + <p> + 3.35808 (0.848871s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long4"></a><p class="title"><b>Table 1.45. Operator *=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 111.27 (7.43118s) + </p> + </td> +<td> + <p> + 67.7078 (7.34138s) + </p> + </td> +<td> + <p> + 43.3851 (7.4075s) + </p> + </td> +<td> + <p> + 25.3089 (7.55455s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0667848s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.108427s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.170738s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.298493s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 46.3718 (3.09693s) + </p> + </td> +<td> + <p> + 28.4639 (3.08626s) + </p> + </td> +<td> + <p> + 18.1719 (3.10264s) + </p> + </td> +<td> + <p> + 10.5223 (3.14083s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 276.674 (18.4776s) + </p> + </td> +<td> + <p> + 169.146 (18.34s) + </p> + </td> +<td> + <p> + 108.491 (18.5236s) + </p> + </td> +<td> + <p> + 63.3261 (18.9024s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator2"></a><p class="title"><b>Table 1.46. Operator /</b></p> +<div class="table-contents"><table class="table" summary="Operator /"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 2.68035 (0.595251s) + </p> + </td> +<td> + <p> + 2.04702 (0.707471s) + </p> + </td> +<td> + <p> + 1.62314 (0.921536s) + </p> + </td> +<td> + <p> + 1.43112 (1.38811s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.222079s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.34561s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.567748s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.969945s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 3.79283 (0.842308s) + </p> + </td> +<td> + <p> + 2.73668 (0.945824s) + </p> + </td> +<td> + <p> + 1.86649 (1.05969s) + </p> + </td> +<td> + <p> + 1.32141 (1.2817s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 13.2531 (2.94324s) + </p> + </td> +<td> + <p> + 11.2054 (3.87271s) + </p> + </td> +<td> + <p> + 9.83293 (5.58262s) + </p> + </td> +<td> + <p> + 13.0164 (12.6252s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int2"></a><p class="title"><b>Table 1.47. Operator /(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 4.06026 (0.225473s) + </p> + </td> +<td> + <p> + 3.45732 (0.340049s) + </p> + </td> +<td> + <p> + 3.00195 (0.547957s) + </p> + </td> +<td> + <p> + 2.80587 (0.978029s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 2.43766 (0.135367s) + </p> + </td> +<td> + <p> + 2.56264 (0.252052s) + </p> + </td> +<td> + <p> + 2.44011 (0.445402s) + </p> + </td> +<td> + <p> + 2.38009 (0.829617s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0555316s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0983563s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.182534s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.348566s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 35.9988 (1.99907s) + </p> + </td> +<td> + <p> + 27.1024 (2.66569s) + </p> + </td> +<td> + <p> + 21.8333 (3.98531s) + </p> + </td> +<td> + <p> + 25.8066 (8.99528s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long5"></a><p class="title"><b>Table 1.48. Operator /(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.50505 (0.705756s) + </p> + </td> +<td> + <p> + 1.39347 (1.58556s) + </p> + </td> +<td> + <p> + 2.63348 (3.57438s) + </p> + </td> +<td> + <p> + 4.75451 (8.52733s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.468925s) + </p> + </td> +<td> + <p> + 1.12378 (1.27869s) + </p> + </td> +<td> + <p> + 2.29966 (3.12128s) + </p> + </td> +<td> + <p> + 4.4844 (8.04288s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 2.17234 (1.01866s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.13785s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.35728s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.79352s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 4.74612 (2.22557s) + </p> + </td> +<td> + <p> + 2.70088 (3.07319s) + </p> + </td> +<td> + <p> + 3.65634 (4.96268s) + </p> + </td> +<td> + <p> + 6.79408 (12.1853s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_unsigned_long_long6"></a><p class="title"><b>Table 1.49. Operator /=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.76281 (0.0574966s) + </p> + </td> +<td> + <p> + 1.76471 (0.0604224s) + </p> + </td> +<td> + <p> + 1.56085 (0.0716403s) + </p> + </td> +<td> + <p> + 1.31422 (0.124043s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0326164s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0342393s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0458981s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0943852s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 20.2862 (0.661664s) + </p> + </td> +<td> + <p> + 19.4043 (0.664389s) + </p> + </td> +<td> + <p> + 14.4881 (0.664976s) + </p> + </td> +<td> + <p> + 7.14238 (0.674135s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 32.9555 (1.07489s) + </p> + </td> +<td> + <p> + 30.1525 (1.0324s) + </p> + </td> +<td> + <p> + 22.8324 (1.04796s) + </p> + </td> +<td> + <p> + 11.7456 (1.10861s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator3"></a><p class="title"><b>Table 1.50. Operator %</b></p> +<div class="table-contents"><table class="table" summary="Operator %"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.8501 (0.364131s) + </p> + </td> +<td> + <p> + 1.46527 (0.476653s) + </p> + </td> +<td> + <p> + 1.27509 (0.689738s) + </p> + </td> +<td> + <p> + 1.20064 (1.11769s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.196817s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.325301s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.540932s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.930916s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 3.2533 (0.640305s) + </p> + </td> +<td> + <p> + 2.15441 (0.700832s) + </p> + </td> +<td> + <p> + 1.47898 (0.800029s) + </p> + </td> +<td> + <p> + 1.07439 (1.00016s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 15.3501 (3.02116s) + </p> + </td> +<td> + <p> + 12.1106 (3.9396s) + </p> + </td> +<td> + <p> + 11.0689 (5.98752s) + </p> + </td> +<td> + <p> + 13.5535 (12.6172s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int3"></a><p class="title"><b>Table 1.51. Operator %(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator %(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.82761 (0.104331s) + </p> + </td> +<td> + <p> + 2.01496 (0.202512s) + </p> + </td> +<td> + <p> + 2.10004 (0.389523s) + </p> + </td> +<td> + <p> + 2.17252 (0.768097s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.78851 (0.102099s) + </p> + </td> +<td> + <p> + 1.96844 (0.197838s) + </p> + </td> +<td> + <p> + 2.02956 (0.376451s) + </p> + </td> +<td> + <p> + 2.07257 (0.73276s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.057086s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.100505s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.185483s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.353552s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 36.3018 (2.07233s) + </p> + </td> +<td> + <p> + 26.3075 (2.64402s) + </p> + </td> +<td> + <p> + 21.9525 (4.07183s) + </p> + </td> +<td> + <p> + 25.6759 (9.07775s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_construct"></a><p class="title"><b>Table 1.52. Operator construct</b></p> +<div class="table-contents"><table class="table" summary="Operator construct"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.40211 (0.0026854s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00278639s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00322813s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0027185s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00191526s) + </p> + </td> +<td> + <p> + 1.40721 (0.00392103s) + </p> + </td> +<td> + <p> + 1.90346 (0.00614463s) + </p> + </td> +<td> + <p> + 2.14621 (0.00583447s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 98.705 (0.189046s) + </p> + </td> +<td> + <p> + 68.9726 (0.192184s) + </p> + </td> +<td> + <p> + 58.8994 (0.190135s) + </p> + </td> +<td> + <p> + 70.0525 (0.190438s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 105.602 (0.202255s) + </p> + </td> +<td> + <p> + 74.1994 (0.206748s) + </p> + </td> +<td> + <p> + 63.6455 (0.205456s) + </p> + </td> +<td> + <p> + 76.8935 (0.209035s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_construct_unsigned"></a><p class="title"><b>Table 1.53. Operator construct(unsigned)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.73436 (0.00348927s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00263476s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0027009s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00318651s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00201185s) + </p> + </td> +<td> + <p> + 1.36851 (0.0036057s) + </p> + </td> +<td> + <p> + 2.07362 (0.00560064s) + </p> + </td> +<td> + <p> + 1.66856 (0.00531688s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 97.2414 (0.195635s) + </p> + </td> +<td> + <p> + 76.3759 (0.201232s) + </p> + </td> +<td> + <p> + 72.7396 (0.196462s) + </p> + </td> +<td> + <p> + 63.8129 (0.20334s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 210.112 (0.422713s) + </p> + </td> +<td> + <p> + 162.652 (0.42855s) + </p> + </td> +<td> + <p> + 158.33 (0.427634s) + </p> + </td> +<td> + <p> + 134.626 (0.428987s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_construct_unsigned_long"></a><p class="title"><b>Table 1.54. Operator construct(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 2.34403 (0.00739542s) + </p> + </td> +<td> + <p> + 1.66376 (0.00713834s) + </p> + </td> +<td> + <p> + 1.22989 (0.0074969s) + </p> + </td> +<td> + <p> + 1.23708 (0.00711417s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00315501s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00429049s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00609561s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0057508s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 222.866 (0.703144s) + </p> + </td> +<td> + <p> + 164.331 (0.705059s) + </p> + </td> +<td> + <p> + 115.363 (0.70321s) + </p> + </td> +<td> + <p> + 122.347 (0.703596s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 218.681 (0.689941s) + </p> + </td> +<td> + <p> + 163.796 (0.702765s) + </p> + </td> +<td> + <p> + 114.57 (0.698376s) + </p> + </td> +<td> + <p> + 122.422 (0.704027s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_gcd"></a><p class="title"><b>Table 1.55. Operator gcd</b></p> +<div class="table-contents"><table class="table" summary="Operator gcd"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.16358 (2.74442s) + </p> + </td> +<td> + <p> + 1.39847 (8.11559s) + </p> + </td> +<td> + <p> + 1.64677 (22.2518s) + </p> + </td> +<td> + <p> + 1.95096 (64.4961s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.35859s) + </p> + </td> +<td> + <p> + 1.30986 (7.60133s) + </p> + </td> +<td> + <p> + 1.67681 (22.6577s) + </p> + </td> +<td> + <p> + 2.0895 (69.0758s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.03392 (2.4386s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (5.80319s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (13.5124s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (33.0586s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 5.25978 (12.4057s) + </p> + </td> +<td> + <p> + 4.4619 (25.8932s) + </p> + </td> +<td> + <p> + 4.15577 (56.1542s) + </p> + </td> +<td> + <p> + 3.91192 (129.323s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_powm"></a><p class="title"><b>Table 1.56. Operator powm</b></p> +<div class="table-contents"><table class="table" summary="Operator powm"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 2.50722 (2.91621s) + </p> + </td> +<td> + <p> + 3.5561 (13.406s) + </p> + </td> +<td> + <p> + 4.37066 (73.483s) + </p> + </td> +<td> + <p> + 4.88831 (473.91s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.93385 (2.24931s) + </p> + </td> +<td> + <p> + 3.18107 (11.9922s) + </p> + </td> +<td> + <p> + 4.20753 (70.7403s) + </p> + </td> +<td> + <p> + 4.8158 (466.88s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.16313s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (3.76986s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (16.8128s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (96.9476s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 1.44081 (1.67584s) + </p> + </td> +<td> + <p> + 1.8794 (7.08507s) + </p> + </td> +<td> + <p> + 2.19115 (36.8394s) + </p> + </td> +<td> + <p> + 2.17186 (210.557s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_str"></a><p class="title"><b>Table 1.57. Operator str</b></p> +<div class="table-contents"><table class="table" summary="Operator str"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.17175 (0.00160006s) + </p> + </td> +<td> + <p> + 1.41999 (0.00329476s) + </p> + </td> +<td> + <p> + 1.40856 (0.00813784s) + </p> + </td> +<td> + <p> + 1.52964 (0.0229767s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00136554s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00232027s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00577741s) + </p> + </td> +<td> + <p> + 1.14754 (0.0172372s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.50501 (0.00205515s) + </p> + </td> +<td> + <p> + 1.52968 (0.00354926s) + </p> + </td> +<td> + <p> + 1.01989 (0.0058923s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.015021s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 12.2161 (0.0166816s) + </p> + </td> +<td> + <p> + 16.9577 (0.0393463s) + </p> + </td> +<td> + <p> + 18.7474 (0.108311s) + </p> + </td> +<td> + <p> + 22.7368 (0.341528s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator4"></a><p class="title"><b>Table 1.58. Operator |</b></p> +<div class="table-contents"><table class="table" summary="Operator |"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0301617s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0423404s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0522358s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0813156s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.0638 (0.0320861s) + </p> + </td> +<td> + <p> + 1.22566 (0.0518951s) + </p> + </td> +<td> + <p> + 1.28515 (0.0671305s) + </p> + </td> +<td> + <p> + 1.16118 (0.094422s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.76553 (0.0532514s) + </p> + </td> +<td> + <p> + 1.51489 (0.0641408s) + </p> + </td> +<td> + <p> + 1.70708 (0.0891706s) + </p> + </td> +<td> + <p> + 1.77346 (0.14421s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 4.37637 (0.131999s) + </p> + </td> +<td> + <p> + 3.46212 (0.146587s) + </p> + </td> +<td> + <p> + 2.91875 (0.152463s) + </p> + </td> +<td> + <p> + 4.19621 (0.341217s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int4"></a><p class="title"><b>Table 1.59. Operator |(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator |(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0289129s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0351119s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0406779s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0525891s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.06091 (0.030674s) + </p> + </td> +<td> + <p> + 1.25979 (0.0442336s) + </p> + </td> +<td> + <p> + 1.36194 (0.0554009s) + </p> + </td> +<td> + <p> + 1.37438 (0.0722772s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 4.92854 (0.142498s) + </p> + </td> +<td> + <p> + 4.34687 (0.152627s) + </p> + </td> +<td> + <p> + 3.71442 (0.151095s) + </p> + </td> +<td> + <p> + 2.981 (0.156768s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 10.9847 (0.317598s) + </p> + </td> +<td> + <p> + 9.37065 (0.329021s) + </p> + </td> +<td> + <p> + 8.53651 (0.347248s) + </p> + </td> +<td> + <p> + 11.2155 (0.589813s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator5"></a><p class="title"><b>Table 1.60. Operator ^</b></p> +<div class="table-contents"><table class="table" summary="Operator ^"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0305149s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.04217s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0525977s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0816632s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.01544 (0.0309861s) + </p> + </td> +<td> + <p> + 1.24872 (0.0526585s) + </p> + </td> +<td> + <p> + 1.26661 (0.066621s) + </p> + </td> +<td> + <p> + 1.15965 (0.0947007s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.64675 (0.0502505s) + </p> + </td> +<td> + <p> + 1.47181 (0.0620663s) + </p> + </td> +<td> + <p> + 1.66038 (0.0873322s) + </p> + </td> +<td> + <p> + 1.67895 (0.137108s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 4.30668 (0.131418s) + </p> + </td> +<td> + <p> + 3.45859 (0.145849s) + </p> + </td> +<td> + <p> + 2.91462 (0.153303s) + </p> + </td> +<td> + <p> + 4.15538 (0.339342s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int5"></a><p class="title"><b>Table 1.61. Operator ^(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator ^(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.01566 (0.0296088s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0356634s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0401898s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0514097s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0291524s) + </p> + </td> +<td> + <p> + 1.2393 (0.0441976s) + </p> + </td> +<td> + <p> + 1.38556 (0.0556856s) + </p> + </td> +<td> + <p> + 1.38899 (0.0714075s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 4.68027 (0.136441s) + </p> + </td> +<td> + <p> + 4.15243 (0.14809s) + </p> + </td> +<td> + <p> + 3.74237 (0.150405s) + </p> + </td> +<td> + <p> + 3.0483 (0.156712s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 10.919 (0.318314s) + </p> + </td> +<td> + <p> + 9.16311 (0.326788s) + </p> + </td> +<td> + <p> + 8.62554 (0.346659s) + </p> + </td> +<td> + <p> + 11.6212 (0.597442s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator6"></a><p class="title"><b>Table 1.62. Operator &</b></p> +<div class="table-contents"><table class="table" summary="Operator &"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.0346 (0.0303431s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0427309s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0535587s) + </p> + </td> +<td> + <p> + 1.06945 (0.0828084s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0293284s) + </p> + </td> +<td> + <p> + 1.10435 (0.04719s) + </p> + </td> +<td> + <p> + 1.05262 (0.0563769s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0774309s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.86057 (0.0545675s) + </p> + </td> +<td> + <p> + 1.58432 (0.0676995s) + </p> + </td> +<td> + <p> + 1.69164 (0.0906018s) + </p> + </td> +<td> + <p> + 1.86625 (0.144505s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 4.4157 (0.129506s) + </p> + </td> +<td> + <p> + 3.60396 (0.154s) + </p> + </td> +<td> + <p> + 2.95985 (0.158525s) + </p> + </td> +<td> + <p> + 4.4032 (0.340944s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator_int6"></a><p class="title"><b>Table 1.63. Operator &(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator &(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + 1.05874 (0.038946s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0483903s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.063842s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.100361s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0367853s) + </p> + </td> +<td> + <p> + 1.05827 (0.0512099s) + </p> + </td> +<td> + <p> + 1.09114 (0.0696605s) + </p> + </td> +<td> + <p> + 1.09432 (0.109826s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 3.92298 (0.144308s) + </p> + </td> +<td> + <p> + 2.99447 (0.144903s) + </p> + </td> +<td> + <p> + 2.228 (0.14224s) + </p> + </td> +<td> + <p> + 1.42296 (0.142809s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 8.79208 (0.323419s) + </p> + </td> +<td> + <p> + 7.02288 (0.339839s) + </p> + </td> +<td> + <p> + 5.65271 (0.36088s) + </p> + </td> +<td> + <p> + 6.27104 (0.629365s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator7"></a><p class="title"><b>Table 1.64. Operator <<</b></p> +<div class="table-contents"><table class="table" summary="Operator <<"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0248801s) + </p> + </td> +<td> + <p> + 1.23196 (0.04s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0424149s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.060157s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.08931 (0.027102s) + </p> + </td> +<td> + <p> + 1.40572 (0.0456418s) + </p> + </td> +<td> + <p> + 1.3475 (0.0571542s) + </p> + </td> +<td> + <p> + 1.24573 (0.0749397s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.05561 (0.0262636s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0324686s) + </p> + </td> +<td> + <p> + 1.09914 (0.0466199s) + </p> + </td> +<td> + <p> + 1.16315 (0.0699719s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 1.60497 (0.0399319s) + </p> + </td> +<td> + <p> + 2.13048 (0.0691737s) + </p> + </td> +<td> + <p> + 2.31219 (0.0980712s) + </p> + </td> +<td> + <p> + 2.74695 (0.165248s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.integer_performance.operator8"></a><p class="title"><b>Table 1.65. Operator >></b></p> +<div class="table-contents"><table class="table" summary="Operator >>"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0213349s) + </p> + </td> +<td> + <p> + 1.02127 (0.0295019s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0327116s) + </p> + </td> +<td> + <p> + 1.13168 (0.0433804s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int(fixed) + </p> + </td> +<td> + <p> + 1.13514 (0.0242181s) + </p> + </td> +<td> + <p> + 1.16938 (0.0337803s) + </p> + </td> +<td> + <p> + 1.46999 (0.0480859s) + </p> + </td> +<td> + <p> + 1.60077 (0.061362s) + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp_int + </p> + </td> +<td> + <p> + 1.26614 (0.0270129s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0288873s) + </p> + </td> +<td> + <p> + 1.42219 (0.0465221s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0383329s) + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath_int + </p> + </td> +<td> + <p> + 12.0066 (0.25616s) + </p> + </td> +<td> + <p> + 10.2837 (0.297067s) + </p> + </td> +<td> + <p> + 9.99696 (0.327017s) + </p> + </td> +<td> + <p> + 16.0943 (0.616942s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0. + The tests were run on 32-bit Windows Vista machine. + </p> +<p> + Linux x86_64 results are broadly similar, except that libtommath performs + much better there. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="float_performance.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational_performance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/overhead.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/overhead.html new file mode 100644 index 0000000000..0bda9c57c6 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/overhead.html @@ -0,0 +1,200 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>The Overhead in the Number Class Wrapper</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="../perf.html" title="Performance Comparison"> +<link rel="next" href="realworld.html" title="Floating-Point Real World Tests"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../perf.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="realworld.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.overhead"></a><a class="link" href="overhead.html" title="The Overhead in the Number Class Wrapper">The Overhead in the + Number Class Wrapper</a> +</h3></div></div></div> +<p> + Using a simple <a href="../../../../performance/arithmetic_backend.hpp" target="_top">backend + class</a> that wraps any built in arithmetic type we can measure the + overhead involved in wrapping a type inside the <code class="computeroutput"><span class="identifier">number</span></code> + frontend, and the effect that turning on expression templates has. The following + table compares the performance between <code class="computeroutput"><span class="keyword">double</span></code> + and a <code class="computeroutput"><span class="keyword">double</span></code> wrapped inside + class <code class="computeroutput"><span class="identifier">number</span></code>: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Type + </p> + </th> +<th> + <p> + Bessel Function Evaluation + </p> + </th> +<th> + <p> + Non-Central T Evaluation + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="keyword">double</span></code> + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0 (0.016s)</strong></span> + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span> (0.46s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">arithmetic_backend</span><span class="special"><</span><span class="keyword">double</span><span class="special">>,</span> + <span class="identifier">et_off</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.2 (0.019s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span>(0.46s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">arithmetic_backend</span><span class="special"><</span><span class="keyword">double</span><span class="special">>,</span> + <span class="identifier">et_on</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.2 (0.019s) + </p> + </td> +<td> + <p> + 1.7 (0.79s) + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + As you can see whether or not there is an overhead, and how large it is depends + on the actual situation, but the overhead is in any cases small. Expression + templates generally add a greater overhead the more complex the expression + becomes due to the logic of figuring out how to best unpack and evaluate + the expression, but of course this is also the situation where you save more + temporaries. For a "trivial" backend like this, saving temporaries + has no benefit, but for larger types it becomes a bigger win. + </p> +<p> + The following table compares arithmetic using either <code class="computeroutput"><span class="keyword">long</span> + <span class="keyword">long</span></code> or <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">arithmetic_backend</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">long</span><span class="special">></span> <span class="special">></span></code> for the <a href="../../../../performance/voronoi_performance.cpp" target="_top">voronoi-diagram + builder test</a>: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Type + </p> + </th> +<th> + <p> + Relative time + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code> + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span>(0.0823s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">arithmetic_backend</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">long</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.05 (0.0875s) + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + This test involves mainly creating a lot of temporaries and performing a + small amount of arithmetic on them, with very little difference in performance + between the native and "wrapped" types. + </p> +<p> + The test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a>-0.42.0. + The tests were run on 32-bit Windows Vista machine. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../perf.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="realworld.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/rational_performance.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/rational_performance.html new file mode 100644 index 0000000000..00c65564ce --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/rational_performance.html @@ -0,0 +1,1958 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Rational Type Performance</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="integer_performance.html" title="Integer Algorithm Performance"> +<link rel="next" href="../map.html" title="Roadmap"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="integer_performance.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../map.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.rational_performance"></a><a class="link" href="rational_performance.html" title="Rational Type Performance">Rational + Type Performance</a> +</h3></div></div></div> +<p> + Note that these tests are carefully designed to test performance of the underlying + algorithms and not memory allocation or variable copying. As usual, performance + results should be taken with a healthy dose of scepticism, and real-world + performance may vary widely depending upon the specifics of the program. + In each table relative times are given first, with the best performer given + a score of 1. Total actual times are given in brackets, measured in seconds + for 500000 operations. + </p> +<div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator"></a><p class="title"><b>Table 1.66. Operator +</b></p> +<div class="table-contents"><table class="table" summary="Operator +"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 5.89417 (18.4116s) + </p> + </td> +<td> + <p> + 6.87256 (47.4698s) + </p> + </td> +<td> + <p> + 6.65008 (107.715s) + </p> + </td> +<td> + <p> + 6.53801 (256.244s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (3.1237s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (6.90715s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (16.1975s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (39.1929s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_int"></a><p class="title"><b>Table 1.67. Operator +(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 3.62367 (2.46488s) + </p> + </td> +<td> + <p> + 4.18291 (2.94603s) + </p> + </td> +<td> + <p> + 4.726 (3.74866s) + </p> + </td> +<td> + <p> + 6.1388 (5.56817s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.680215s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.704303s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.7932s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.907046s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long"></a><p class="title"><b>Table 1.68. Operator +(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.1527 (2.6378s) + </p> + </td> +<td> + <p> + 1.31751 (3.09863s) + </p> + </td> +<td> + <p> + 1.58996 (4.00714s) + </p> + </td> +<td> + <p> + 2.15642 (5.75702s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.28837s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.35189s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.52028s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.66971s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long0"></a><p class="title"><b>Table 1.69. Operator +=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator +=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.18436 (2.7059s) + </p> + </td> +<td> + <p> + 1.32279 (3.11099s) + </p> + </td> +<td> + <p> + 1.61398 (4.05389s) + </p> + </td> +<td> + <p> + 2.20048 (5.84623s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.2847s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.35183s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.51174s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.6568s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator0"></a><p class="title"><b>Table 1.70. Operator -</b></p> +<div class="table-contents"><table class="table" summary="Operator -"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 5.81893 (18.3457s) + </p> + </td> +<td> + <p> + 6.82209 (47.1928s) + </p> + </td> +<td> + <p> + 6.64143 (107.498s) + </p> + </td> +<td> + <p> + 6.51362 (255.137s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (3.15277s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (6.91765s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (16.1859s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (39.1698s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_int0"></a><p class="title"><b>Table 1.71. Operator -(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 3.72441 (2.48756s) + </p> + </td> +<td> + <p> + 4.27663 (2.98713s) + </p> + </td> +<td> + <p> + 4.62109 (3.72114s) + </p> + </td> +<td> + <p> + 6.17605 (5.56503s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.667908s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.698479s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.805252s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.901066s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long1"></a><p class="title"><b>Table 1.72. Operator -(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.15627 (2.63239s) + </p> + </td> +<td> + <p> + 1.32096 (3.12092s) + </p> + </td> +<td> + <p> + 1.61044 (4.00106s) + </p> + </td> +<td> + <p> + 2.19378 (5.7644s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.27663s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.36262s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.48445s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.62761s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long2"></a><p class="title"><b>Table 1.73. Operator -=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator -=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.1984 (2.73444s) + </p> + </td> +<td> + <p> + 1.34141 (3.15698s) + </p> + </td> +<td> + <p> + 1.64159 (4.06997s) + </p> + </td> +<td> + <p> + 2.23017 (5.88108s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.28174s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.35348s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.47929s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (2.63706s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator1"></a><p class="title"><b>Table 1.74. Operator *</b></p> +<div class="table-contents"><table class="table" summary="Operator *"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 5.4306 (32.5882s) + </p> + </td> +<td> + <p> + 6.91805 (89.9436s) + </p> + </td> +<td> + <p> + 6.94556 (207.307s) + </p> + </td> +<td> + <p> + 6.88704 (492.151s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (6.00084s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (13.0013s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (29.8475s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (71.4604s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_int1"></a><p class="title"><b>Table 1.75. Operator *(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 2.12892 (2.51376s) + </p> + </td> +<td> + <p> + 2.47245 (3.07841s) + </p> + </td> +<td> + <p> + 2.86832 (3.93619s) + </p> + </td> +<td> + <p> + 3.94086 (6.02565s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.18077s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.24508s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.3723s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.52902s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long3"></a><p class="title"><b>Table 1.76. Operator *(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.32254 (5.43565s) + </p> + </td> +<td> + <p> + 1.56078 (6.73163s) + </p> + </td> +<td> + <p> + 1.97701 (9.32522s) + </p> + </td> +<td> + <p> + 2.85404 (15.1573s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.11002s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.313s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.71682s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (5.31082s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long4"></a><p class="title"><b>Table 1.77. Operator *=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator *=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 6.29806 (58.1188s) + </p> + </td> +<td> + <p> + 6.30556 (59.5076s) + </p> + </td> +<td> + <p> + 6.3385 (62.1007s) + </p> + </td> +<td> + <p> + 6.55345 (67.6905s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.22804s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.43733s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.79739s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (10.329s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator2"></a><p class="title"><b>Table 1.78. Operator /</b></p> +<div class="table-contents"><table class="table" summary="Operator /"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 4.4269 (66.8031s) + </p> + </td> +<td> + <p> + 6.40103 (173.527s) + </p> + </td> +<td> + <p> + 6.32347 (348.193s) + </p> + </td> +<td> + <p> + 6.61148 (824.063s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (15.0903s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (27.1093s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (55.0637s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (124.641s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_int2"></a><p class="title"><b>Table 1.79. Operator /(int)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(int)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.78772 (2.50984s) + </p> + </td> +<td> + <p> + 2.10623 (3.10606s) + </p> + </td> +<td> + <p> + 2.46986 (3.99358s) + </p> + </td> +<td> + <p> + 3.37428 (5.96678s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.40393s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.4747s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.61693s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (1.76831s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long5"></a><p class="title"><b>Table 1.80. Operator /(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 1.29695 (5.45454s) + </p> + </td> +<td> + <p> + 1.55248 (6.85353s) + </p> + </td> +<td> + <p> + 1.93237 (9.28765s) + </p> + </td> +<td> + <p> + 2.75211 (14.8541s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.20568s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.41458s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (4.80635s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (5.39734s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long6"></a><p class="title"><b>Table 1.81. Operator /=(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator /=(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 6.19401 (58.4278s) + </p> + </td> +<td> + <p> + 6.20135 (59.643s) + </p> + </td> +<td> + <p> + 6.21327 (62.0338s) + </p> + </td> +<td> + <p> + 6.40576 (67.6778s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.43295s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.61774s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (9.98407s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (10.5652s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_construct"></a><p class="title"><b>Table 1.82. Operator construct</b></p> +<div class="table-contents"><table class="table" summary="Operator construct"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00978288s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0100574s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0101393s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0101847s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + 39.1516 (0.383015s) + </p> + </td> +<td> + <p> + 38.3523 (0.385725s) + </p> + </td> +<td> + <p> + 37.5812 (0.381048s) + </p> + </td> +<td> + <p> + 37.6007 (0.382953s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_construct_unsigned"></a><p class="title"><b>Table 1.83. Operator construct(unsigned)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0548151s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0557542s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.055825s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0552808s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + 7.21073 (0.395257s) + </p> + </td> +<td> + <p> + 7.1016 (0.395944s) + </p> + </td> +<td> + <p> + 7.02046 (0.391917s) + </p> + </td> +<td> + <p> + 7.16881 (0.396297s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_construct_unsigned_long"></a><p class="title"><b>Table 1.84. Operator construct(unsigned long long)</b></p> +<div class="table-contents"><table class="table" summary="Operator construct(unsigned long long)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0605156s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0616657s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0592056s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0603081s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + 35.1604 (2.12775s) + </p> + </td> +<td> + <p> + 34.7575 (2.14335s) + </p> + </td> +<td> + <p> + 35.7232 (2.11502s) + </p> + </td> +<td> + <p> + 35.0437 (2.11342s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.rational_performance.operator_str"></a><p class="title"><b>Table 1.85. Operator str</b></p> +<div class="table-contents"><table class="table" summary="Operator str"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + 128 Bits + </p> + </th> +<th> + <p> + 256 Bits + </p> + </th> +<th> + <p> + 512 Bits + </p> + </th> +<th> + <p> + 1024 Bits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_rational + </p> + </td> +<td> + <p> + 5.48898 (0.0208949s) + </p> + </td> +<td> + <p> + 8.49668 (0.0546688s) + </p> + </td> +<td> + <p> + 10.107 (0.121897s) + </p> + </td> +<td> + <p> + 10.5339 (0.310584s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpq_rational + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0038067s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.00643413s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0120606s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1</strong></span> (0.0294843s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0. + The tests were run on 32-bit Windows Vista machine. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="integer_performance.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../map.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/perf/realworld.html b/libs/multiprecision/doc/html/boost_multiprecision/perf/realworld.html new file mode 100644 index 0000000000..a847792299 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/perf/realworld.html @@ -0,0 +1,284 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Floating-Point Real World Tests</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../perf.html" title="Performance Comparison"> +<link rel="prev" href="overhead.html" title="The Overhead in the Number Class Wrapper"> +<link rel="next" href="int_real_world.html" title="Integer Real World Tests"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="overhead.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="int_real_world.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.perf.realworld"></a><a class="link" href="realworld.html" title="Floating-Point Real World Tests">Floating-Point Real + World Tests</a> +</h3></div></div></div> +<p> + These tests test the total time taken to execute all of Boost.Math's test + cases for these functions. In each case the best performing library gets + a relative score of 1, with the total execution time given in brackets. The + first three libraries listed are the various floating point types provided + by this library, while for comparison, two popular C++ front-ends to <a href="http://www.mpfr.org" target="_top">MPFR</a> ( <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + and <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a>) are + also shown. + </p> +<div class="table"> +<a name="boost_multiprecision.perf.realworld.bessel_function_performance"></a><p class="title"><b>Table 1.12. Bessel Function Performance</b></p> +<div class="table-contents"><table class="table" summary="Bessel Function Performance"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Library + </p> + </th> +<th> + <p> + 50 Decimal Digits + </p> + </th> +<th> + <p> + 100 Decimal Digits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.2 (5.78s) + </p> + </td> +<td> + <p> + 1.2 (9.56s) + </p> + </td> +</tr> +<tr> +<td> + <p> + static_mpfr_float + </p> + </td> +<td> + <p> + 1.1 (5.47s) + </p> + </td> +<td> + <p> + 1.1 (9.09s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpf_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span> (4.82s) + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span>(8.07s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 1.8 (8.54s) + </p> + </td> +<td> + <p> + 2.6 (20.66s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + </p> + </td> +<td> + <p> + 1.3 (6.28s) + </p> + </td> +<td> + <p> + 1.2(10.06s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> + </p> + </td> +<td> + <p> + 2.0 (9.54s) + </p> + </td> +<td> + <p> + 1.7 (14.08s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.perf.realworld.non_central_t_distribution_perfo"></a><p class="title"><b>Table 1.13. Non-Central T Distribution Performance</b></p> +<div class="table-contents"><table class="table" summary="Non-Central T Distribution Performance"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Library + </p> + </th> +<th> + <p> + 50 Decimal Digits + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + mpfr_float + </p> + </td> +<td> + <p> + 1.3 (263.27s) + </p> + </td> +</tr> +<tr> +<td> + <p> + static_mpfr_float + </p> + </td> +<td> + <p> + 1.2 (232.88s) + </p> + </td> +</tr> +<tr> +<td> + <p> + mpf_float + </p> + </td> +<td> + <p> + <span class="bold"><strong>1.0</strong></span> (195.73s) + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_dec_float + </p> + </td> +<td> + <p> + 1.9 (366.38s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">mpfr_class</a> + </p> + </td> +<td> + <p> + 1.5 (286.94s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpreal</a> + </p> + </td> +<td> + <p> + 2.0 (388.70s) + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + Test code was compiled with Microsoft Visual Studio 2010 with all optimisations + turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0. + The tests were run on 32-bit Windows Vista machine. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="overhead.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="int_real_world.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref.html new file mode 100644 index 0000000000..0c1bc8b179 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref.html @@ -0,0 +1,57 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Reference</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="prev" href="tut/input_output.html" title="Input Output"> +<link rel="next" href="ref/number.html" title="number"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tut/input_output.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ref/number.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="boost_multiprecision.ref"></a><a class="link" href="ref.html" title="Reference">Reference</a> +</h2></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="ref/number.html">number</a></span></dt> +<dt><span class="section"><a href="ref/cpp_int_ref.html">cpp_int</a></span></dt> +<dt><span class="section"><a href="ref/gmp_int_ref.html">gmp_int</a></span></dt> +<dt><span class="section"><a href="ref/tom_int_ref.html">tom_int</a></span></dt> +<dt><span class="section"><a href="ref/mpf_ref.html">gmp_float</a></span></dt> +<dt><span class="section"><a href="ref/mpfr_ref.html">mpfr_float_backend</a></span></dt> +<dt><span class="section"><a href="ref/cpp_bin_float_ref.html">cpp_bin_float</a></span></dt> +<dt><span class="section"><a href="ref/cpp_dec_ref.html">cpp_dec_float</a></span></dt> +<dt><span class="section"><a href="ref/internals.html">Internal Support + Code</a></span></dt> +<dt><span class="section"><a href="ref/backendconc.html">Backend Requirements</a></span></dt> +<dt><span class="section"><a href="ref/headers.html">Header File Structure</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tut/input_output.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ref/number.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/backendconc.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/backendconc.html new file mode 100644 index 0000000000..ff86a64dde --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/backendconc.html @@ -0,0 +1,3970 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Backend Requirements</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="internals.html" title="Internal Support Code"> +<link rel="next" href="headers.html" title="Header File Structure"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="internals.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="headers.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.backendconc"></a><a class="link" href="backendconc.html" title="Backend Requirements">Backend Requirements</a> +</h3></div></div></div> +<p> + The requirements on the <code class="computeroutput"><span class="identifier">Backend</span></code> + template argument to <code class="computeroutput"><span class="identifier">number</span></code> + are split up into sections: compulsory and optional. + </p> +<p> + Compulsory requirements have no default implementation in the library, therefore + if the feature they implement is to be supported at all, then they must be + implemented by the backend. + </p> +<p> + Optional requirements have default implementations that are called if the + backend doesn't provide it's own. Typically the backend will implement these + to improve performance. + </p> +<p> + In the following tables, type B is the <code class="computeroutput"><span class="identifier">Backend</span></code> + template argument to <code class="computeroutput"><span class="identifier">number</span></code>, + <code class="computeroutput"><span class="identifier">b</span></code> and <code class="computeroutput"><span class="identifier">b2</span></code> + are a variables of type B, <code class="computeroutput"><span class="identifier">cb</span></code>, + <code class="computeroutput"><span class="identifier">cb2</span></code> and <code class="computeroutput"><span class="identifier">cb3</span></code> + are constant variables of type <code class="computeroutput"><span class="keyword">const</span> + <span class="identifier">B</span></code>, <code class="computeroutput"><span class="identifier">rb</span></code> + is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">&&</span></code>, + <code class="computeroutput"><span class="identifier">a</span></code> and <code class="computeroutput"><span class="identifier">a2</span></code> + are variables of Arithmetic type, <code class="computeroutput"><span class="identifier">s</span></code> + is a variable of type <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code>, <code class="computeroutput"><span class="identifier">ui</span></code> is a variable of type <code class="computeroutput"><span class="keyword">unsigned</span></code>, <code class="computeroutput"><span class="identifier">bb</span></code> + is a variable of type <code class="computeroutput"><span class="keyword">bool</span></code>, + <code class="computeroutput"><span class="identifier">pa</span></code> is a variable of type + pointer-to-arithmetic-type, <code class="computeroutput"><span class="identifier">exp</span></code> + is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exp_type</span></code>, <code class="computeroutput"><span class="identifier">pexp</span></code> + is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exp_type</span><span class="special">*</span></code>, + <code class="computeroutput"><span class="identifier">i</span></code> is a variable of type + <code class="computeroutput"><span class="keyword">int</span></code>, <code class="computeroutput"><span class="identifier">pi</span></code> + pointer to a variable of type <code class="computeroutput"><span class="keyword">int</span></code>, + B2 is another type that meets these requirements, b2 is a variable of type + B2, <code class="computeroutput"><span class="identifier">ss</span></code> is variable of type + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">streamsize</span></code> and <code class="computeroutput"><span class="identifier">ff</span></code> + is a variable of type <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">fmtflags</span></code>. + </p> +<div class="table"> +<a name="boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b"></a><p class="title"><b>Table 1.8. Compulsory Requirements on the Backend type.</b></p> +<div class="table-contents"><table class="table" summary="Compulsory Requirements on the Backend type."> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Expression + </p> + </th> +<th> + <p> + Return Type + </p> + </th> +<th> + <p> + Comments + </p> + </th> +<th> + <p> + Throws + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special"><</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + A list of signed integral types that can be assigned to type B. + The types shall be listed in order of size, smallest first, and + shall terminate in the type that is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">intmax_t</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special"><</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + A list of unsigned integral types that can be assigned to type + B. The types shall be listed in order of size, smallest first, + and shall terminate in the type that is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">uintmax_t</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special"><</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + A list of floating-point types that can be assigned to type B.The + types shall be listed in order of size, smallest first, and shall + terminate in type <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code> + </p> + </td> +<td> + <p> + A signed integral type. + </p> + </td> +<td> + <p> + The type of the exponent of type B. This type is required only + for floating point types. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">()</span></code> + </p> + </td> +<td> + </td> +<td> + <p> + Default constructor. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + </td> +<td> + <p> + Copy Constructor. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span> + <span class="identifier">b</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">&</span></code> + </p> + </td> +<td> + <p> + Assignment operator. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span> + <span class="identifier">a</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">&</span></code> + </p> + </td> +<td> + <p> + Assignment from an Arithmetic type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span> + <span class="identifier">s</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">&</span></code> + </p> + </td> +<td> + <p> + Assignment from a string. + </p> + </td> +<td> + <p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> if the string could + not be interpreted as a valid number. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">swap</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Swaps the contents of its arguments. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">str</span><span class="special">(</span><span class="identifier">ss</span><span class="special">,</span> + <span class="identifier">ff</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code> + </p> + </td> +<td> + <p> + Returns the string representation of <code class="computeroutput"><span class="identifier">b</span></code> + with <code class="computeroutput"><span class="identifier">ss</span></code> digits + and formatted according to the flags set in <code class="computeroutput"><span class="identifier">ff</span></code>. + If <code class="computeroutput"><span class="identifier">ss</span></code> is zero, + then returns as many digits as are required to reconstruct the + original value. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Negates <code class="computeroutput"><span class="identifier">b</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">int</span></code> + </p> + </td> +<td> + <p> + Compares <code class="computeroutput"><span class="identifier">cb</span></code> and + <code class="computeroutput"><span class="identifier">cb2</span></code>, returns a + value less than zero if <code class="computeroutput"><span class="identifier">cb</span> + <span class="special"><</span> <span class="identifier">cb2</span></code>, + a value greater than zero if <code class="computeroutput"><span class="identifier">cb</span> + <span class="special">></span> <span class="identifier">cb2</span></code> + and zero if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">==</span> <span class="identifier">cb2</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">int</span></code> + </p> + </td> +<td> + <p> + Compares <code class="computeroutput"><span class="identifier">cb</span></code> and + <code class="computeroutput"><span class="identifier">a</span></code>, returns a value + less than zero if <code class="computeroutput"><span class="identifier">cb</span> + <span class="special"><</span> <span class="identifier">a</span></code>, + a value greater than zero if <code class="computeroutput"><span class="identifier">cb</span> + <span class="special">></span> <span class="identifier">a</span></code> + and zero if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">==</span> <span class="identifier">a</span></code>. + The type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Adds <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">b</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Subtracts <code class="computeroutput"><span class="identifier">cb</span></code> from + <code class="computeroutput"><span class="identifier">b</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">b</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Divides <code class="computeroutput"><span class="identifier">b</span></code> by <code class="computeroutput"><span class="identifier">cb</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the + value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span> <span class="special">>::</span><span class="identifier">has_infinity</span> <span class="special">==</span> + <span class="keyword">false</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">%=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the + value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">|=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">^=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_complement</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes the ones-complement of <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>, + only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an integer type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special"><<=</span> + <span class="identifier">ui</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">>>=</span> + <span class="identifier">ui</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_convert_to</span><span class="special">(</span><span class="identifier">pa</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Converts <code class="computeroutput"><span class="identifier">cb</span></code> to + the type of <code class="computeroutput"><span class="special">*</span><span class="identifier">pa</span></code> + and store the result in <code class="computeroutput"><span class="special">*</span><span class="identifier">pa</span></code>. Type <code class="computeroutput"><span class="identifier">B</span></code> + shall support conversion to at least types <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">intmax_t</span></code>, + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">uintmax_t</span></code> and <code class="computeroutput"><span class="keyword">long</span> + <span class="keyword">long</span></code>. Conversion to other + arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_frexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">pexp</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores values in <code class="computeroutput"><span class="identifier">b</span></code> + and <code class="computeroutput"><span class="special">*</span><span class="identifier">pexp</span></code> + such that the value of <code class="computeroutput"><span class="identifier">cb</span></code> + is b * 2<sup>*pexp</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code> + is a floating-point type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_ldexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">exp</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores a value in <code class="computeroutput"><span class="identifier">b</span></code> + that is cb * 2<sup>exp</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code> + is a floating-point type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_frexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">pi</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores values in <code class="computeroutput"><span class="identifier">b</span></code> + and <code class="computeroutput"><span class="special">*</span><span class="identifier">pi</span></code> + such that the value of <code class="computeroutput"><span class="identifier">cb</span></code> + is b * 2<sup>*pi</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code> + is a floating-point type. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> if the exponent + of cb is too large to be stored in an <code class="computeroutput"><span class="keyword">int</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_ldexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">i</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores a value in <code class="computeroutput"><span class="identifier">b</span></code> + that is cb * 2<sup>i</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code> + is a floating-point type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_floor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores the floor of <code class="computeroutput"><span class="identifier">cb</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_ceil</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores the ceiling of <code class="computeroutput"><span class="identifier">cb</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_sqrt</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Stores the square root of <code class="computeroutput"><span class="identifier">cb</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point + type. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">B</span><span class="special">>::</span><span class="identifier">type</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">N</span></code> is one of the + values <code class="computeroutput"><span class="identifier">number_kind_integer</span></code>, + <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>, + <code class="computeroutput"><span class="identifier">number_kind_rational</span></code> + or <code class="computeroutput"><span class="identifier">number_kind_fixed_point</span></code>. + Defaults to <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac"></a><p class="title"><b>Table 1.9. Optional Requirements on the Backend Type</b></p> +<div class="table-contents"><table class="table" summary="Optional Requirements on the Backend Type"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Expression + </p> + </th> +<th> + <p> + Returns + </p> + </th> +<th> + <p> + Comments + </p> + </th> +<th> + <p> + Throws + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <span class="emphasis"><em>Construct and assign:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">rb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span></code> + </p> + </td> +<td> + <p> + Move constructor. Afterwards variable <code class="computeroutput"><span class="identifier">rb</span></code> + shall be in sane state, albeit with unspecified value. Only destruction + and assignment to the moved-from variable <code class="computeroutput"><span class="identifier">rb</span></code> + need be supported after the operation. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span> + <span class="identifier">rb</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">&</span></code> + </p> + </td> +<td> + <p> + Move-assign. Afterwards variable <code class="computeroutput"><span class="identifier">rb</span></code> + shall be in sane state, albeit with unspecified value. Only destruction + and assignment to the moved-from variable <code class="computeroutput"><span class="identifier">rb</span></code> + need be supported after the operation. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span></code> + </p> + </td> +<td> + <p> + Direct construction from an arithmetic type. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + this operation is simulated using default-construction followed + by assignment. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">b2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span></code> + </p> + </td> +<td> + <p> + Copy constructor from a different back-end type. When not provided, + a generic interconversion routine is used. This constructor may + be <code class="computeroutput"><span class="keyword">explicit</span></code> if the + corresponding frontend constructor should also be <code class="computeroutput"><span class="keyword">explicit</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span> + <span class="identifier">b2</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">b</span><span class="special">&</span></code> + </p> + </td> +<td> + <p> + Assignment operator from a different back-end type. When not provided, + a generic interconversion routine is used. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">assign_components</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Assigns to <code class="computeroutput"><span class="identifier">b</span></code> the + two components in the following arguments. Only applies to rational + and complex number types. When not provided, arithmetic operations + are used to synthesise the result from the two values. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">assign_components</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Assigns to <code class="computeroutput"><span class="identifier">b</span></code> the + two components in the following arguments. Only applies to rational + and complex number types. When not provided, arithmetic operations + are used to synthesise the result from the two values. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <span class="emphasis"><em>Comparisons:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">cb2</span></code> + are equal in value. When not provided, the default implementation + returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span> + <span class="special">==</span> <span class="number">0</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code> + are equal in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + return the equivalent of <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code> + are equal in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version returns <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is less than <code class="computeroutput"><span class="identifier">cb2</span></code> in value. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span> <span class="special"><</span> + <span class="number">0</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is less than <code class="computeroutput"><span class="identifier">a</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> is less than <code class="computeroutput"><span class="identifier">cb</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is greater than <code class="computeroutput"><span class="identifier">cb2</span></code> in value. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span> <span class="special">></span> + <span class="number">0</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">noexcept</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is greater than <code class="computeroutput"><span class="identifier">a</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> is greater than <code class="computeroutput"><span class="identifier">cb</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default implementation returns <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_is_zero</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is zero, otherwise <code class="computeroutput"><span class="keyword">false</span></code>. The default version of this + function returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">ui_type</span><span class="special">(</span><span class="number">0</span><span class="special">))</span> <span class="special">==</span> + <span class="number">0</span></code>, where <code class="computeroutput"><span class="identifier">ui_type</span></code> + is <code class="computeroutput"><span class="identifier">ui_type</span></code> is + <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special"><</span><span class="keyword">typename</span> + <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">>::</span><span class="identifier">type</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">int</span></code> + </p> + </td> +<td> + <p> + Returns a value < zero if <code class="computeroutput"><span class="identifier">cb</span></code> + is negative, a value > zero if <code class="computeroutput"><span class="identifier">cb</span></code> + is positive, and zero if <code class="computeroutput"><span class="identifier">cb</span></code> + is zero. The default version of this function returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">ui_type</span><span class="special">(</span><span class="number">0</span><span class="special">))</span></code>, + where <code class="computeroutput"><span class="identifier">ui_type</span></code> is + <code class="computeroutput"><span class="identifier">ui_type</span></code> is <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special"><</span><span class="keyword">typename</span> + <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">>::</span><span class="identifier">type</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <span class="emphasis"><em>Basic arithmetic:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Adds <code class="computeroutput"><span class="identifier">a</span></code> to <code class="computeroutput"><span class="identifier">b</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Add <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">cb2</span></code> and stores the result in + <code class="computeroutput"><span class="identifier">b</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Add <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">a</span></code> and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Add <code class="computeroutput"><span class="identifier">a</span></code> to <code class="computeroutput"><span class="identifier">cb</span></code> and stores the result in + <code class="computeroutput"><span class="identifier">b</span></code>. The type of + <code class="computeroutput"><span class="identifier">a</span></code> shall be listed + in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Subtracts <code class="computeroutput"><span class="identifier">a</span></code> from + <code class="computeroutput"><span class="identifier">b</span></code>. The type of + <code class="computeroutput"><span class="identifier">a</span></code> shall be listed + in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Subtracts <code class="computeroutput"><span class="identifier">cb2</span></code> from + <code class="computeroutput"><span class="identifier">cb</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. When + not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Subtracts <code class="computeroutput"><span class="identifier">a</span></code> from + <code class="computeroutput"><span class="identifier">cb</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Subtracts <code class="computeroutput"><span class="identifier">cb</span></code> from + <code class="computeroutput"><span class="identifier">a</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">();</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">b</span></code> by + <code class="computeroutput"><span class="identifier">a</span></code>. The type of + <code class="computeroutput"><span class="identifier">a</span></code> shall be listed + in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and stores + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">a</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and adds the + result to <code class="computeroutput"><span class="identifier">b</span></code>. When + not provided does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span> <span class="identifier">t</span></code> + and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code> and adds the + result to <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided + does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span> + <span class="identifier">t</span></code> and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code> and adds the + result to <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided + does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and subtracts + the result from <code class="computeroutput"><span class="identifier">b</span></code>. + When not provided does the equivalent of creating a temporary + <code class="computeroutput"><span class="identifier">B</span> <span class="identifier">t</span></code> + and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code> and subtracts + the result from <code class="computeroutput"><span class="identifier">b</span></code>. + The type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided + does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span> + <span class="identifier">t</span></code> and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by + <code class="computeroutput"><span class="identifier">cb</span></code> and subtracts + the result from <code class="computeroutput"><span class="identifier">b</span></code>. + The type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided + does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and adds the + result to <code class="computeroutput"><span class="identifier">cb3</span></code> storing + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + When not provided does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>. For brevity, only a version showing + all arguments of type <code class="computeroutput"><span class="identifier">B</span></code> + is shown here, but you can replace up to any 2 of <code class="computeroutput"><span class="identifier">cb</span></code>, <code class="computeroutput"><span class="identifier">cb2</span></code> + and <code class="computeroutput"><span class="identifier">cb3</span></code> with any + type listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and subtracts + from the result <code class="computeroutput"><span class="identifier">cb3</span></code> + storing the result in <code class="computeroutput"><span class="identifier">b</span></code>. + When not provided does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>. For brevity, only a version showing + all arguments of type <code class="computeroutput"><span class="identifier">B</span></code> + is shown here, but you can replace up to any 2 of <code class="computeroutput"><span class="identifier">cb</span></code>, <code class="computeroutput"><span class="identifier">cb2</span></code> + and <code class="computeroutput"><span class="identifier">cb3</span></code> with any + type listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Divides <code class="computeroutput"><span class="identifier">b</span></code> by <code class="computeroutput"><span class="identifier">a</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the + type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> + or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span> + <span class="special">>::</span><span class="identifier">has_infinity</span> + <span class="special">==</span> <span class="keyword">false</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Divides <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">cb2</span></code> and stores + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">cb2</span></code> has the value zero, and + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span> + <span class="special">>::</span><span class="identifier">has_infinity</span> + <span class="special">==</span> <span class="keyword">false</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Divides <code class="computeroutput"><span class="identifier">cb</span></code> by + <code class="computeroutput"><span class="identifier">a</span></code> and stores the + result in <code class="computeroutput"><span class="identifier">b</span></code>. The + type of <code class="computeroutput"><span class="identifier">a</span></code> shall + be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span> + <span class="special">>::</span><span class="identifier">has_infinity</span> + <span class="special">==</span> <span class="keyword">false</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Divides <code class="computeroutput"><span class="identifier">a</span></code> by <code class="computeroutput"><span class="identifier">cb</span></code> and stores the result in + <code class="computeroutput"><span class="identifier">b</span></code>. The type of + <code class="computeroutput"><span class="identifier">a</span></code> shall be listed + in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">cb</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the + value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span> <span class="special">>::</span><span class="identifier">has_infinity</span> <span class="special">==</span> + <span class="keyword">false</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_increment</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + void + </p> + </td> +<td> + <p> + Increments the value of <code class="computeroutput"><span class="identifier">b</span></code> + by one. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">ui_type</span><span class="special">>(</span><span class="number">1u</span><span class="special">))</span></code>. + Where <code class="computeroutput"><span class="identifier">ui_type</span></code> is + <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special"><</span><span class="keyword">typename</span> + <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">>::</span><span class="identifier">type</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_decrement</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + void + </p> + </td> +<td> + <p> + Decrements the value of <code class="computeroutput"><span class="identifier">b</span></code> + by one. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">ui_type</span><span class="special">>(</span><span class="number">1u</span><span class="special">))</span></code>. + Where <code class="computeroutput"><span class="identifier">ui_type</span></code> is + <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special"><</span><span class="keyword">typename</span> + <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">>::</span><span class="identifier">type</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <span class="emphasis"><em>Integer specific operations:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">%=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span> + <span class="identifier">cb2</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">cb</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&</span> + <span class="identifier">cb2</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">|=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span> + <span class="identifier">cb2</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">^=</span> + <span class="identifier">cb</span></code>, only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code> + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">^</span> + <span class="identifier">cb2</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">^</span> + <span class="identifier">a</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">a</span> <span class="special">^</span> + <span class="identifier">cb</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided, + does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special"><<</span> + <span class="identifier">ui</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">>></span> + <span class="identifier">ui</span></code> and stores the result + in <code class="computeroutput"><span class="identifier">b</span></code>, only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span> + <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_qr</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">,</span> + <span class="identifier">b</span><span class="special">,</span> + <span class="identifier">b2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result + of <code class="computeroutput"><span class="identifier">cb</span> <span class="special">/</span> + <span class="identifier">cb2</span></code> and <code class="computeroutput"><span class="identifier">b2</span></code> to the result of <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span> + <span class="identifier">cb2</span></code>. Only required when + <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_integer_modulus</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">unsigned</span></code> + </p> + </td> +<td> + <p> + Returns the result of <code class="computeroutput"><span class="identifier">cb</span> + <span class="special">%</span> <span class="identifier">ui</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an integer type. The default version of this function is synthesised + from other operations above. + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lsb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">unsigned</span></code> + </p> + </td> +<td> + <p> + Returns the index of the least significant bit that is set. Only + required when <code class="computeroutput"><span class="identifier">B</span></code> + is an integer type. The default version of this function is synthesised + from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_msb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">unsigned</span></code> + </p> + </td> +<td> + <p> + Returns the index of the most significant bit that is set. Only + required when <code class="computeroutput"><span class="identifier">B</span></code> + is an integer type. The default version of this function is synthesised + from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bit_test</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span></code> + </p> + </td> +<td> + <p> + Returns true if <code class="computeroutput"><span class="identifier">cb</span></code> + has bit <code class="computeroutput"><span class="identifier">ui</span></code> set. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an integer type. The default version of this function is synthesised + from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bit_set</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets the bit at index <code class="computeroutput"><span class="identifier">ui</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bit_unset</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Unsets the bit at index <code class="computeroutput"><span class="identifier">ui</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_bit_flip</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">ui</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Flips the bit at index <code class="computeroutput"><span class="identifier">ui</span></code> + in <code class="computeroutput"><span class="identifier">b</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest + common divisor of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least + common multiple of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The default version of this function is synthesised from + other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest + common divisor of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version + of this function calls <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least + common multiple of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version + of this function calls <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest + common divisor of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">a</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version + of this function calls <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least + common multiple of <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">a</span></code>. Only required + when <code class="computeroutput"><span class="identifier">B</span></code> is an integer + type. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version + of this function calls <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">,</span> + <span class="identifier">cb3</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result + of <span class="emphasis"><em>(cb^cb2)%cb3</em></span>. The default version of this + function is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result + of <span class="emphasis"><em>(cb^cb2)%a</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version + of this function is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result + of <span class="emphasis"><em>(cb^a)%cb2</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version + of this function is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">a</span><span class="special">,</span> + <span class="identifier">a2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result + of <span class="emphasis"><em>(cb^a)%a2</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code> + shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version + of this function is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_integer_sqrt</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the largest + integer which when squared is less than <code class="computeroutput"><span class="identifier">cb</span></code>, + also sets <code class="computeroutput"><span class="identifier">b2</span></code> to + the remainder, ie to <span class="emphasis"><em>cb - b<sup>2</sup></em></span>. The default + version of this function is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <span class="emphasis"><em>Sign manipulation:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_abs</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Set <code class="computeroutput"><span class="identifier">b</span></code> to the absolute + value of <code class="computeroutput"><span class="identifier">cb</span></code>. The + default version of this functions assigns <code class="computeroutput"><span class="identifier">cb</span></code> + to <code class="computeroutput"><span class="identifier">b</span></code>, and then + calls <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code> + if <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span> <span class="special"><</span> + <span class="number">0</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_fabs</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Set <code class="computeroutput"><span class="identifier">b</span></code> to the absolute + value of <code class="computeroutput"><span class="identifier">cb</span></code>. The + default version of this functions assigns <code class="computeroutput"><span class="identifier">cb</span></code> + to <code class="computeroutput"><span class="identifier">b</span></code>, and then + calls <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code> + if <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span> <span class="special"><</span> + <span class="number">0</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <span class="emphasis"><em>Floating point functions:</em></span> + </p> + </td> +<td class="auto-generated"> </td> +<td class="auto-generated"> </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_fpclassify</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">int</span></code> + </p> + </td> +<td> + <p> + Returns one of the same values returned by <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">fpclassify</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + will only test for zero <code class="computeroutput"><span class="identifier">cb</span></code>. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_trunc</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">trunc</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_round</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">round</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_exp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_log</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_log10</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_sin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_cos</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_tan</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_asin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_acos</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_atan</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_sinh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_cosh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_tanh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span></code> + on argument <code class="computeroutput"><span class="identifier">cb</span></code> + and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_fmod</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">fmod</span></code> + on arguments <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_pow</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code> + on arguments <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_atan2</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">cb2</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span></code> + on arguments <code class="computeroutput"><span class="identifier">cb</span></code> + and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store + the result in <code class="computeroutput"><span class="identifier">b</span></code>. + Only required when <code class="computeroutput"><span class="identifier">B</span></code> + is an floating-point type. The default version of this function + is synthesised from other operations above. + </p> + </td> +<td> + <p> +   + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_scalbn</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">,</span> + <span class="identifier">e</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Scales value <code class="computeroutput"><span class="identifier">cb</span></code> + by <span class="emphasis"><em>r<sup>e</sup></em></span>, where <span class="emphasis"><em>r</em></span> is the + radix of the type. The default version of this function is implemented + in terms of eval_ldexp, consequently this function must be provided + for types with a radix other than 2. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_ilogb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code> + </p> + </td> +<td> + <p> + Returns the exponent <span class="emphasis"><em>e</em></span> of value <code class="computeroutput"><span class="identifier">cb</span></code> such that <span class="emphasis"><em>1 <= + cb*r<sup>-e</sup> < r</em></span>, where <span class="emphasis"><em>r</em></span> is the radix + of type B. The default version of this function is implemented + in terms of eval_frexp, consequently this function must be provided + for types with a radix other than 2. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">eval_logb</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> + <span class="identifier">cb</span><span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code> + </p> + </td> +<td> + <p> + Sets <code class="computeroutput"><span class="identifier">b</span></code> to the exponent + <span class="emphasis"><em>e</em></span> of value <code class="computeroutput"><span class="identifier">cb</span></code> + such that <span class="emphasis"><em>1 <= cb*r<sup>-b</sup> < r</em></span>, where <span class="emphasis"><em>r</em></span> + is the radix of type B. The default version of this function is + implemented in terms of <code class="computeroutput"><span class="identifier">eval_ilogb</span></code>. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><p> + When the tables above place no <span class="emphasis"><em>throws</em></span> requirements on + an operation, then it is up to each type modelling this concept to decide + when or whether throwing an exception is desirable. However, thrown exceptions + should always either be the type, or inherit from the type <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>. + For example, a floating point type might choose to throw <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + whenever the result of an operation would be infinite, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code> + whenever it would round to zero. + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + The non-member functions are all named with an "eval_" prefix + to avoid conflicts with template classes of the same name - in point of + fact this naming convention shouldn't be necessary, but rather works around + some compiler bugs. + </p></td></tr> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="internals.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="headers.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html new file mode 100644 index 0000000000..315c32ec7f --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html @@ -0,0 +1,186 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>cpp_bin_float</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="mpfr_ref.html" title="mpfr_float_backend"> +<link rel="next" href="cpp_dec_ref.html" title="cpp_dec_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpfr_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_dec_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.cpp_bin_float_ref"></a><a class="link" href="cpp_bin_float_ref.html" title="cpp_bin_float">cpp_bin_float</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">enum</span> <span class="identifier">digit_base_type</span> +<span class="special">{</span> + <span class="identifier">digit_base_2</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> + <span class="identifier">digit_base_10</span> <span class="special">=</span> <span class="number">10</span> +<span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">digit_base_type</span> <span class="identifier">base</span> <span class="special">=</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Exponent</span> <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">ExponentMin</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">ExponentMax</span> <span class="special">=</span> <span class="number">0</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_bin_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_100</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">24</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">126</span><span class="special">,</span> <span class="number">127</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_single</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">1022</span><span class="special">,</span> <span class="number">1023</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">64</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double_extended</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">113</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_quad</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The class takes six template parameters: + </p> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">Digits</span></dt> +<dd><p> + The number of digits precision the type should support. This is normally + expressed as base-10 digits, but that can be changed via the second + template parameter. + </p></dd> +<dt><span class="term">base</span></dt> +<dd><p> + An enumerated value (either <code class="computeroutput"><span class="identifier">digit_base_10</span></code> + or <code class="computeroutput"><span class="identifier">digit_base_2</span></code>) that + indicates whether <code class="computeroutput"><span class="identifier">Digits</span></code> + is base-10 or base-2 + </p></dd> +<dt><span class="term">Allocator</span></dt> +<dd><p> + The allocator used: defaults to type <code class="computeroutput"><span class="keyword">void</span></code>, + meaning all storage is within the class, and no dynamic allocation + is performed, but can be set to a standard library allocator if dynamic + allocation makes more sense. + </p></dd> +<dt><span class="term">Exponent</span></dt> +<dd><p> + A signed integer type to use as the type of the exponent - defaults + to <code class="computeroutput"><span class="keyword">int</span></code>. + </p></dd> +<dt><span class="term">ExponentMin</span></dt> +<dd><p> + The smallest (most negative) permitted exponent, defaults to zero, + meaning "define as small as possible given the limitations of + the type and our internal requirements". + </p></dd> +<dt><span class="term">ExponentMax</span></dt> +<dd><p> + The largest (most positive) permitted exponent, defaults to zero, meaning + "define as large as possible given the limitations of the type + and our internal requirements". + </p></dd> +</dl> +</div> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_floating_point</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/floats/cpp_bin_float.html" title="cpp_bin_float">tutorial</a>. + </p> +<h5> +<a name="boost_multiprecision.ref.cpp_bin_float_ref.h0"></a> + <span class="phrase"><a name="boost_multiprecision.ref.cpp_bin_float_ref.implementation_notes"></a></span><a class="link" href="cpp_bin_float_ref.html#boost_multiprecision.ref.cpp_bin_float_ref.implementation_notes">Implementation + Notes</a> + </h5> +<p> + Internally, an N-bit <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + is represented as an N-bit unsigned integer along with an exponent and a + sign. The integer part is normalized so that it's most significant bit is + always 1. The decimal point is assumed to be directly after the most significant + bit of the integer part. The special values zero, infinity and NaN all have + the integer part set to zero, and the exponent to one of 3 special values + above the maximum permitted exponent. + </p> +<p> + Multiplication is trivial: multiply the two N-bit integer mantissa's to obtain + a 2N-bit number, then round and adjust the sign and exponent. + </p> +<p> + Addition and subtraction proceed similarly - if the exponents are such that + there is overlap between the two values, then left shift the larger value + to produce a number with between N and 2N bits, then perform integer addition + or subtraction, round, and adjust the exponent. + </p> +<p> + Division proceeds as follows: first scale the numerator by some power of + 2 so that integer division will produce either an N-bit or N+1 bit result + plus a remainder. If we get an N bit result then the size of twice the remainder + compared to the denominator gives us the rounding direction. Otherwise we + have one extra bit in the result which we can use to determine rounding (in + this case ties occur only if the remainder is zero and the extra bit is a + 1). + </p> +<p> + Square root uses integer square root in a manner analogous to division. + </p> +<p> + Decimal string to binary conversion proceeds as follows: first parse the + digits to produce an integer multiplied by a decimal exponent. Note that + we stop parsing digits once we have parsed as many as can possibly effect + the result - this stops the integer part growing too large when there are + a very large number of input digits provided. At this stage if the decimal + exponent is positive then the result is an integer and we can in principle + simply multiply by 10^N to get an exact integer result. In practice however, + that could produce some very large integers. We also need to be able to divide + by 10^N in the event that the exponent is negative. Therefore calculation + of the 10^N values plus the multiplication or division are performed using + limited precision integer arithmetic, plus an exponent, and a track of the + accumulated error. At the end of the calculation we will either be able to + round unambiguously, or the error will be such that we can't tell which way + to round. In the latter case we simply up the precision and try again until + we have an unambiguously rounded result. + </p> +<p> + Binary to decimal conversion proceeds very similarly to the above, our aim + is to calculate <code class="computeroutput"><span class="identifier">mantissa</span> <span class="special">*</span> <span class="number">2</span><span class="special">^</span><span class="identifier">shift</span> <span class="special">*</span> <span class="number">10</span><span class="special">^</span><span class="identifier">E</span></code> + where <code class="computeroutput"><span class="identifier">E</span></code> is the decimal exponent + and <code class="computeroutput"><span class="identifier">shift</span></code> is calculated so + that the result is an N bit integer assuming we want N digits printed in + the result. As before we use limited precision arithmetic to calculate the + result and up the precision as necessary until the result is unambiguously + correctly rounded. In addition our initial calculation of the decimal exponent + may be out by 1, so we have to correct that and loop as well in the that + case. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpfr_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_dec_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_dec_ref.html new file mode 100644 index 0000000000..f786543b92 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -0,0 +1,92 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>cpp_dec_float</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="cpp_bin_float_ref.html" title="cpp_bin_float"> +<link rel="next" href="internals.html" title="Internal Support Code"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_bin_float_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="internals.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.cpp_dec_ref"></a><a class="link" href="cpp_dec_ref.html" title="cpp_dec_float">cpp_dec_float</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExponentType</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int32_t</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_dec_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_100</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The class takes three template parameters: + </p> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">Digits10</span></dt> +<dd><p> + The number of decimal digits precision the type should support. Note + that this type does not normally perform any dynamic memory allocation, + and as a result the <code class="computeroutput"><span class="identifier">Digits10</span></code> + template argument should not be set too high or the class's size will + grow unreasonably large. + </p></dd> +<dt><span class="term">ExponentType</span></dt> +<dd><p> + A signed integer type that represents the exponent of the number + </p></dd> +<dt><span class="term">Allocator</span></dt> +<dd><p> + The allocator used: defaults to type <code class="computeroutput"><span class="keyword">void</span></code>, + meaning all storage is within the class, and no dynamic allocation + is performed, but can be set to a standard library allocator if dynamic + allocation makes more sense. + </p></dd> +</dl> +</div> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_floating_point</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/floats/cpp_dec_float.html" title="cpp_dec_float">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_bin_float_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="internals.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_int_ref.html new file mode 100644 index 0000000000..c16b92223b --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -0,0 +1,157 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>cpp_int</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="number.html" title="number"> +<link rel="next" href="gmp_int_ref.html" title="gmp_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="number.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_int_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.cpp_int_ref"></a><a class="link" href="cpp_int_ref.html" title="cpp_int">cpp_int</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">typedef</span> <span class="identifier">unspecified</span><span class="special">-</span><span class="identifier">type</span> <span class="identifier">limb_type</span><span class="special">;</span> + +<span class="keyword">enum</span> <span class="identifier">cpp_integer_type</span> <span class="special">{</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span> <span class="special">};</span> +<span class="keyword">enum</span> <span class="identifier">cpp_int_check_type</span> <span class="special">{</span> <span class="identifier">checked</span><span class="special">,</span> <span class="identifier">unchecked</span> <span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">MinDigits</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> + <span class="keyword">unsigned</span> <span class="identifier">MaxDits</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> + <span class="identifier">cpp_integer_type</span> <span class="identifier">SignType</span> <span class="special">=</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> + <span class="identifier">cpp_int_check_type</span> <span class="identifier">Checked</span> <span class="special">=</span> <span class="identifier">unchecked</span><span class="special">,</span> + <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span><span class="special"><</span><span class="identifier">limb_type</span><span class="special">></span> <span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_int_backend</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// Expression templates default to et_off if there is no allocator:</span> +<span class="comment">//</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">MinDigits</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">MaxDigits</span><span class="special">,</span> <span class="identifier">cpp_integer_type</span> <span class="identifier">SignType</span><span class="special">,</span> <span class="identifier">cpp_int_check_type</span> <span class="identifier">Checked</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">MinDigits</span><span class="special">,</span> <span class="identifier">MaxDigits</span><span class="special">,</span> <span class="identifier">SignType</span><span class="special">,</span> <span class="identifier">Checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> +<span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_off</span><span class="special">;</span> <span class="special">};</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><></span> <span class="special">></span> <span class="identifier">cpp_int</span><span class="special">;</span> <span class="comment">// arbitrary precision integer</span> +<span class="keyword">typedef</span> <span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><></span> <span class="special">></span> <span class="identifier">cpp_rational_backend</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_rational_backend</span><span class="special">></span> <span class="identifier">cpp_rational</span><span class="special">;</span> <span class="comment">// arbitrary precision rational number</span> + +<span class="comment">// Fixed precision unsigned types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint1024_t</span><span class="special">;</span> + +<span class="comment">// Fixed precision signed types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int1024_t</span><span class="special">;</span> + +<span class="comment">// Over again, but with checking enabled this time:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_cpp_int</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_cpp_rational_backend</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_rational_backend</span><span class="special">></span> <span class="identifier">checked_cpp_rational</span><span class="special">;</span> + +<span class="comment">// Checked fixed precision unsigned types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint1024_t</span><span class="special">;</span> + +<span class="comment">// Fixed precision signed types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int1024_t</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The template arguments are: + </p> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">MinBits</span></dt> +<dd><p> + Determines the number of Bits to store directly within the object before + resorting to dynamic memory allocation. When zero, this field is determined + automatically based on how many bits can be stored in union with the + dynamic storage header: setting a larger value may improve performance + as larger integer values will be stored internally before memory allocation + is required. + </p></dd> +<dt><span class="term">MaxBits</span></dt> +<dd><p> + Determines the maximum number of bits to be stored in the type: resulting + in a fixed precision type. When this value is the same as MinBits, + then the Allocator parameter is ignored, as no dynamic memory allocation + will ever be performed: in this situation the Allocator parameter should + be set to type <code class="computeroutput"><span class="keyword">void</span></code>. Note + that this parameter should not be used simply to prevent large memory + allocations, not only is that role better performed by the allocator, + but fixed precision integers have a tendency to allocate all of MaxBits + of storage more often than one would expect. + </p></dd> +<dt><span class="term">SignType</span></dt> +<dd><p> + Determines whether the resulting type is signed or not. Note that for + <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> types this parameter must be <code class="computeroutput"><span class="identifier">signed_magnitude</span></code>. + For fixed precision types then this type may be either <code class="computeroutput"><span class="identifier">signed_magnitude</span></code> or <code class="computeroutput"><span class="identifier">unsigned_magnitude</span></code>. + </p></dd> +<dt><span class="term">Checked</span></dt> +<dd><p> + This parameter has two values: <code class="computeroutput"><span class="identifier">checked</span></code> + or <code class="computeroutput"><span class="identifier">unchecked</span></code>. See the + <a class="link" href="../tut/ints/cpp_int.html" title="cpp_int">tutorial</a> + for more information. + </p></dd> +<dt><span class="term">Allocator</span></dt> +<dd><p> + The allocator to use for dynamic memory allocation, or type <code class="computeroutput"><span class="keyword">void</span></code> if MaxBits == MinBits. + </p></dd> +</dl> +</div> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_integer</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/ints/cpp_int.html" title="cpp_int">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="number.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_int_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/gmp_int_ref.html new file mode 100644 index 0000000000..adb1ecea4e --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -0,0 +1,63 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>gmp_int</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="cpp_int_ref.html" title="cpp_int"> +<link rel="next" href="tom_int_ref.html" title="tom_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tom_int_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.gmp_int_ref"></a><a class="link" href="gmp_int_ref.html" title="gmp_int">gmp_int</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">gmp_int</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span> <span class="special">></span> <span class="identifier">mpz_int</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">gmp_int</span></code> fulfils + all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_integer</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/ints/gmp_int.html" title="gmp_int">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tom_int_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/headers.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/headers.html new file mode 100644 index 0000000000..d8ff404fe3 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/headers.html @@ -0,0 +1,424 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Header File Structure</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="backendconc.html" title="Backend Requirements"> +<link rel="next" href="../perf.html" title="Performance Comparison"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="backendconc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../perf.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.headers"></a><a class="link" href="headers.html" title="Header File Structure">Header File Structure</a> +</h3></div></div></div> +<div class="table"> +<a name="boost_multiprecision.ref.headers.top_level_headers"></a><p class="title"><b>Table 1.10. Top level headers</b></p> +<div class="table-contents"><table class="table" summary="Top level headers"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Header + </p> + </th> +<th> + <p> + Contains + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int.hpp + </p> + </td> +<td> + <p> + The <code class="computeroutput"><span class="identifier">cpp_int</span></code> backend + type. + </p> + </td> +</tr> +<tr> +<td> + <p> + gmp.hpp + </p> + </td> +<td> + <p> + Defines all <a href="http://gmplib.org" target="_top">GMP</a> related + backends. + </p> + </td> +</tr> +<tr> +<td> + <p> + miller_rabin.hpp + </p> + </td> +<td> + <p> + Miller Rabin primality testing code. + </p> + </td> +</tr> +<tr> +<td> + <p> + number.hpp + </p> + </td> +<td> + <p> + Defines the <code class="computeroutput"><span class="identifier">number</span></code> + backend, is included by all the backend headers. + </p> + </td> +</tr> +<tr> +<td> + <p> + mpfr.hpp + </p> + </td> +<td> + <p> + Defines the mpfr_float_backend backend. + </p> + </td> +</tr> +<tr> +<td> + <p> + random.hpp + </p> + </td> +<td> + <p> + Defines code to interoperate with Boost.Random. + </p> + </td> +</tr> +<tr> +<td> + <p> + rational_adaptor.hpp + </p> + </td> +<td> + <p> + Defines the <code class="computeroutput"><span class="identifier">rational_adaptor</span></code> + backend. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_dec_float.hpp + </p> + </td> +<td> + <p> + Defines the <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + backend. + </p> + </td> +</tr> +<tr> +<td> + <p> + tommath.hpp + </p> + </td> +<td> + <p> + Defines the <code class="computeroutput"><span class="identifier">tommath_int</span></code> + backend. + </p> + </td> +</tr> +<tr> +<td> + <p> + concepts/number_archetypes.hpp + </p> + </td> +<td> + <p> + Defines a backend concept archetypes for testing use. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.ref.headers.implementation_headers"></a><p class="title"><b>Table 1.11. Implementation Headers</b></p> +<div class="table-contents"><table class="table" summary="Implementation Headers"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Header + </p> + </th> +<th> + <p> + Contains + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + cpp_int/add.hpp + </p> + </td> +<td> + <p> + Add and subtract operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/bitwise.hpp + </p> + </td> +<td> + <p> + Bitwise operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/checked.hpp + </p> + </td> +<td> + <p> + Helper functions for checked arithmetic for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/comparison.hpp + </p> + </td> +<td> + <p> + Comparison operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/cpp_int_config.hpp + </p> + </td> +<td> + <p> + Basic setup and configuration for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/divide.hpp + </p> + </td> +<td> + <p> + Division and modulus operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/limits.hpp + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/misc.hpp + </p> + </td> +<td> + <p> + Miscellaneous operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int/multiply.hpp + </p> + </td> +<td> + <p> + Multiply operators for <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/big_lanczos.hpp + </p> + </td> +<td> + <p> + Lanczos support for Boost.Math integration. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/default_ops.hpp + </p> + </td> +<td> + <p> + Default versions of the optional backend non-member functions. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/generic_interconvert.hpp + </p> + </td> +<td> + <p> + Generic interconversion routines. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/number_base.hpp + </p> + </td> +<td> + <p> + All the expression template code, metaprogramming, and operator + overloads for <code class="computeroutput"><span class="identifier">number</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/no_et_ops.hpp + </p> + </td> +<td> + <p> + The non-expression template operators. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/functions/constants.hpp + </p> + </td> +<td> + <p> + Defines constants used by the floating point functions. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/functions/pow.hpp + </p> + </td> +<td> + <p> + Defines default versions of the power and exponential related floating + point functions. + </p> + </td> +</tr> +<tr> +<td> + <p> + detail/functions/trig.hpp + </p> + </td> +<td> + <p> + Defines default versions of the trigonometric related floating + point functions. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="backendconc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../perf.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/internals.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/internals.html new file mode 100644 index 0000000000..02a514eade --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/internals.html @@ -0,0 +1,114 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Internal Support Code</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="cpp_dec_ref.html" title="cpp_dec_float"> +<link rel="next" href="backendconc.html" title="Backend Requirements"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_dec_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="backendconc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.internals"></a><a class="link" href="internals.html" title="Internal Support Code">Internal Support + Code</a> +</h3></div></div></div> +<p> + There are some traits classes which authors of new backends should be aware + of: + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span> + +<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">From</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">To</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_explicitly_convertible</span><span class="special">;</span> + +<span class="special">}}}</span> +</pre> +<p> + Inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">integral_constant</span><span class="special"><</span><span class="keyword">bool</span><span class="special">,</span><span class="keyword">true</span><span class="special">></span></code> if type <code class="computeroutput"><span class="identifier">From</span></code> + has an explicit conversion from <code class="computeroutput"><span class="identifier">To</span></code>. + </p> +<p> + For compilers that support C++11 SFINAE-expressions this trait should "just + work". Otherwise it inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_convertible</span><span class="special"><</span><span class="identifier">From</span><span class="special">,</span> <span class="identifier">To</span><span class="special">>::</span><span class="identifier">type</span></code>, and will need to be specialised for + Backends that have constructors marked as <code class="computeroutput"><span class="keyword">explicit</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">From</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">To</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_lossy_conversion</span> +<span class="special">{</span> + <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">see</span> <span class="identifier">below</span><span class="special">;</span> +<span class="special">};</span> +</pre> +<p> + Member <code class="computeroutput"><span class="identifier">value</span></code> is true if the + conversion from <code class="computeroutput"><span class="identifier">From</span></code> to + <code class="computeroutput"><span class="identifier">To</span></code> would result in a loss + of precision, and <code class="computeroutput"><span class="keyword">false</span></code> otherwise. + </p> +<p> + The default version of this trait simply checks whether the <span class="emphasis"><em>kind</em></span> + of conversion (for example from a floating point to an integer type) is inherently + lossy. Note that if either of the types <code class="computeroutput"><span class="identifier">From</span></code> + or <code class="computeroutput"><span class="identifier">To</span></code> are of an unknown number + category (because <code class="computeroutput"><span class="identifier">number_category</span></code> + is not specialised for that type) then this trait will be <code class="computeroutput"><span class="keyword">true</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">From</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">To</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_restricted_conversion</span> +<span class="special">{</span> + <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">see</span> <span class="identifier">below</span><span class="special">;</span> +<span class="special">};</span> +</pre> +<p> + Member <code class="computeroutput"><span class="identifier">value</span></code> is <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">From</span></code> + is only explicitly convertible to <code class="computeroutput"><span class="identifier">To</span></code> + and not implicitly convertible, or if <code class="computeroutput"><span class="identifier">is_lossy_conversion</span><span class="special"><</span><span class="identifier">From</span><span class="special">,</span> <span class="identifier">To</span><span class="special">>::</span><span class="identifier">value</span></code> is <code class="computeroutput"><span class="keyword">true</span></code>. + Otherwise <code class="computeroutput"><span class="keyword">false</span></code>. + </p> +<p> + Note that while this trait is the ultimate arbiter of which constructors + are marked as <code class="computeroutput"><span class="keyword">explicit</span></code> in class + <code class="computeroutput"><span class="identifier">number</span></code>, authors of backend + types should generally specialise one of the traits above, rather than this + one directly. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="identifier">is_signed_number</span><span class="special">;</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="identifier">is_unsigned_number</span><span class="special">;</span> +</pre> +<p> + These two traits inherit from either <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> + or <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>, by default types are assumed to + be signed unless <code class="computeroutput"><span class="identifier">is_unsigned_number</span></code> + is specialized for that type. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_dec_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="backendconc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/mpf_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/mpf_ref.html new file mode 100644 index 0000000000..cdfa14f097 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -0,0 +1,79 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>gmp_float</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="tom_int_ref.html" title="tom_int"> +<link rel="next" href="mpfr_ref.html" title="mpfr_float_backend"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tom_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mpfr_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.mpf_ref"></a><a class="link" href="mpf_ref.html" title="gmp_float">gmp_float</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">gmp_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_100</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_500</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_1000</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">gmp_float</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The class takes a single template parameter - <code class="computeroutput"><span class="identifier">Digits10</span></code> + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + <code class="computeroutput"><span class="identifier">number</span><span class="special">::</span><span class="identifier">default_precision</span></code> and <code class="computeroutput"><span class="identifier">number</span><span class="special">::</span><span class="identifier">precision</span></code>. + Note that this type does not in any way change the GMP library's global state + (for example it does not change the default precision of the mpf_t data type), + therefore you can safely mix this type with existing code that uses GMP, + and also mix <code class="computeroutput"><span class="identifier">gmp_float</span></code>s of + differing precision. + </p> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_floating_point</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/floats/gmp_float.html" title="gmp_float">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tom_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mpfr_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/mpfr_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/mpfr_ref.html new file mode 100644 index 0000000000..72ace3a62b --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -0,0 +1,79 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>mpfr_float_backend</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="mpf_ref.html" title="gmp_float"> +<link rel="next" href="cpp_bin_float_ref.html" title="cpp_bin_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpf_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_bin_float_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.mpfr_ref"></a><a class="link" href="mpfr_ref.html" title="mpfr_float_backend">mpfr_float_backend</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">mpfr_float_backend</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_100</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_500</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_1000</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The class takes a single template parameter - <code class="computeroutput"><span class="identifier">Digits10</span></code> + - which is the number of decimal digits precision the type should support. + When this parameter is zero, then the precision can be set at runtime via + <code class="computeroutput"><span class="identifier">number</span><span class="special">::</span><span class="identifier">default_precision</span></code> and <code class="computeroutput"><span class="identifier">number</span><span class="special">::</span><span class="identifier">precision</span></code>. + Note that this type does not in any way change the GMP or MPFR library's + global state (for example it does not change the default precision of the + mpfr_t data type), therefore you can safely mix this type with existing code + that uses GMP or MPFR, and also mix <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>s + of differing precision. + </p> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_floating_point</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpf_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_bin_float_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/number.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/number.html new file mode 100644 index 0000000000..b272c7d984 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/number.html @@ -0,0 +1,1330 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>number</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="../ref.html" title="Reference"> +<link rel="next" href="cpp_int_ref.html" title="cpp_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td 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href="number.html#boost_multiprecision.ref.number.synopsis">Synopsis</a> + </h5> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">enum</span> <span class="identifier">expression_template_option</span> <span class="special">{</span> <span class="identifier">et_on</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">et_off</span> <span class="special">=</span> <span class="number">0</span> <span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">expression_template_default</span> +<span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_on</span><span class="special">;</span> <span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span> <span class="special">=</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>::</span><span class="identifier">value</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">number</span> +<span class="special">{</span> + <span class="identifier">number</span><span class="special">();</span> + <span class="identifier">number</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">=(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="identifier">assign</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> + + <span class="comment">// Member operators</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">++();</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">--();</span> + <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">++(</span><span class="keyword">int</span><span class="special">);</span> + <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">--(</span><span class="keyword">int</span><span class="special">);</span> + + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">%=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">&=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">|=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">^=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> + <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">>>=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> + + <span class="comment">// Use in Boolean context:</span> + <span class="keyword">operator</span> <span class="emphasis"><em>convertible-to-bool-type</em></span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="comment">// swap:</span> + <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special">&</span> <span class="identifier">other</span><span class="special">);</span> + <span class="comment">// Sign:</span> + <span class="keyword">bool</span> <span class="identifier">is_zero</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="keyword">int</span> <span class="identifier">sign</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="comment">// string conversion:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">str</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="comment">// Generic conversion mechanism</span> + <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> + <span class="identifier">T</span> <span class="identifier">convert_to</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> + <span class="keyword">explicit</span> <span class="keyword">operator</span> <span class="identifier">T</span> <span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="comment">// precision control:</span> + <span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="identifier">default_precision</span><span class="special">();</span> + <span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">default_precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> + <span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + <span class="keyword">void</span> <span class="identifier">precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> + <span class="comment">// Comparison:</span> + <span class="keyword">int</span> <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> + <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> + <span class="keyword">typename</span> <span class="identifier">enable_if</span><span class="special"><</span><span class="identifier">is_convertible</span><span class="special"><</span><span class="identifier">V</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">int</span><span class="special">>::</span><span class="identifier">type</span> + <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> + <span class="comment">// Access to the underlying implementation:</span> + <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">();</span> + <span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +<span class="special">};</span> + +<span class="comment">// Non member operators:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="comment">// Integer only operations:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">%(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">&(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">|(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">^(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special"><<(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">>>(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +<span class="comment">// Comparison operators:</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">></span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">>=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> + +<span class="comment">// Swap:</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="comment">// iostream support:</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>unmentionable-expression-template-type</em></span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> + +<span class="comment">// Arithmetic with a higher precision result:</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="comment">// Non-member function standard library support:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">abs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fabs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">floor</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ceil</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">trunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">itrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ltrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">round</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">iround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">exp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log10</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">acos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">asin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cosh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sinh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tanh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> + +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ldexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">frexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">*);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmod</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan2</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">logb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>integer-type</em></span> <span class="identifier">ilogb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> + +<span class="comment">// Traits support:</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">component_type</span><span class="special">;</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">number_category</span><span class="special">;</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_number</span><span class="special">;</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_number_expression</span><span class="special">;</span> + +<span class="comment">// Integer specific functions:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">gcd</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lcm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">unsigned</span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">m</span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">>&);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> + <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">val</span><span class="special">);</span> +<span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +<span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> + +<span class="comment">// Rational number support:</span> +<span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">numerator</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> + +<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> + +<span class="comment">// Boost.Math interoperability functions:</span> +<span class="keyword">int</span> <span class="identifier">fpclassify</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isfinite</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isnan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isinf</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isnormal</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> + +<span class="comment">// numeric_limits support:</span> +<span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">></span> +<span class="special">{</span> + <span class="comment">/* Usual members here */</span> +<span class="special">};</span> + +<span class="special">}</span> +</pre> +<h5> +<a name="boost_multiprecision.ref.number.h1"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.description"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.description">Description</a> + </h5> +<pre class="programlisting"><span class="keyword">enum</span> <span class="identifier">expression_template_option</span> <span class="special">{</span> <span class="identifier">et_on</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">et_off</span> <span class="special">=</span> <span class="number">0</span> <span class="special">};</span> +</pre> +<p> + This enumerated type is used to specify whether expression templates are + turned on (et_on) or turned off (et_off). + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">expression_template_default</span> +<span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_on</span><span class="special">;</span> <span class="special">};</span> +</pre> +<p> + This traits class specifies the default expression template option to be + used with a particular Backend type. It defaults to <code class="computeroutput"><span class="identifier">et_on</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span> <span class="special">=</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>::</span><span class="identifier">value</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">number</span><span class="special">;</span> +</pre> +<p> + Class <code class="computeroutput"><span class="identifier">number</span></code> has two template + arguments: + </p> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">Backend</span></dt> +<dd><p> + The actual arithmetic back-end that does all the work. + </p></dd> +<dt><span class="term">ExpressionTemplates</span></dt> +<dd><p> + A Boolean value: when <code class="computeroutput"><span class="identifier">et_on</span></code>, + then expression templates are enabled, otherwise when set to <code class="computeroutput"><span class="identifier">et_off</span></code> they are disabled. The default + for this parameter is computed via the traits class <code class="computeroutput"><span class="identifier">expression_template_default</span></code> + whose member <code class="computeroutput"><span class="identifier">value</span></code> + defaults to <code class="computeroutput"><span class="identifier">et_on</span></code> unless + the traits class is specialized for a particular backend. + </p></dd> +</dl> +</div> +<pre class="programlisting"><span class="identifier">number</span><span class="special">();</span> +<span class="identifier">number</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">=(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="identifier">assign</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> +</pre> +<p> + Type <code class="computeroutput"><span class="identifier">number</span></code> is default constructible, + and both copy constructible and assignable from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Itself. + </li> +<li class="listitem"> + An expression template which is the result of one of the arithmetic operators. + </li> +<li class="listitem"> + Any builtin arithmetic type, as long as the result would not be lossy + (for example float to integer conversion). + </li> +<li class="listitem"> + Any type that the Backend is implicitly constructible or assignable from. + </li> +<li class="listitem"> + An rvalue reference to another <code class="computeroutput"><span class="identifier">number</span></code>. + Move-semantics are used for construction if the backend also supports + rvalue reference construction. In the case of assignment, move semantics + are always supported when the argument is an rvalue reference irrespective + of the backend. + </li> +<li class="listitem"> + Any type in the same family, as long as no loss of precision is involved. + For example from <code class="computeroutput"><span class="identifier">int128_t</span></code> + to <code class="computeroutput"><span class="identifier">int256_t</span></code>, or <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> to <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code>. + </li> +</ul></div> +<p> + Type <code class="computeroutput"><span class="identifier">number</span></code> is explicitly + constructible from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Any type mentioned above. + </li> +<li class="listitem"> + A <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code> or any type which is convertible + to <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code>. + </li> +<li class="listitem"> + Any arithmetic type (including those that would result in lossy conversions). + </li> +<li class="listitem"> + Any type in the same family, including those that result in loss of precision. + </li> +<li class="listitem"> + Any type that the Backend is explicitly constructible from. + </li> +<li class="listitem"> + Any pair of types for which a generic interconversion exists: that is + from integer to integer, integer to rational, integer to float, rational + to rational, rational to float, or float to float. + </li> +</ul></div> +<p> + The assign member function is available for any type for which an explicit + converting constructor exists. It is intended to be used where a temporary + generated from an explicit assignment would be expensive, for example: + </p> +<pre class="programlisting"><span class="identifier">mpfr_float_50</span> <span class="identifier">f50</span><span class="special">;</span> +<span class="identifier">mpfr_float_100</span> <span class="identifier">f100</span><span class="special">;</span> + +<span class="identifier">f50</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">mpfr_float_50</span><span class="special">>(</span><span class="identifier">f100</span><span class="special">);</span> <span class="comment">// explicit cast create a temporary</span> +<span class="identifier">f50</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">f100</span><span class="special">);</span> <span class="comment">// explicit call to assign create no temporary</span> +</pre> +<p> + In addition, if the type has multiple components (for example rational or + complex number types), then there is a two argument constructor: + </p> +<pre class="programlisting"><span class="identifier">number</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">);</span> +</pre> +<p> + Where the two args must either be arithmetic types, or types that are convertible + to the two components of <code class="computeroutput"><span class="keyword">this</span></code>. + </p> +<pre class="programlisting"><span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">++();</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">--();</span> +<span class="identifier">number</span> <span class="keyword">operator</span><span class="special">++(</span><span class="keyword">int</span><span class="special">);</span> +<span class="identifier">number</span> <span class="keyword">operator</span><span class="special">--(</span><span class="keyword">int</span><span class="special">);</span> +<span class="comment">// Integer only operations:</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">%=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">&=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">|=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">^=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">>>=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +</pre> +<p> + These operators all take their usual arithmetic meanings. + </p> +<p> + The arguments to these operators is either: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Another <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> + <span class="identifier">ExpressionTemplates</span><span class="special">></span></code>. + </li> +<li class="listitem"> + An expression template derived from <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">></span></code>. + </li> +<li class="listitem"> + Any type implicitly convertible to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span></code>, including some other instance of + class <code class="computeroutput"><span class="identifier">number</span></code>. + </li> +</ul></div> +<p> + For the left and right shift operations, the argument must be a builtin integer + type with a positive value (negative values result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown). + </p> +<pre class="programlisting"><span class="keyword">operator</span> <span class="emphasis"><em>convertible-to-bool-type</em></span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Returns an <span class="emphasis"><em>unmentionable-type</em></span> that is usable in Boolean + contexts (this allows <code class="computeroutput"><span class="identifier">number</span></code> + to be used in any Boolean context - if statements, conditional statements, + or as an argument to a logical operator - without type <code class="computeroutput"><span class="identifier">number</span></code> + being convertible to type <code class="computeroutput"><span class="keyword">bool</span></code>. + </p> +<p> + This operator also enables the use of <code class="computeroutput"><span class="identifier">number</span></code> + with any of the following operators: <code class="computeroutput"><span class="special">!</span></code>, + <code class="computeroutput"><span class="special">||</span></code>, <code class="computeroutput"><span class="special">&&</span></code> + and <code class="computeroutput"><span class="special">?:</span></code>. + </p> +<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special">&</span> <span class="identifier">other</span><span class="special">);</span> +</pre> +<p> + Swaps <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> + with <code class="computeroutput"><span class="identifier">other</span></code>. + </p> +<pre class="programlisting"><span class="keyword">bool</span> <span class="identifier">is_zero</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> is <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> is zero, + otherwise <code class="computeroutput"><span class="keyword">false</span></code>. + </p> +<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">sign</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Returns a value less than zero if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> is negative, a value greater than zero + if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> + is positive, and zero if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> + is zero. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">str</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">,</span> <span class="keyword">bool</span> <span class="identifier">scientific</span> <span class="special">=</span> <span class="keyword">true</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Returns the number formatted as a string, with at least <span class="emphasis"><em>precision</em></span> + digits, and in scientific format if <span class="emphasis"><em>scientific</em></span> is true. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="identifier">T</span> <span class="identifier">convert_to</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">explicit</span> <span class="keyword">operator</span> <span class="identifier">T</span> <span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Provides a generic conversion mechanism to convert <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> to type <code class="computeroutput"><span class="identifier">T</span></code>. + Type <code class="computeroutput"><span class="identifier">T</span></code> may be any arithmetic + type. Optionally other types may also be supported by specific <code class="computeroutput"><span class="identifier">Backend</span></code> types. + </p> +<pre class="programlisting"><span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="identifier">default_precision</span><span class="special">();</span> +<span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">default_precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> +<span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +<span class="keyword">void</span> <span class="identifier">precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> +</pre> +<p> + These functions are only available if the Backend template parameter supports + runtime changes to precision. They get and set the default precision and + the precision of <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> + respectively. + </p> +<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> +<span class="keyword">typename</span> <span class="identifier">enable_if</span><span class="special"><</span><span class="identifier">is_convertible</span><span class="special"><</span><span class="identifier">V</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">int</span><span class="special">>::</span><span class="identifier">type</span> + <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">other</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + Returns: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + A value less that 0 for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> <span class="special"><</span> <span class="identifier">other</span></code> + </li> +<li class="listitem"> + A value greater that 0 for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> <span class="special">></span> <span class="identifier">other</span></code> + </li> +<li class="listitem"> +<p class="simpara"> + Zero for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> + <span class="special">==</span> <span class="identifier">other</span></code> + </p> +<pre class="programlisting"><span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">();</span> +<span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +</li> +</ul></div> +<p> + Returns the underlying back-end instance used by <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h2"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.non_member_operators"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.non_member_operators">Non-member + operators</a> + </h5> +<pre class="programlisting"><span class="comment">// Non member operators:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="comment">// Integer only operations:</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">%(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">&(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">|(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">^(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special"><<(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">>>(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> +<span class="comment">// Comparison operators:</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">></span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">>=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> +</pre> +<p> + These operators all take their usual arithmetic meanings. + </p> +<p> + The arguments to these functions must contain at least one of the following: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + A <code class="computeroutput"><span class="identifier">number</span></code>. + </li> +<li class="listitem"> + An expression template type derived from <code class="computeroutput"><span class="identifier">number</span></code>. + </li> +<li class="listitem"> + Any type for which <code class="computeroutput"><span class="identifier">number</span></code> + has an implicit constructor - for example a builtin arithmetic type. + </li> +</ul></div> +<p> + The return type of these operators is either: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + An <span class="emphasis"><em>unmentionable-type</em></span> expression template type when + <code class="computeroutput"><span class="identifier">ExpressionTemplates</span></code> is + <code class="computeroutput"><span class="keyword">true</span></code>. + </li> +<li class="listitem"> + Type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> + <span class="identifier">et_off</span><span class="special">></span></code> + when <code class="computeroutput"><span class="identifier">ExpressionTemplates</span></code> + is <code class="computeroutput"><span class="keyword">false</span></code>. + </li> +<li class="listitem"> + Type <code class="computeroutput"><span class="keyword">bool</span></code> if the operator + is a comparison operator. + </li> +</ul></div> +<p> + Finally note that the second argument to the left and right shift operations + must be a builtin integer type, and that the argument must be positive (negative + arguments result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown). + </p> +<h5> +<a name="boost_multiprecision.ref.number.h3"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.swap"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.swap">swap</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Swaps <code class="computeroutput"><span class="identifier">a</span></code> and <code class="computeroutput"><span class="identifier">b</span></code>. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h4"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.iostream_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.iostream_support">Iostream + Support</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Unspecified</span><span class="special">...></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">unmentionable</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">inline</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">)</span> +</pre> +<p> + These operators provided formatted input-output operations on <code class="computeroutput"><span class="identifier">number</span></code> types, and expression templates + derived from them. + </p> +<p> + It's down to the back-end type to actually implement string conversion. However, + the back-ends provided with this library support all of the iostream formatting + flags, field width and precision settings. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h5"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.arithmetic_with_a_higher_precisi"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.arithmetic_with_a_higher_precisi">Arithmetic + with a higher precision result</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + These functions apply the named operator to the arguments <span class="emphasis"><em>a</em></span> + and <span class="emphasis"><em>b</em></span> and store the result in <span class="emphasis"><em>result</em></span>, + returning <span class="emphasis"><em>result</em></span>. In all cases they behave "as + if" arguments <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> were + first promoted to type <code class="computeroutput"><span class="identifier">ResultType</span></code> + before applying the operator, though particular backends may well avoid that + step by way of an optimization. + </p> +<p> + The type <code class="computeroutput"><span class="identifier">ResultType</span></code> must + be an instance of class <code class="computeroutput"><span class="identifier">number</span></code>, + and the types <code class="computeroutput"><span class="identifier">Source1</span></code> and + <code class="computeroutput"><span class="identifier">Source2</span></code> may be either instances + of class <code class="computeroutput"><span class="identifier">number</span></code> or native + integer types. The latter is an optimization that allows arithmetic to be + performed on native integer types producing an extended precision result. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h6"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.non_member_standard_library_func"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.non_member_standard_library_func">Non-member + standard library function support</a> + </h5> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">abs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fabs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">floor</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ceil</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">trunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">itrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ltrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">round</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">iround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">exp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log10</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">acos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">asin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cosh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sinh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tanh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> + +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ldexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">frexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">*);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmod</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan2</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> +<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">logb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="emphasis"><em>integer-type</em></span> <span class="identifier">ilogb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +</pre> +<p> + These functions all behave exactly as their standard library C++11 counterparts + do: their argument is either an instance of <code class="computeroutput"><span class="identifier">number</span></code> + or an expression template derived from it; If the argument is of type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></span></code> + then that is also the return type, otherwise the return type is an expression + template. + </p> +<p> + The integer type arguments to <code class="computeroutput"><span class="identifier">ldexp</span></code>, + <code class="computeroutput"><span class="identifier">frexp</span></code>, <code class="computeroutput"><span class="identifier">scalbn</span></code> + and <code class="computeroutput"><span class="identifier">ilogb</span></code> may be either type + <code class="computeroutput"><span class="keyword">int</span></code>, or the actual type of the + exponent of the number type. + </p> +<p> + These functions are normally implemented by the Backend type. However, default + versions are provided for Backend types that don't have native support for + these functions. Please note however, that this default support requires + the precision of the type to be a compile time constant - this means for + example that the <a href="http://gmplib.org" target="_top">GMP</a> MPF Backend will + not work with these functions when that type is used at variable precision. + </p> +<p> + Also note that with the exception of <code class="computeroutput"><span class="identifier">abs</span></code> + that these functions can only be used with floating-point Backend types (if + any other types such as fixed precision or complex types are added to the + library later, then these functions may be extended to support those number + types). + </p> +<p> + The precision of these functions is generally determined by the backend implementation. + For example the precision of these functions when used with <a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float">mpfr_float</a> + is determined entirely by <a href="http://www.mpfr.org" target="_top">MPFR</a>. + When these functions use our own implementations, the accuracy of the transcendental + functions is generally a few epsilon. Note however, that the trigonometrical + functions incur the usual accuracy loss when reducing arguments by large + multiples of π. Also note that both <a class="link" href="../tut/floats/gmp_float.html" title="gmp_float">gmp_float</a> + and <a class="link" href="../tut/floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> + have a number of guard digits beyond their stated precision, so the error + rates listed for these are in some sense artificially low. + </p> +<p> + The following table shows the error rates we observe for these functions + with various backend types, functions not listed here are exact (tested on + Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + mpfr_float_50 + </p> + </th> +<th> + <p> + mpf_float_50 + </p> + </th> +<th> + <p> + cpp_dec_float_50 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + sqrt + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + exp + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + log + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + log10 + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + cos + </p> + </td> +<td> + <p> + 700eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + sin + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + tan + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + acos + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + asin + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + atan + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + cosh + </p> + </td> +<td> + <p> + 1045eps<a href="#ftn.boost_multiprecision.ref.number.f0" class="footnote" name="boost_multiprecision.ref.number.f0"><sup class="footnote">[1]</sup></a> + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + sinh + </p> + </td> +<td> + <p> + 2eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + tanh + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +<tr> +<td> + <p> + pow + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 4eps + </p> + </td> +<td> + <p> + 3eps + </p> + </td> +</tr> +<tr> +<td> + <p> + atan2 + </p> + </td> +<td> + <p> + 1eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +<td> + <p> + 0eps + </p> + </td> +</tr> +</tbody> +<tbody class="footnotes"><tr><td colspan="4"><div id="ftn.boost_multiprecision.ref.number.f0" class="footnote"><p><a href="#boost_multiprecision.ref.number.f0" class="para"><sup class="para">[1] </sup></a> + It's likely that the inherent error in the input values to our + test cases are to blame here. + </p></div></td></tr></tbody> +</table></div> +<h5> +<a name="boost_multiprecision.ref.number.h7"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.traits_class_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.traits_class_support">Traits Class + Support</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">component_type</span><span class="special">;</span> +</pre> +<p> + If this is a type with multiple components (for example rational or complex + types), then this trait has a single member <code class="computeroutput"><span class="identifier">type</span></code> + that is the type of those components. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">number_category</span><span class="special">;</span> +</pre> +<p> + A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + where <code class="computeroutput"><span class="identifier">N</span></code> is one of the enumerated + values <code class="computeroutput"><span class="identifier">number_kind_integer</span></code>, + <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>, + <code class="computeroutput"><span class="identifier">number_kind_rational</span></code>, <code class="computeroutput"><span class="identifier">number_kind_fixed_point</span></code>, or <code class="computeroutput"><span class="identifier">number_kind_unknown</span></code>. This traits class + is specialized for any type that has <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> + support as well as for classes in this library: which means it can be used + for generic code that must work with built in arithmetic types as well as + multiprecision ones. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_number</span><span class="special">;</span> +</pre> +<p> + A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> + if T is an instance of <code class="computeroutput"><span class="identifier">number</span><span class="special"><></span></code>, otherwise from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">is_number_expression</span><span class="special">;</span> +</pre> +<p> + A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> + if T is an expression template type derived from <code class="computeroutput"><span class="identifier">number</span><span class="special"><></span></code>, otherwise from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h8"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.integer_functions"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.integer_functions">Integer + functions</a> + </h5> +<p> + In addition to functioning with types from this library, these functions + are also overloaded for built in integer types if you include <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>. + Further, when used with fixed precision types (whether built in integers + or multiprecision ones), the functions will promote to a wider type internally + when the algorithm requires it. Versions overloaded for built in integer + types return that integer type rather than an expression template. + </p> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">gcd</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> + that divides both <code class="computeroutput"><span class="identifier">a</span></code> and + <code class="computeroutput"><span class="identifier">b</span></code>. + </p> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lcm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns the smallest integer <code class="computeroutput"><span class="identifier">x</span></code> + that is divisible by both <code class="computeroutput"><span class="identifier">a</span></code> + and <code class="computeroutput"><span class="identifier">b</span></code>. + </p> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">p</span><span class="special">);</span> +</pre> +<p> + Returns <span class="emphasis"><em>b<sup>p</sup></em></span> as an expression template. Note that this + function should be used with extreme care as the result can grow so large + as to take "effectively forever" to compute, or else simply run + the host machine out of memory. This is the one function in this category + that is not overloaded for built in integer types, further, it's probably + not a good idea to use it with fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s + either. + </p> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">m</span><span class="special">);</span> +</pre> +<p> + Returns <span class="emphasis"><em>b<sup>p</sup> mod m</em></span> as an expression template. Fixed precision + types are promoted internally to ensure accuracy. + </p> +<pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">);</span> +</pre> +<p> + Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> + such that <code class="computeroutput"><span class="identifier">x</span> <span class="special">*</span> + <span class="identifier">x</span> <span class="special"><</span> + <span class="identifier">a</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> +</pre> +<p> + Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> + such that <code class="computeroutput"><span class="identifier">x</span> <span class="special">*</span> + <span class="identifier">x</span> <span class="special"><</span> + <span class="identifier">a</span></code>, and sets the remainder <code class="computeroutput"><span class="identifier">r</span></code> such that <code class="computeroutput"><span class="identifier">r</span> + <span class="special">=</span> <span class="identifier">a</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">*</span> + <span class="identifier">x</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> + <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> +</pre> +<p> + Divides x by y and returns both the quotient and remainder. After the call + <code class="computeroutput"><span class="identifier">q</span> <span class="special">=</span> + <span class="identifier">x</span> <span class="special">/</span> <span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">r</span> + <span class="special">=</span> <span class="identifier">x</span> <span class="special">%</span> <span class="identifier">y</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns the absolute value of <code class="computeroutput"><span class="identifier">x</span> + <span class="special">%</span> <span class="identifier">val</span></code>. + </p> +<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + Returns the (zero-based) index of the least significant bit that is set to + 1. + </p> +<p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> if the argument is <= 0. + </p> +<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + Returns the (zero-based) index of the most significant bit. + </p> +<p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> if the argument is <= 0. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if the bit at + <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span> is set. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Sets the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, and + returns <span class="emphasis"><em>val</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Unsets the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, + and returns <span class="emphasis"><em>val</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Flips the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, + and returns <span class="emphasis"><em>val</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> +</pre> +<p> + Tests to see if the number <span class="emphasis"><em>n</em></span> is probably prime - the + test excludes the vast majority of composite numbers by excluding small prime + factors and performing a single Fermat test. Then performs <span class="emphasis"><em>trials</em></span> + Miller-Rabin tests. Returns <code class="computeroutput"><span class="keyword">false</span></code> + if <span class="emphasis"><em>n</em></span> is definitely composite, or <code class="computeroutput"><span class="keyword">true</span></code> + if <span class="emphasis"><em>n</em></span> is probably prime with the probability of it being + composite less than 0.25^trials. Fixed precision types are promoted internally + to ensure accuracy. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h9"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.rational_number_functions"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.rational_number_functions">Rational + Number Functions</a> + </h5> +<pre class="programlisting"><span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">numerator</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +<span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> +</pre> +<p> + These functions return the numerator and denominator of a rational number + respectively. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h10"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.boost_math_interoperability_supp"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.boost_math_interoperability_supp">Boost.Math + Interoperability Support</a> + </h5> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> + +<span class="keyword">int</span> <span class="identifier">fpclassify</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isfinite</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isnan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isinf</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">isnormal</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + These floating-point classification functions behave exactly as their Boost.Math + equivalents. + </p> +<p> + Other Boost.Math functions and templates may also be specialized or overloaded + to ensure interoperability. + </p> +<h5> +<a name="boost_multiprecision.ref.number.h11"></a> + <span class="phrase"><a name="boost_multiprecision.ref.number.std_numeric_limits_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.std_numeric_limits_support">std::numeric_limits + support</a> + </h5> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">></span> +<span class="special">{</span> + <span class="comment">/* Usual members here */</span> +<span class="special">};</span> + +<span class="special">}</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> is specialized for all instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> whose precision + is known at compile time, plus those types whose precision is unlimited (though + it is much less useful in those cases). It is not specialized for types whose + precision can vary at compile time (such as <code class="computeroutput"><span class="identifier">mpf_float</span></code>). + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_int_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/ref/tom_int_ref.html b/libs/multiprecision/doc/html/boost_multiprecision/ref/tom_int_ref.html new file mode 100644 index 0000000000..bd48e112a7 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/ref/tom_int_ref.html @@ -0,0 +1,63 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>tom_int</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ref.html" title="Reference"> +<link rel="prev" href="gmp_int_ref.html" title="gmp_int"> +<link rel="next" href="mpf_ref.html" title="gmp_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mpf_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.ref.tom_int_ref"></a><a class="link" href="tom_int_ref.html" title="tom_int">tom_int</a> +</h3></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">tommath_int</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">tommath_int</span> <span class="special">></span> <span class="identifier">tom_int</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + Class template <code class="computeroutput"><span class="identifier">tommath_int</span></code> + fulfils all of the requirements for a <a class="link" href="backendconc.html" title="Backend Requirements">Backend</a> + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. + </p> +<p> + The type of <code class="computeroutput"><span class="identifier">number_category</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special"><</span><span class="identifier">Args</span><span class="special">...></span> <span class="special">>::</span><span class="identifier">type</span></code> is <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">number_kind_integer</span><span class="special">></span></code>. + </p> +<p> + More information on this type can be found in the <a class="link" href="../tut/ints/tom_int.html" title="tom_int">tutorial</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_int_ref.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mpf_ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut.html b/libs/multiprecision/doc/html/boost_multiprecision/tut.html new file mode 100644 index 0000000000..6c79552511 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut.html @@ -0,0 +1,131 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Tutorial</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="prev" href="intro.html" title="Introduction"> +<link rel="next" href="tut/ints.html" title="Integer Types"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> +<td align="center"><a href="../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="intro.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tut/ints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h2 class="title" style="clear: both"> +<a name="boost_multiprecision.tut"></a><a class="link" href="tut.html" title="Tutorial">Tutorial</a> +</h2></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="tut/ints.html">Integer Types</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/ints/cpp_int.html">cpp_int</a></span></dt> +<dt><span class="section"><a href="tut/ints/gmp_int.html">gmp_int</a></span></dt> +<dt><span class="section"><a href="tut/ints/tom_int.html">tom_int</a></span></dt> +<dt><span class="section"><a href="tut/ints/egs.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/ints/egs/factorials.html">Factorials</a></span></dt> +<dt><span class="section"><a href="tut/ints/egs/bitops.html">Bit Operations</a></span></dt> +</dl></dd> +</dl></dd> +<dt><span class="section"><a href="tut/floats.html">Floating Point Numbers</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/floats/cpp_bin_float.html">cpp_bin_float</a></span></dt> +<dt><span class="section"><a href="tut/floats/cpp_dec_float.html">cpp_dec_float</a></span></dt> +<dt><span class="section"><a href="tut/floats/gmp_float.html">gmp_float</a></span></dt> +<dt><span class="section"><a href="tut/floats/mpfr_float.html">mpfr_float</a></span></dt> +<dt><span class="section"><a href="tut/floats/float128.html">float128</a></span></dt> +<dt><span class="section"><a href="tut/floats/fp_eg.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/floats/fp_eg/aos.html">Area of + Circle</a></span></dt> +<dt><span class="section"><a href="tut/floats/fp_eg/jel.html">Defining + a Special Function.</a></span></dt> +<dt><span class="section"><a href="tut/floats/fp_eg/nd.html">Calculating + a Derivative</a></span></dt> +<dt><span class="section"><a href="tut/floats/fp_eg/gi.html">Calculating + an Integral</a></span></dt> +<dt><span class="section"><a href="tut/floats/fp_eg/poly_eg.html">Polynomial + Evaluation</a></span></dt> +</dl></dd> +</dl></dd> +<dt><span class="section"><a href="tut/interval.html">Interval Number Types</a></span></dt> +<dd><dl><dt><span class="section"><a href="tut/interval/mpfi.html">mpfi_float</a></span></dt></dl></dd> +<dt><span class="section"><a href="tut/rational.html">Rational Number Types</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/rational/cpp_rational.html">cpp_rational</a></span></dt> +<dt><span class="section"><a href="tut/rational/gmp_rational.html">gmp_rational</a></span></dt> +<dt><span class="section"><a href="tut/rational/tommath_rational.html">tommath_rational</a></span></dt> +<dt><span class="section"><a href="tut/rational/br.html">Use With Boost.Rational</a></span></dt> +<dt><span class="section"><a href="tut/rational/rational_adaptor.html">rational_adaptor</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="tut/misc.html">Miscellaneous Number Types.</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/misc/logged_adaptor.html">logged_adaptor</a></span></dt> +<dt><span class="section"><a href="tut/misc/debug_adaptor.html">debug_adaptor</a></span></dt> +<dt><span class="section"><a href="tut/misc/visualizers.html">Visual C++ + Debugger Visualizers</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="tut/conversions.html">Constructing and + Interconverting Between Number Types</a></span></dt> +<dt><span class="section"><a href="tut/random.html">Generating Random Numbers</a></span></dt> +<dt><span class="section"><a href="tut/primetest.html">Primality Testing</a></span></dt> +<dt><span class="section"><a href="tut/lits.html">Literal Types and <code class="computeroutput"><span class="keyword">constexpr</span></code> Support</a></span></dt> +<dt><span class="section"><a href="tut/rounding.html">Rounding Rules for + Conversions</a></span></dt> +<dt><span class="section"><a href="tut/mixed.html">Mixed Precision Arithmetic</a></span></dt> +<dt><span class="section"><a href="tut/gen_int.html">Generic Integer Operations</a></span></dt> +<dt><span class="section"><a href="tut/serial.html">Boost.Serialization + Support</a></span></dt> +<dt><span class="section"><a href="tut/limits.html">Numeric Limits</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="tut/limits/constants.html">std::numeric_limits<> + constants</a></span></dt> +<dt><span class="section"><a href="tut/limits/functions.html">std::numeric_limits<> + functions</a></span></dt> +<dt><span class="section"><a href="tut/limits/limits32.html">Numeric limits + for 32-bit platform</a></span></dt> +<dt><span class="section"><a href="tut/limits/how_to_tell.html">How to + Determine the Kind of a Number From <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code></a></span></dt> +</dl></dd> +<dt><span class="section"><a href="tut/input_output.html">Input Output</a></span></dt> +</dl></div> +<p> + In order to use this library you need to make two choices: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + What kind of number do I want (<a class="link" href="tut/ints.html" title="Integer Types">integer</a>, + <a class="link" href="tut/floats.html" title="Floating Point Numbers">floating point</a> or + <a class="link" href="tut/rational.html" title="Rational Number Types">rational</a>). + </li> +<li class="listitem"> + Which back-end do I want to perform the actual arithmetic (Boost-supplied, + GMP, MPFR, Tommath etc)? + </li> +</ul></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="intro.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tut/ints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/conversions.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/conversions.html new file mode 100644 index 0000000000..1550ecef0a --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/conversions.html @@ -0,0 +1,216 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Constructing and Interconverting Between Number Types</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="misc/visualizers.html" title="Visual C++ Debugger Visualizers"> +<link rel="next" href="random.html" title="Generating Random Numbers"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="misc/visualizers.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="random.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.conversions"></a><a class="link" href="conversions.html" title="Constructing and Interconverting Between Number Types">Constructing and + Interconverting Between Number Types</a> +</h3></div></div></div> +<p> + All of the number types that are based on <code class="computeroutput"><span class="identifier">number</span></code> + have certain conversion rules in common. In particular: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> +<p class="simpara"> + Any number type can be constructed (or assigned) from any builtin arithmetic + type, as long as the conversion isn't lossy (for example float to int + conversion): + </p> +<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span> <span class="comment">// OK construction from double</span> +<span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">450</span><span class="special">);</span> <span class="comment">// OK constructs from signed int</span> +<span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, lossy conversion.</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + A number can be explicitly constructed from an arithmetic type, even + when the conversion is lossy: + </p> +<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK explicit conversion</span> +<span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="number">3.14</span><span class="special">)</span> <span class="comment">// OK explicit conversion</span> +<span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK, explicit assign and avoid a temporary from the cast above</span> +<span class="identifier">i</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit assignment operator for lossy conversion.</span> +<span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit constructor for lossy conversion.</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + A <code class="computeroutput"><span class="identifier">number</span></code> can be converted + to any built in type, via the <code class="computeroutput"><span class="identifier">convert_to</span></code> + member function: + </p> +<pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> +<span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">.</span><span class="keyword">template</span> <span class="identifier">convert_to</span><span class="special"><</span><span class="keyword">int</span><span class="special">>();</span> <span class="comment">// sets i to 2</span> +</pre> +</li> +<li class="listitem"> + Conversions to rational numbers from floating point ones are always allowed, + and are exact and implicit as long as the rational number uses an unbounded + integer type. Please be aware that constructing a rational number from + an extended precision floating point type with a large exponent range + can effectively run the system out of memory, as in the extreme case + <span class="emphasis"><em>2<sup>max_exponent</sup> / CHAR_BITS</em></span> bytes of storage may be + required. This does not represent a problem for built in floating point + types however, as the exponent range for these is rather limited. + </li> +<li class="listitem"> + Conversions to floating point numbers from rational ones are rounded + to nearest (less than 0.5ulp error) as long as the floating point number + is binary, and the integer type used by the rational number is unbounded. + </li> +</ul></div> +<p> + Additional conversions may be supported by particular backends. + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> +<p class="simpara"> + A <code class="computeroutput"><span class="identifier">number</span></code> can be converted + to any built in type, via an explicit conversion operator: this functionality + is only available on compilers supporting C++11's explicit conversion + syntax. + </p> +<pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> +<span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// Error, implicit conversion not allowed.</span> +<span class="keyword">int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">z</span><span class="special">);</span> <span class="comment">// OK explicit conversion.</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Any number type can be <span class="emphasis"><em>explicitly</em></span> constructed (or + assigned) from a <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code> + or a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>: + </p> +<pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">);</span> +<span class="comment">// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:</span> +<span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="string">"0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000"</span><span class="special">);</span> +<span class="comment">// Invalid input always results in a std::runtime_error being thrown:</span> +<span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="string">"3.14"</span><span class="special">);</span> +<span class="comment">// implicit conversions from strings are not allowed:</span> +<span class="identifier">i</span> <span class="special">=</span> <span class="string">"23"</span><span class="special">;</span> <span class="comment">// Error, no assignment operator for implicit conversion from string</span> +<span class="comment">// assign member function, avoids having to create a temporary via a static_cast:</span> +<span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="string">"23"</span><span class="special">);</span> <span class="comment">// OK</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Any number type will interoperate with the builtin types in arithmetic + expressions as long as the conversions are not lossy: + </p> +<pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> +<span class="comment">// Multiply by 2 - using an integer literal here is usually more efficient</span> +<span class="comment">// than constructing a temporary:</span> +<span class="identifier">df</span> <span class="special">*=</span> <span class="number">2</span><span class="special">;</span> + +<span class="comment">// You can't mix integer types with floats though:</span> +<span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> +<span class="identifier">i</span> <span class="special">*=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no *= operator will be found.</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Any number type can be streamed to and from the C++ iostreams: + </p> +<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> +<span class="comment">// Now print at full precision:</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">df</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> +<span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> +<span class="identifier">i</span> <span class="special"><<=</span> <span class="number">256</span><span class="special">;</span> +<span class="comment">// Now print in hex format with prefix:</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">i</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Interconversions between number types of the same family are allowed + and are implicit conversions if no loss of precision is involved, and + explicit if it is: + </p> +<pre class="programlisting"><span class="identifier">int128_t</span> <span class="identifier">i128</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> +<span class="identifier">int266_t</span> <span class="identifier">i256</span> <span class="special">=</span> <span class="identifier">i128</span><span class="special">;</span> <span class="comment">// OK implicit widening conversion</span> +<span class="identifier">i128_t</span> <span class="special">=</span> <span class="identifier">i256</span><span class="special">;</span> <span class="comment">// Error, no assignment operator found, narrowing conversion is explicit</span> +<span class="identifier">i128_t</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">int128_t</span><span class="special">>(</span><span class="identifier">i256</span><span class="special">);</span> <span class="comment">// OK, explicit narrowing conversion</span> + +<span class="identifier">mpz_int</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> +<span class="identifier">mpf_float</span> <span class="identifier">f</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// OK, GMP handles this conversion natively, and it's not lossy and therefore implicit</span> + +<span class="identifier">mpf_float_50</span> <span class="identifier">f50</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> +<span class="identifier">f</span> <span class="special">=</span> <span class="identifier">f50</span><span class="special">;</span> <span class="comment">// OK, conversion from fixed to variable precision, f will have 50 digits precision.</span> +<span class="identifier">f50</span> <span class="special">=</span> <span class="identifier">f</span><span class="special">;</span> <span class="comment">// Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Some interconversions between number types are completely generic, and + are always available, albeit the conversions are always <span class="emphasis"><em>explicit</em></span>: + </p> +<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">cppi</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> +<span class="comment">// We can always convert between numbers of the same category -</span> +<span class="comment">// int to int, rational to rational, or float to float, so this is OK</span> +<span class="comment">// as long as we use an explicit conversion:</span> +<span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> +<span class="comment">// We can always promote from int to rational, int to float, or rational to float:</span> +<span class="identifier">cpp_rational</span> <span class="identifier">cppr</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to rational</span> +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to float</span> +<span class="identifier">df</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>(</span><span class="identifier">cppr</span><span class="special">);</span> <span class="comment">// OK, explicit rational to float conversion</span> +<span class="comment">// However narrowing and/or implicit conversions always fail:</span> +<span class="identifier">cppi</span> <span class="special">=</span> <span class="identifier">df</span><span class="special">;</span> <span class="comment">// Compiler error, conversion not allowed</span> +</pre> +</li> +<li class="listitem"> +<p class="simpara"> + Other interconversions may be allowed as special cases, whenever the + backend allows it: + </p> +<pre class="programlisting"><span class="identifier">mpf_t</span> <span class="identifier">m</span><span class="special">;</span> <span class="comment">// Native GMP type.</span> +<span class="identifier">mpf_init_set_ui</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="number">0</span><span class="special">);</span> <span class="comment">// set to a value;</span> +<span class="identifier">mpf_float</span> <span class="identifier">i</span><span class="special">(</span><span class="identifier">m</span><span class="special">);</span> <span class="comment">// copies the value of the native type.</span> +</pre> +</li> +</ul></div> +<p> + More information on what additional types a backend supports conversions + from are given in the tutorial for each backend. The converting constructor + will be implicit if the backend's converting constructor is also implicit, + and explicit if the backends converting constructor is also explicit. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="misc/visualizers.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="random.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats.html new file mode 100644 index 0000000000..e99ebb1d42 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats.html @@ -0,0 +1,277 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Floating Point Numbers</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="ints/egs/bitops.html" title="Bit Operations"> +<link rel="next" href="floats/cpp_bin_float.html" title="cpp_bin_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="ints/egs/bitops.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="floats/cpp_bin_float.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.floats"></a><a class="link" href="floats.html" title="Floating Point Numbers">Floating Point Numbers</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="floats/cpp_bin_float.html">cpp_bin_float</a></span></dt> +<dt><span class="section"><a href="floats/cpp_dec_float.html">cpp_dec_float</a></span></dt> +<dt><span class="section"><a href="floats/gmp_float.html">gmp_float</a></span></dt> +<dt><span class="section"><a href="floats/mpfr_float.html">mpfr_float</a></span></dt> +<dt><span class="section"><a href="floats/float128.html">float128</a></span></dt> +<dt><span class="section"><a href="floats/fp_eg.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="floats/fp_eg/aos.html">Area of + Circle</a></span></dt> +<dt><span class="section"><a href="floats/fp_eg/jel.html">Defining + a Special Function.</a></span></dt> +<dt><span class="section"><a href="floats/fp_eg/nd.html">Calculating + a Derivative</a></span></dt> +<dt><span class="section"><a href="floats/fp_eg/gi.html">Calculating + an Integral</a></span></dt> +<dt><span class="section"><a href="floats/fp_eg/poly_eg.html">Polynomial + Evaluation</a></span></dt> +</dl></dd> +</dl></div> +<p> + The following back-ends provide floating point arithmetic: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend Type + </p> + </th> +<th> + <p> + Header + </p> + </th> +<th> + <p> + Radix + </p> + </th> +<th> + <p> + Dependencies + </p> + </th> +<th> + <p> + Pros + </p> + </th> +<th> + <p> + Cons + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/cpp_bin_float.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + None + </p> + </td> +<td> + <p> + Header only, all C++ implementation. Boost licence. + </p> + </td> +<td> + <p> + Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a> + or <a href="http://gmplib.org" target="_top">GMP</a> libraries. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/cpp_dec_float.hpp + </p> + </td> +<td> + <p> + 10 + </p> + </td> +<td> + <p> + None + </p> + </td> +<td> + <p> + Header only, all C++ implementation. Boost licence. + </p> + </td> +<td> + <p> + Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a> + or <a href="http://gmplib.org" target="_top">GMP</a> libraries. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/gmp.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://gmplib.org" target="_top">GMP</a> + </p> + </td> +<td> + <p> + Very fast and efficient back-end. + </p> + </td> +<td> + <p> + Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a> + library. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/mpfr.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://gmplib.org" target="_top">GMP</a> and <a href="http://www.mpfr.org" target="_top">MPFR</a> + </p> + </td> +<td> + <p> + Very fast and efficient back-end, with its own standard library + implementation. + </p> + </td> +<td> + <p> + Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a> + and <a href="http://www.mpfr.org" target="_top">MPFR</a> libraries. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">float128</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/float128.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + Either <a href="http://gcc.gnu.org/onlinedocs/libquadmath/" target="_top">libquadmath</a> + or the Intel C++ Math library. + </p> + </td> +<td> + <p> + Very fast and efficient back-end for 128-bit floating point values + (113-bit mantissa, equivalent to FORTRAN's QUAD real) + </p> + </td> +<td> + <p> + Depends on the compiler being either recent GCC or Intel C++ versions. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="ints/egs/bitops.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="floats/cpp_bin_float.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html new file mode 100644 index 0000000000..ea235149e7 --- /dev/null +++ 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+<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../floats.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_dec_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.floats.cpp_bin_float"></a><a class="link" href="cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">enum</span> <span class="identifier">digit_base_type</span> +<span class="special">{</span> + <span class="identifier">digit_base_2</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> + <span class="identifier">digit_base_10</span> <span class="special">=</span> <span class="number">10</span> +<span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">digit_base_type</span> <span class="identifier">base</span> <span class="special">=</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Exponent</span> <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">ExponentMin</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">ExponentMax</span> <span class="special">=</span> <span class="number">0</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_bin_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_bin_float_100</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">24</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">126</span><span class="special">,</span> <span class="number">127</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_single</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">1022</span><span class="special">,</span> <span class="number">1023</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">64</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_double_extended</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">backends</span><span class="special">::</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">113</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">>,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">cpp_bin_float_quad</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> back-end + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: + It acts as an entirely C++ (header only and dependency free) floating-point + number type that is a drop-in replacement for the native C++ floating-point + types, but with much greater precision. + </p> +<p> + Type <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> can + be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits</span></code> + template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_bin_float_50</span></code> + and <code class="computeroutput"><span class="identifier">cpp_bin_float_100</span></code> provide + arithmetic types at 50 and 100 decimal digits precision respectively. + </p> +<p> + Optionally, you can specify whether the precision is specified in decimal + digits or binary bits - for example to declare a <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + with exactly the same precision as <code class="computeroutput"><span class="keyword">double</span></code> + one would use <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">digit_base_2</span><span class="special">></span> <span class="special">></span></code>. + The typedefs <code class="computeroutput"><span class="identifier">cpp_bin_float_single</span></code>, + <code class="computeroutput"><span class="identifier">cpp_bin_float_double</span></code>, + <code class="computeroutput"><span class="identifier">cpp_bin_float_quad</span></code> and + <code class="computeroutput"><span class="identifier">cpp_bin_float_double_extended</span></code> + provide software analogues of the IEEE single, double and quad float data + types, plus the Intel-extended-double type respectively. Note that while + these types are functionally equivalent to the native IEEE types, but they + do not have the same size or bit-layout as true IEEE compatible types. + </p> +<p> + Normally <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + allocates no memory: all of the space required for its digits are allocated + directly within the class. As a result care should be taken not to use + the class with too high a digit count as stack space requirements can grow + out of control. If that represents a problem then providing an allocator + as a template parameter causes <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + to dynamically allocate the memory it needs: this significantly reduces + the size of <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> + and increases the viable upper limit on the number of digits at the expense + of performance. However, please bear in mind that arithmetic operations + rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows: + the current implementation really isn't optimized or designed for large + digit counts. Note that since the actual type of the objects allocated + is completely opaque, the suggestion would be to use an allocator with + <code class="computeroutput"><span class="keyword">void</span></code> <code class="computeroutput"><span class="identifier">value_type</span></code>, + for example: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">1000</span><span class="special">,</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span><span class="special"><</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="special">></span></code>. + </p> +<p> + The final template parameters determine the type and range of the exponent: + parameter <code class="computeroutput"><span class="identifier">Exponent</span></code> can + be any signed integer type, but note that <code class="computeroutput"><span class="identifier">MinExponent</span></code> + and <code class="computeroutput"><span class="identifier">MaxExponent</span></code> can not + go right up to the limits of the <code class="computeroutput"><span class="identifier">Exponent</span></code> + type as there has to be a little extra headroom for internal calculations. + You will get a compile time error if this is the case. In addition if MinExponent + or MaxExponent are zero, then the library will choose suitable values that + are as large as possible given the constraints of the type and need for + extra headroom for internal calculations. + </p> +<p> + There is full standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support available for this type. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code>s + have a value of zero. + </li> +<li class="listitem"> + The radix of this type is 2, even when the precision is specified as + decimal digits. + </li> +<li class="listitem"> + The type supports both infinities and NaN's. An infinity is generated + whenever the result would overflow, and a NaN is generated for any + mathematically undefined operation. + </li> +<li class="listitem"> + There is a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for + this type. + </li> +<li class="listitem"> + Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated + on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code> + instantiated on this type - for example you can convert from <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">SomeOtherValue</span><span class="special">></span> <span class="special">></span></code>. + Narrowing conversions round to nearest and are <code class="computeroutput"><span class="keyword">explicit</span></code>. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + All arithmetic operations are correctly rounded to nearest. String + conversions and the <code class="computeroutput"><span class="identifier">sqrt</span></code> + function are also correctly rounded, but transcendental functions (sin, + cos, pow, exp etc) are not. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.floats.cpp_bin_float.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.floats.cpp_bin_float.cpp_bin_float_example"></a></span><a class="link" href="cpp_bin_float.html#boost_multiprecision.tut.floats.cpp_bin_float.cpp_bin_float_example">cpp_bin_float + example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_bin_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> + <span class="identifier">cpp_bin_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_100</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> + <span class="comment">// We can also use any function from Boost.Math:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// These even work when the argument is an expression template:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// And since we have an extended exponent range we can generate some really large </span> + <span class="comment">// numbers here (4.0238726007709377354370243e+2564):</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">cpp_bin_float_100</span><span class="special">(</span><span class="number">1000</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../floats.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cpp_dec_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html new file mode 100644 index 0000000000..09f5c827d0 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -0,0 +1,176 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>cpp_dec_float</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../floats.html" title="Floating Point Numbers"> +<link rel="prev" href="cpp_bin_float.html" title="cpp_bin_float"> +<link rel="next" href="gmp_float.html" title="gmp_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_bin_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.floats.cpp_dec_float"></a><a class="link" href="cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExponentType</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">int32_t</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_dec_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_100</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> back-end + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: + It acts as an entirely C++ (header only and dependency free) floating-point + number type that is a drop-in replacement for the native C++ floating-point + types, but with much greater precision. + </p> +<p> + Type <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> can + be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> + template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> + and <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code> provide + arithmetic types at 50 and 100 decimal digits precision respectively. Optionally, + you can specify an integer type to use for the exponent, this defaults + to a 32-bit integer type which is more than large enough for the vast majority + of use cases, but larger types such as <code class="computeroutput"><span class="keyword">long</span> + <span class="keyword">long</span></code> can also be specified if you + need a truly huge exponent range. In any case the ExponentType must be + a built in signed integer type at least 2 bytes and 16-bits wide. + </p> +<p> + Normally <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + allocates no memory: all of the space required for its digits are allocated + directly within the class. As a result care should be taken not to use + the class with too high a digit count as stack space requirements can grow + out of control. If that represents a problem then providing an allocator + as the final template parameter causes <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + to dynamically allocate the memory it needs: this significantly reduces + the size of <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + and increases the viable upper limit on the number of digits at the expense + of performance. However, please bear in mind that arithmetic operations + rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows: + the current implementation really isn't optimized or designed for large + digit counts. + </p> +<p> + There is full standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support available for this type. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>s + have a value of zero. + </li> +<li class="listitem"> + The radix of this type is 10. As a result it can behave subtly differently + from base-2 types. + </li> +<li class="listitem"> + The type has a number of internal guard digits over and above those + specified in the template argument. Normally these should not be visible + to the user. + </li> +<li class="listitem"> + The type supports both infinities and NaN's. An infinity is generated + whenever the result would overflow, and a NaN is generated for any + mathematically undefined operation. + </li> +<li class="listitem"> + There is a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for + this type. + </li> +<li class="listitem"> + Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated + on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code> + instantiated on this type - for example you can convert from <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="identifier">SomeOtherValue</span><span class="special">></span> <span class="special">></span></code>. + Narrowing conversions are truncating and <code class="computeroutput"><span class="keyword">explicit</span></code>. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + The actual precision of a <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + is always slightly higher than the number of digits specified in the + template parameter, actually how much higher is an implementation detail + but is always at least 8 decimal digits. + </li> +<li class="listitem"> + Operations involving <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + are always truncating. However, note that since their are guard digits + in effect, in practice this has no real impact on accuracy for most + use cases. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.floats.cpp_dec_float.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example"></a></span><a class="link" href="cpp_dec_float.html#boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example">cpp_dec_float + example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> + <span class="identifier">cpp_dec_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// Note that digits10 is the same as digits, since we're base 10! :</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_100</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_100</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> + <span class="comment">// We can also use any function from Boost.Math:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// These even work when the argument is an expression template:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// And since we have an extended exponent range we can generate some really large </span> + <span class="comment">// numbers here (4.0238726007709377354370243e+2564):</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">cpp_dec_float_100</span><span class="special">(</span><span class="number">1000</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_bin_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/float128.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/float128.html new file mode 100644 index 0000000000..e4ba6f389b --- /dev/null +++ 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href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpfr_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.floats.float128"></a><a class="link" href="float128.html" title="float128">float128</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">float128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">float128_backend</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">float128_backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">float128</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">float128</span></code> number type + is a very thin wrapper around GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data types + and provides an real-number type that is a drop-in replacement for the + native C++ floating-point types, but with a 113 bit mantissa, and compatible + with FORTRAN's 128-bit QUAD real. + </p> +<p> + All the usual standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support are available, performance should be equivalent to the underlying + native types: for example the LINPACK benchmarks for GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">float128</span></code> both achieved 5.6 MFLOPS<a href="#ftn.boost_multiprecision.tut.floats.float128.f0" class="footnote" name="boost_multiprecision.tut.floats.float128.f0"><sup class="footnote">[3]</sup></a>. + </p> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">float128</span></code> are copy constructible + and assignable from GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + and Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data + types. + </p> +<p> + It's also possible to access the underlying <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + or <code class="computeroutput"><span class="identifier">_Quad</span></code> type via the + <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> + member function of <code class="computeroutput"><span class="identifier">float128_backend</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">float128</span></code>s + have the value zero. + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +<li class="listitem"> + It is not possible to round-trip objects of this type to and from a + string and get back exactly the same value when compiled with Intel's + C++ compiler and using <code class="computeroutput"><span class="identifier">_Quad</span></code> + as the underlying type: this is a current limitation of our code. Round + tripping when using <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + as the underlying type is possible (both for GCC and Intel). + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + Division by zero results in an infinity being produced. + </li> +<li class="listitem"> + Type <code class="computeroutput"><span class="identifier">float128</span></code> can be + used as a literal type (constexpr support). + </li> +<li class="listitem"> + When using the Intel compiler, the underlying type defaults to <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code> + if it's available and <code class="computeroutput"><span class="identifier">_Quad</span></code> + if not. You can override the default by defining either <code class="computeroutput"><span class="identifier">BOOST_MP_USE_FLOAT128</span></code> or <code class="computeroutput"><span class="identifier">BOOST_MP_USE_QUAD</span></code>. + </li> +<li class="listitem"> + When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> + type, the code must be compiled with the compiler option <code class="computeroutput"><span class="special">-</span><span class="identifier">Qoption</span><span class="special">,</span><span class="identifier">cpp</span><span class="special">,--</span><span class="identifier">extended_float_type</span></code>. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.floats.float128.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.floats.float128.float128_example"></a></span><a class="link" href="float128.html#boost_multiprecision.tut.floats.float128.float128_example">float128 + example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">float128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at 128-bit precision and full numeric_limits support:</span> + <span class="identifier">float128</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="comment">// There are 113-bits of precision:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// Or 34 decimal places:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2) = 0.693147180559945309417232121458176575</span> + <span class="comment">// We can also use any function from Boost.Math:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// And since we have an extended exponent range we can generate some really large </span> + <span class="comment">// numbers here (4.02387260077093773543702433923004111e+2564):</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">float128</span><span class="special">(</span><span class="number">1000</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// We can declare constants using GCC or Intel's native types, and the Q suffix,</span> + <span class="comment">// these can be declared constexpr if required:</span> + + <span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.1415926535897932384626433832795028841971693993751058</span><span class="identifier">Q</span><span class="special">;</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<div class="footnotes"> +<br><hr style="width:100; text-align:left;margin-left: 0"> +<div id="ftn.boost_multiprecision.tut.floats.float128.f0" class="footnote"><p><a href="#boost_multiprecision.tut.floats.float128.f0" class="para"><sup class="para">[3] </sup></a> + On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800. + </p></div> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mpfr_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg.html new file mode 100644 index 0000000000..f3f3aa33ca --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg.html @@ -0,0 +1,55 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Examples</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../floats.html" title="Floating Point Numbers"> +<link rel="prev" href="float128.html" title="float128"> +<link rel="next" href="fp_eg/aos.html" title="Area of Circle"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="float128.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg/aos.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.floats.fp_eg"></a><a class="link" href="fp_eg.html" title="Examples">Examples</a> +</h4></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="fp_eg/aos.html">Area of + Circle</a></span></dt> +<dt><span class="section"><a href="fp_eg/jel.html">Defining + a Special Function.</a></span></dt> +<dt><span class="section"><a href="fp_eg/nd.html">Calculating + a Derivative</a></span></dt> +<dt><span class="section"><a href="fp_eg/gi.html">Calculating + an Integral</a></span></dt> +<dt><span class="section"><a href="fp_eg/poly_eg.html">Polynomial + Evaluation</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="float128.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg/aos.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html new file mode 100644 index 0000000000..563ea65f07 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html @@ -0,0 +1,119 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Area of Circle</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="../fp_eg.html" title="Examples"> +<link rel="next" href="jel.html" title="Defining a Special Function."> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jel.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.floats.fp_eg.aos"></a><a class="link" href="aos.html" title="Area of Circle">Area of + Circle</a> +</h5></div></div></div> +<p> + Generic numeric programming employs templates to use the same code for + different floating-point types and functions. Consider the area of a + circle a of radius r, given by + </p> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>a = π * r<sup>2</sup></em></span> + </p></blockquote></div> +<p> + The area of a circle can be computed in generic programming using Boost.Math + for the constant π as shown below: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">area_of_a_circle</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">r</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> + <span class="keyword">return</span> <span class="identifier">pi</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + It is possible to use <code class="computeroutput"><span class="identifier">area_of_a_circle</span><span class="special">()</span></code> with built-in floating-point types + as well as floating-point types from Boost.Multiprecision. In particular, + consider a system with 4-byte single-precision float, 8-byte double-precision + double and also the <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> + data type from Boost.Multiprecision with 50 decimal digits of precision. + </p> +<p> + We can compute and print the approximate area of a circle with radius + 123/100 for <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> + with the program below. + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">;</span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">char</span><span class="special">**)</span> +<span class="special">{</span> + <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">r_f</span><span class="special">(</span><span class="keyword">float</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">);</span> + <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">a_f</span> <span class="special">=</span> <span class="identifier">area_of_a_circle</span><span class="special">(</span><span class="identifier">r_f</span><span class="special">);</span> + + <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">r_d</span><span class="special">(</span><span class="keyword">double</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">);</span> + <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">a_d</span> <span class="special">=</span> <span class="identifier">area_of_a_circle</span><span class="special">(</span><span class="identifier">r_d</span><span class="special">);</span> + + <span class="keyword">const</span> <span class="identifier">cpp_dec_float_50</span> <span class="identifier">r_mp</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">);</span> + <span class="keyword">const</span> <span class="identifier">cpp_dec_float_50</span> <span class="identifier">a_mp</span> <span class="special">=</span> <span class="identifier">area_of_a_circle</span><span class="special">(</span><span class="identifier">r_mp</span><span class="special">);</span> + + <span class="comment">// 4.75292</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">float</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">a_f</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 4.752915525616</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">a_d</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 4.7529155256159981904701331745635599135018975843146</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">a_mp</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + In the next example we'll look at calling both standard library and Boost.Math + functions from within generic code. We'll also show how to cope with + template arguments which are expression-templates rather than number + types. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jel.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html new file mode 100644 index 0000000000..73a46081dd --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html @@ -0,0 +1,158 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Calculating an Integral</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="nd.html" title="Calculating a Derivative"> +<link rel="next" href="poly_eg.html" title="Polynomial Evaluation"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="nd.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="poly_eg.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.floats.fp_eg.gi"></a><a class="link" href="gi.html" title="Calculating an Integral">Calculating + an Integral</a> +</h5></div></div></div> +<p> + Similar to the generic derivative example, we can calculate integrals + in a similar manner: + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">function_type</span><span class="special">></span> +<span class="keyword">inline</span> <span class="identifier">value_type</span> <span class="identifier">integral</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">b</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">tol</span><span class="special">,</span> + <span class="identifier">function_type</span> <span class="identifier">func</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">unsigned</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">1U</span><span class="special">;</span> + + <span class="identifier">value_type</span> <span class="identifier">h</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">b</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">);</span> + <span class="identifier">value_type</span> <span class="identifier">I</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">func</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">b</span><span class="special">))</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">h</span> <span class="special">/</span> <span class="number">2</span><span class="special">);</span> + + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">0U</span><span class="special">;</span> <span class="identifier">k</span> <span class="special"><</span> <span class="number">8U</span><span class="special">;</span> <span class="identifier">k</span><span class="special">++)</span> + <span class="special">{</span> + <span class="identifier">h</span> <span class="special">/=</span> <span class="number">2</span><span class="special">;</span> + + <span class="identifier">value_type</span> <span class="identifier">sum</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">1U</span><span class="special">;</span> <span class="identifier">j</span> <span class="special"><=</span> <span class="identifier">n</span><span class="special">;</span> <span class="identifier">j</span><span class="special">++)</span> + <span class="special">{</span> + <span class="identifier">sum</span> <span class="special">+=</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">value_type</span><span class="special">((</span><span class="identifier">j</span> <span class="special">*</span> <span class="number">2</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">h</span><span class="special">));</span> + <span class="special">}</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">I0</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">;</span> + <span class="identifier">I</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">I</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">h</span> <span class="special">*</span> <span class="identifier">sum</span><span class="special">);</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">ratio</span> <span class="special">=</span> <span class="identifier">I0</span> <span class="special">/</span> <span class="identifier">I</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">delta</span> <span class="special">=</span> <span class="identifier">ratio</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">delta_abs</span> <span class="special">=</span> <span class="special">((</span><span class="identifier">delta</span> <span class="special"><</span> <span class="number">0</span><span class="special">)</span> <span class="special">?</span> <span class="special">-</span><span class="identifier">delta</span> <span class="special">:</span> <span class="identifier">delta</span><span class="special">);</span> + + <span class="keyword">if</span><span class="special">((</span><span class="identifier">k</span> <span class="special">></span> <span class="number">1U</span><span class="special">)</span> <span class="special">&&</span> <span class="special">(</span><span class="identifier">delta_abs</span> <span class="special"><</span> <span class="identifier">tol</span><span class="special">))</span> + <span class="special">{</span> + <span class="keyword">break</span><span class="special">;</span> + <span class="special">}</span> + + <span class="identifier">n</span> <span class="special">*=</span> <span class="number">2U</span><span class="special">;</span> + <span class="special">}</span> + + <span class="keyword">return</span> <span class="identifier">I</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + The following sample program shows how the function can be called, we + begin by defining a function object, which when integrated should yield + the Bessel J function: + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cyl_bessel_j_integral_rep</span> +<span class="special">{</span> +<span class="keyword">public</span><span class="special">:</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&</span> <span class="identifier">X</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">n</span><span class="special">(</span><span class="identifier">N</span><span class="special">),</span> <span class="identifier">x</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span> <span class="special">{</span> <span class="special">}</span> + + <span class="identifier">value_type</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span> + <span class="special">{</span> + <span class="comment">// pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt]</span> + <span class="keyword">return</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">t</span><span class="special">)</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">n</span> <span class="special">*</span> <span class="identifier">t</span><span class="special">));</span> + <span class="special">}</span> + +<span class="keyword">private</span><span class="special">:</span> + <span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">x</span><span class="special">;</span> +<span class="special">};</span> +</pre> +<pre class="programlisting"> <span class="comment">/* The function can now be called as follows: */</span> +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">char</span><span class="special">**)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> <span class="identifier">mp_type</span><span class="special">;</span> + + <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">j2_f</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="number">0.0F</span><span class="special">,</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> + <span class="number">0.01F</span><span class="special">,</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="number">1.23F</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="keyword">float</span><span class="special">>();</span> + + <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">j2_d</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="number">0.0</span><span class="special">,</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> + <span class="number">0.0001</span><span class="special">,</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="number">1.23</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>();</span> + + <span class="keyword">const</span> <span class="identifier">mp_type</span> <span class="identifier">j2_mp</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="identifier">mp_type</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> + <span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>(),</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="number">1.0E-20</span><span class="special">),</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="identifier">mp_type</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>();</span> + + <span class="comment">// 0.166369</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">float</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_f</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 0.166369383786814</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_d</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 0.16636938378681407351267852431513159437103348245333</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_mp</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">//</span> + <span class="comment">// Print true value for comparison:</span> + <span class="comment">// 0.166369383786814073512678524315131594371033482453329</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">mp_type</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="nd.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="poly_eg.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html new file mode 100644 index 0000000000..ce943eed69 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html @@ -0,0 +1,215 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Defining a Special Function.</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="aos.html" title="Area of Circle"> +<link rel="next" href="nd.html" title="Calculating a Derivative"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td 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title="Defining a Special Function.">Defining + a Special Function.</a> +</h5></div></div></div> +<p> + In this example we'll show several implementations of the <a href="http://mathworld.wolfram.com/LambdaFunction.html" target="_top">Jahnke + and Emden Lambda function</a>, each implementation a little more + sophisticated than the last. + </p> +<p> + The Jahnke-Emden Lambda function is defined by the equation: + </p> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>JahnkeEmden(v, z) = Γ(v+1) * J<sub>v</sub>(z) / (z / 2)<sup>v</sup></em></span> + </p></blockquote></div> +<p> + If we were to implement this at double precision using Boost.Math's facilities + for the Gamma and Bessel function calls it would look like this: + </p> +<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">JEL1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">z</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">z</span> <span class="special">/</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + Calling this function as: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">JEL1</span><span class="special">(</span><span class="number">2.5</span><span class="special">,</span> <span class="number">0.5</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Yields the output: + </p> +<pre class="programlisting">9.822663964796047e-001</pre> +<p> + Now let's implement the function again, but this time using the multiprecision + type <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> + as the argument type: + </p> +<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> + <span class="identifier">JEL2</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> <span class="identifier">z</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">z</span> <span class="special">/</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + The implementation is almost the same as before, but with one key difference + - we can no longer call <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code>, + instead we must call the version inside the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span></code> + namespace. In point of fact, we could have omitted the namespace prefix + on the call to <code class="computeroutput"><span class="identifier">pow</span></code> since + the right overload would have been found via <a href="http://en.wikipedia.org/wiki/Argument-dependent_name_lookup" target="_top">argument + dependent lookup</a> in any case. + </p> +<p> + Note also that the first argument to <code class="computeroutput"><span class="identifier">pow</span></code> + along with the argument to <code class="computeroutput"><span class="identifier">tgamma</span></code> + in the above code are actually expression templates. The <code class="computeroutput"><span class="identifier">pow</span></code> and <code class="computeroutput"><span class="identifier">tgamma</span></code> + functions will handle these arguments just fine. + </p> +<p> + Here's an example of how the function may be called: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">JEL2</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">2.5</span><span class="special">),</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">0.5</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Which outputs: + </p> +<pre class="programlisting">9.82266396479604757017335009796882833995903762577173e-01</pre> +<p> + Now that we've seen some non-template examples, lets repeat the code + again, but this time as a template that can be called either with a builtin + type (<code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> etc), or with a multiprecision + type: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Float</span><span class="special">></span> +<span class="identifier">Float</span> <span class="identifier">JEL3</span><span class="special">(</span><span class="identifier">Float</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">Float</span> <span class="identifier">z</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z</span> <span class="special">/</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + Once again the code is almost the same as before, but the call to <code class="computeroutput"><span class="identifier">pow</span></code> has changed yet again. We need + the call to resolve to either <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code> + (when the argument is a builtin type), or to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">pow</span></code> + (when the argument is a multiprecision type). We do that by making the + call unqualified so that versions of <code class="computeroutput"><span class="identifier">pow</span></code> + defined in the same namespace as type <code class="computeroutput"><span class="identifier">Float</span></code> + are found via argument dependent lookup, while the <code class="computeroutput"><span class="keyword">using</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code> directive makes the standard library + versions visible for builtin floating point types. + </p> +<p> + Let's call the function with both <code class="computeroutput"><span class="keyword">double</span></code> + and multiprecision arguments: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">JEL3</span><span class="special">(</span><span class="number">2.5</span><span class="special">,</span> <span class="number">0.5</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">JEL3</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">2.5</span><span class="special">),</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">0.5</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Which outputs: + </p> +<pre class="programlisting">9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +</pre> +<p> + Unfortunately there is a problem with this version: if we were to call + it like this: + </p> +<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> <span class="identifier">v</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">z</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span> +<span class="identifier">JEL3</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">,</span> <span class="identifier">z</span><span class="special">);</span> +</pre> +<p> + Then we would get a long and inscrutable error message from the compiler: + the problem here is that the first argument to <code class="computeroutput"><span class="identifier">JEL3</span></code> + is not a number type, but an expression template. We could obviously + add a typecast to fix the issue: + </p> +<pre class="programlisting"><span class="identifier">JEL</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">),</span> <span class="identifier">z</span><span class="special">);</span> +</pre> +<p> + However, if we want the function JEL to be truly reusable, then a better + solution might be preferred. To achieve this we can borrow some code + from Boost.Math which calculates the return type of mixed-argument functions, + here's how the new code looks now: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Float1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Float2</span><span class="special">></span> +<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">Float1</span><span class="special">,</span> <span class="identifier">Float2</span><span class="special">>::</span><span class="identifier">type</span> + <span class="identifier">JEL4</span><span class="special">(</span><span class="identifier">Float1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">Float2</span> <span class="identifier">z</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z</span> <span class="special">/</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + As you can see the two arguments to the function are now separate template + types, and the return type is computed using the <code class="computeroutput"><span class="identifier">promote_args</span></code> + metafunction from Boost.Math. + </p> +<p> + Now we can call: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_100</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">JEL4</span><span class="special">(</span><span class="identifier">cpp_dec_float_100</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">,</span> <span class="identifier">cpp_dec_float_100</span><span class="special">(</span><span class="number">0.5</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + And get 100 digits of output: + </p> +<pre class="programlisting">9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01</pre> +<p> + As a bonus, we can now call the function not just with expression templates, + but with other mixed types as well: for example <code class="computeroutput"><span class="keyword">float</span></code> + and <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">int</span></code> and <code class="computeroutput"><span class="keyword">double</span></code>, + and the correct return type will be computed in each case. + </p> +<p> + Note that while in this case we didn't have to change the body of the + function, in the general case any function like this which creates local + variables internally would have to use <code class="computeroutput"><span class="identifier">promote_args</span></code> + to work out what type those variables should be, for example: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Float1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Float2</span><span class="special">></span> +<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">Float1</span><span class="special">,</span> <span class="identifier">Float2</span><span class="special">>::</span><span class="identifier">type</span> + <span class="identifier">JEL5</span><span class="special">(</span><span class="identifier">Float1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">Float2</span> <span class="identifier">z</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">Float1</span><span class="special">,</span> <span class="identifier">Float2</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">variable_type</span><span class="special">;</span> + <span class="identifier">variable_type</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z</span> <span class="special">/</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">t</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="aos.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="nd.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html new file mode 100644 index 0000000000..373dc97e74 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html @@ -0,0 +1,199 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Calculating a Derivative</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="jel.html" title="Defining a Special Function."> +<link rel="next" href="gi.html" title="Calculating an Integral"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="jel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gi.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.floats.fp_eg.nd"></a><a class="link" href="nd.html" title="Calculating a Derivative">Calculating + a Derivative</a> +</h5></div></div></div> +<p> + In this example we'll add even more power to generic numeric programming + using not only different floating-point types but also function objects + as template parameters. Consider some well-known central difference rules + for numerically computing the first derivative of a function <span class="emphasis"><em>f′(x)</em></span> + with <span class="emphasis"><em>x ∈ ℜ</em></span>: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../../floating_point_eg1.png"></span> + </p> +<p> + Where the difference terms <span class="emphasis"><em>m<sub>n</sub></em></span> are given by: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../../floating_point_eg2.png"></span> + </p> +<p> + and <span class="emphasis"><em>dx</em></span> is the step-size of the derivative. + </p> +<p> + The third formula in Equation 1 is a three-point central difference rule. + It calculates the first derivative of <span class="emphasis"><em>f′(x)</em></span> to <span class="emphasis"><em>O(dx<sup>6</sup>)</em></span>, + where <span class="emphasis"><em>dx</em></span> is the given step-size. For example, if + the step-size is 0.01 this derivative calculation has about 6 decimal + digits of precision - just about right for the 7 decimal digits of single-precision + float. Let's make a generic template subroutine using this three-point + central difference rule. In particular: + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">function_type</span><span class="special">></span> + <span class="identifier">value_type</span> <span class="identifier">derivative</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">dx</span><span class="special">,</span> <span class="identifier">function_type</span> <span class="identifier">func</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// Compute d/dx[func(*first)] using a three-point</span> + <span class="comment">// central difference rule of O(dx^6).</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">dx1</span> <span class="special">=</span> <span class="identifier">dx</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">dx2</span> <span class="special">=</span> <span class="identifier">dx1</span> <span class="special">*</span> <span class="number">2</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">dx3</span> <span class="special">=</span> <span class="identifier">dx1</span> <span class="special">*</span> <span class="number">3</span><span class="special">;</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">m1</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">dx1</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">dx1</span><span class="special">))</span> <span class="special">/</span> <span class="number">2</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">m2</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">dx2</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">dx2</span><span class="special">))</span> <span class="special">/</span> <span class="number">4</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">m3</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">dx3</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">dx3</span><span class="special">))</span> <span class="special">/</span> <span class="number">6</span><span class="special">;</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">fifteen_m1</span> <span class="special">=</span> <span class="number">15</span> <span class="special">*</span> <span class="identifier">m1</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">six_m2</span> <span class="special">=</span> <span class="number">6</span> <span class="special">*</span> <span class="identifier">m2</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">ten_dx1</span> <span class="special">=</span> <span class="number">10</span> <span class="special">*</span> <span class="identifier">dx1</span><span class="special">;</span> + + <span class="keyword">return</span> <span class="special">((</span><span class="identifier">fifteen_m1</span> <span class="special">-</span> <span class="identifier">six_m2</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">m3</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">ten_dx1</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">derivative</span><span class="special">()</span></code> + template function can be used to compute the first derivative of any + function to <span class="emphasis"><em>O(dx<sup>6</sup>)</em></span>. For example, consider the first + derivative of <span class="emphasis"><em>sin(x)</em></span> evaluated at <span class="emphasis"><em>x = + π/3</em></span>. In other words, + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../../floating_point_eg3.png"></span> + </p> +<p> + The code below computes the derivative in Equation 3 for float, double + and boost's multiple-precision type cpp_dec_float_50. + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">char</span><span class="special">**)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// We'll pass a function pointer for the function object passed to derivative,</span> + <span class="comment">// the typecast is needed to select the correct overload of std::sin:</span> + <span class="comment">//</span> + <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">d_f</span> <span class="special">=</span> <span class="identifier">derivative</span><span class="special">(</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">float</span><span class="special">>()</span> <span class="special">/</span> <span class="number">3</span><span class="special">,</span> + <span class="number">0.01F</span><span class="special">,</span> + <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">float</span><span class="special">(*)(</span><span class="keyword">float</span><span class="special">)>(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">)</span> + <span class="special">);</span> + + <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">d_d</span> <span class="special">=</span> <span class="identifier">derivative</span><span class="special">(</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>()</span> <span class="special">/</span> <span class="number">3</span><span class="special">,</span> + <span class="number">0.001</span><span class="special">,</span> + <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">double</span><span class="special">(*)(</span><span class="keyword">double</span><span class="special">)>(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">)</span> + <span class="special">);</span> + <span class="comment">//</span> + <span class="comment">// In the cpp_dec_float_50 case, the sin function is multiply overloaded</span> + <span class="comment">// to handle expression templates etc. As a result it's hard to take its</span> + <span class="comment">// address without knowing about its implementation details. We'll use a </span> + <span class="comment">// C++11 lambda expression to capture the call.</span> + <span class="comment">// We also need a typecast on the first argument so we don't accidentally pass</span> + <span class="comment">// an expression template to a template function:</span> + <span class="comment">//</span> + <span class="keyword">const</span> <span class="identifier">cpp_dec_float_50</span> <span class="identifier">d_mp</span> <span class="special">=</span> <span class="identifier">derivative</span><span class="special">(</span> + <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>()</span> <span class="special">/</span> <span class="number">3</span><span class="special">),</span> + <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">1.0E-9</span><span class="special">),</span> + <span class="special">[](</span><span class="keyword">const</span> <span class="identifier">cpp_dec_float_50</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">-></span> <span class="identifier">cpp_dec_float_50</span> + <span class="special">{</span> + <span class="keyword">return</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> + <span class="special">}</span> + <span class="special">);</span> + + <span class="comment">// 5.000029e-001</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">float</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">d_f</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 4.999999999998876e-001</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">d_d</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// 4.99999999999999999999999999999999999999999999999999e-01</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">d_mp</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + The expected value of the derivative is 0.5. This central difference + rule in this example is ill-conditioned, meaning it suffers from slight + loss of precision. With that in mind, the results agree with the expected + value of 0.5. + </p> +<p> + We can take this a step further and use our derivative function to compute + a partial derivative. For example if we take the incomplete gamma function + <span class="emphasis"><em>P(a, z)</em></span>, and take the derivative with respect to + <span class="emphasis"><em>z</em></span> at <span class="emphasis"><em>(2,2)</em></span> then we can calculate + the result as shown below, for good measure we'll compare with the "correct" + result obtained from a call to <span class="emphasis"><em>gamma_p_derivative</em></span>, + the results agree to approximately 44 digits: + </p> +<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">gd</span> <span class="special">=</span> <span class="identifier">derivative</span><span class="special">(</span> + <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> + <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">1.0E-9</span><span class="special">),</span> + <span class="special">[](</span><span class="keyword">const</span> <span class="identifier">cpp_dec_float_50</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">-></span><span class="identifier">cpp_dec_float_50</span> + <span class="special">{</span> + <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_p</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">x</span><span class="special">);</span> + <span class="special">}</span> +<span class="special">);</span> +<span class="comment">// 2.70670566473225383787998989944968806815263091819151e-01</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">gd</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="comment">// 2.70670566473225383787998989944968806815253190143120e-01</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_p_derivative</span><span class="special">(</span><span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">cpp_dec_float_50</span><span class="special">(</span><span class="number">2</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="jel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gi.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html new file mode 100644 index 0000000000..fd8b5ca300 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html @@ -0,0 +1,152 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Polynomial Evaluation</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="gi.html" title="Calculating an Integral"> +<link rel="next" href="../../interval.html" title="Interval Number Types"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a 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name="boost_multiprecision.tut.floats.fp_eg.poly_eg"></a><a class="link" href="poly_eg.html" title="Polynomial Evaluation">Polynomial + Evaluation</a> +</h5></div></div></div> +<p> + In this example we'll look at polynomial evaluation, this is not only + an important use case, but it's one that <code class="computeroutput"><span class="identifier">number</span></code> + performs particularly well at because the expression templates <span class="emphasis"><em>completely + eliminate all temporaries</em></span> from a <a href="http://en.wikipedia.org/wiki/Horner%27s_method" target="_top">Horner + polynomial evaluation scheme</a>. + </p> +<p> + The following code evaluates <code class="computeroutput"><span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> as a polynomial, accurate to at least + 64 decimal places: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">64</span><span class="special">></span> <span class="special">></span> <span class="identifier">mp_type</span><span class="special">;</span> + +<span class="identifier">mp_type</span> <span class="identifier">mysin</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mp_type</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// Approximation of sin(x * pi/2) for -1 <= x <= 1, using an order 63 polynomial.</span> + <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">,</span> <span class="number">32U</span><span class="special">></span> <span class="identifier">coefs</span> <span class="special">=</span> + <span class="special">{{</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+1.5707963267948966192313216916397514420985846996875529104874722961539082031431044993140174126711"</span><span class="special">),</span> <span class="comment">//"),</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-0.64596409750624625365575656389794573337969351178927307696134454382929989411386887578263960484"</span><span class="special">),</span> <span class="comment">// ^3</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+0.07969262624616704512050554949047802252091164235106119545663865720995702920146198554317279"</span><span class="special">),</span> <span class="comment">// ^5</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-0.0046817541353186881006854639339534378594950280185010575749538605102665157913157426229824"</span><span class="special">),</span> <span class="comment">// ^7</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+0.00016044118478735982187266087016347332970280754062061156858775174056686380286868007443"</span><span class="special">),</span> <span class="comment">// ^9</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-3.598843235212085340458540018208389404888495232432127661083907575106196374913134E-6"</span><span class="special">),</span> <span class="comment">// ^11</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+5.692172921967926811775255303592184372902829756054598109818158853197797542565E-8"</span><span class="special">),</span> <span class="comment">// ^13</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-6.688035109811467232478226335783138689956270985704278659373558497256423498E-10"</span><span class="special">),</span> <span class="comment">// ^15</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+6.066935731106195667101445665327140070166203261129845646380005577490472E-12"</span><span class="special">),</span> <span class="comment">// ^17</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-4.377065467313742277184271313776319094862897030084226361576452003432E-14"</span><span class="special">),</span> <span class="comment">// ^19</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+2.571422892860473866153865950420487369167895373255729246889168337E-16"</span><span class="special">),</span> <span class="comment">// ^21</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-1.253899540535457665340073300390626396596970180355253776711660E-18"</span><span class="special">),</span> <span class="comment">// ^23</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+5.15645517658028233395375998562329055050964428219501277474E-21"</span><span class="special">),</span> <span class="comment">// ^25</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-1.812399312848887477410034071087545686586497030654642705E-23"</span><span class="special">),</span> <span class="comment">// ^27</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+5.50728578652238583570585513920522536675023562254864E-26"</span><span class="special">),</span> <span class="comment">// ^29</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-1.461148710664467988723468673933026649943084902958E-28"</span><span class="special">),</span> <span class="comment">// ^31</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+3.41405297003316172502972039913417222912445427E-31"</span><span class="special">),</span> <span class="comment">// ^33</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-7.07885550810745570069916712806856538290251E-34"</span><span class="special">),</span> <span class="comment">// ^35</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+1.31128947968267628970845439024155655665E-36"</span><span class="special">),</span> <span class="comment">// ^37</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-2.18318293181145698535113946654065918E-39"</span><span class="special">),</span> <span class="comment">// ^39</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+3.28462680978498856345937578502923E-42"</span><span class="special">),</span> <span class="comment">// ^41</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-4.48753699028101089490067137298E-45"</span><span class="special">),</span> <span class="comment">// ^43</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+5.59219884208696457859353716E-48"</span><span class="special">),</span> <span class="comment">// ^45</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-6.38214503973500471720565E-51"</span><span class="special">),</span> <span class="comment">// ^47</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+6.69528558381794452556E-54"</span><span class="special">),</span> <span class="comment">// ^49</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-6.47841373182350206E-57"</span><span class="special">),</span> <span class="comment">// ^51</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+5.800016389666445E-60"</span><span class="special">),</span> <span class="comment">// ^53</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-4.818507347289E-63"</span><span class="special">),</span> <span class="comment">// ^55</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+3.724683686E-66"</span><span class="special">),</span> <span class="comment">// ^57</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-2.6856479E-69"</span><span class="special">),</span> <span class="comment">// ^59</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"+1.81046E-72"</span><span class="special">),</span> <span class="comment">// ^61</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="string">"-1.133E-75"</span><span class="special">),</span> <span class="comment">// ^63</span> + <span class="special">}};</span> + + <span class="keyword">const</span> <span class="identifier">mp_type</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">x</span> <span class="special">*</span> <span class="number">2</span> <span class="special">/</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>();</span> + <span class="keyword">const</span> <span class="identifier">mp_type</span> <span class="identifier">x2</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">v</span> <span class="special">*</span> <span class="identifier">v</span><span class="special">);</span> + <span class="comment">//</span> + <span class="comment">// Polynomial evaluation follows, if mp_type allocates memory then</span> + <span class="comment">// just one such allocation occurs - to initialize the variable "sum" -</span> + <span class="comment">// and no temporaries are created at all.</span> + <span class="comment">//</span> + <span class="keyword">const</span> <span class="identifier">mp_type</span> <span class="identifier">sum</span> <span class="special">=</span> <span class="special">(((((((((((((((((((((((((((((((</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">31U</span><span class="special">]</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">30U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">29U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">28U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">27U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">26U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">25U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">24U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">23U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">22U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">21U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">20U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">19U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">18U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">17U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">16U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">15U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">14U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">13U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">12U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">11U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">10U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">9U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">8U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">7U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">6U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">5U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">4U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">3U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">2U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">1U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">x2</span> <span class="special">+</span> <span class="identifier">coefs</span><span class="special">[</span><span class="number">0U</span><span class="special">])</span> + <span class="special">*</span> <span class="identifier">v</span><span class="special">;</span> + + <span class="keyword">return</span> <span class="identifier">sum</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Calling the function like so: + </p> +<pre class="programlisting"><span class="identifier">mp_type</span> <span class="identifier">pid4</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>()</span> <span class="special">/</span> <span class="number">4</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span> <span class="special">::</span><span class="identifier">mp_type</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mysin</span><span class="special">(</span><span class="identifier">pid4</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Yields the expected output: + </p> +<pre class="programlisting">7.0710678118654752440084436210484903928483593768847403658833986900e-01</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gi.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../interval.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/gmp_float.html new file mode 100644 index 0000000000..748ab6ff86 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/gmp_float.html @@ -0,0 +1,194 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>gmp_float</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../floats.html" title="Floating Point Numbers"> +<link rel="prev" href="cpp_dec_float.html" title="cpp_dec_float"> +<link rel="next" href="mpfr_float.html" title="mpfr_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td 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href="gmp_float.html" title="gmp_float">gmp_float</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">gmp_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_100</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_500</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_1000</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">gmp_float</span></code> back-end + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code> + : it acts as a thin wrapper around the <a href="http://gmplib.org" target="_top">GMP</a> + <code class="computeroutput"><span class="identifier">mpf_t</span></code> to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. + </p> +<p> + Type <code class="computeroutput"><span class="identifier">gmp_float</span></code> can be used + at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpf_float provides a variable precision type + whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s + member functions. + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + This type only provides standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support when the precision is fixed at compile time. + </p></td></tr> +</table></div> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable + from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>, + <code class="computeroutput"><span class="identifier">mpq_t</span></code>. + </li> +<li class="listitem"> + The <code class="computeroutput"><span class="identifier">number</span></code> wrappers + around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>, + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code>. + </li> +</ul></div> +<p> + It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpf_t</span></code> + via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> + member function of <code class="computeroutput"><span class="identifier">gmp_float</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">gmp_float</span></code>s + have the value zero (this is the <a href="http://gmplib.org" target="_top">GMP</a> + library's default behavior). + </li> +<li class="listitem"> + No changes are made to the <a href="http://gmplib.org" target="_top">GMP</a> + library's global settings, so this type can be safely mixed with existing + <a href="http://gmplib.org" target="_top">GMP</a> code. + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +<li class="listitem"> + It is not possible to round-trip objects of this type to and from a + string and get back exactly the same value. This appears to be a limitation + of <a href="http://gmplib.org" target="_top">GMP</a>. + </li> +<li class="listitem"> + Since the underlying <a href="http://gmplib.org" target="_top">GMP</a> types + have no notion of infinities or NaN's, care should be taken to avoid + numeric overflow or division by zero. That latter will result in a + std::overflow_error being thrown, while generating excessively large + exponents may result in instability of the underlying <a href="http://gmplib.org" target="_top">GMP</a> + library (in testing, converting a number with an excessively large + or small exponent to a string caused <a href="http://gmplib.org" target="_top">GMP</a> + to segfault). + </li> +<li class="listitem"> + This type can equally be used with <a href="http://mpir.org/" target="_top">MPIR</a> + as the underlying implementation - indeed that is the recommended option + on Win32. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.floats.gmp_float.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.floats.gmp_float.gmp_example"></a></span><a class="link" href="gmp_float.html#boost_multiprecision.tut.floats.gmp_float.gmp_example"> GMP example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at variable precision and limited standard library support:</span> + <span class="identifier">mpf_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span> + + <span class="comment">// Operations at fixed precision and full standard library support:</span> + <span class="identifier">mpf_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mpf_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> + <span class="comment">// We can also use any function from Boost.Math:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// These even work when the argument is an expression template:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// Access the underlying representation:</span> + <span class="identifier">mpf_t</span> <span class="identifier">f</span><span class="special">;</span> + <span class="identifier">mpf_init</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> + <span class="identifier">mpf_set</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> + <span class="identifier">mpf_clear</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_dec_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mpfr_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/mpfr_float.html new file mode 100644 index 0000000000..3acd47f141 --- /dev/null +++ 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title="mpfr_float">mpfr_float</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">enum</span> <span class="identifier">mpfr_allocation_type</span> +<span class="special">{</span> + <span class="identifier">allocate_stack</span><span class="special">,</span> + <span class="identifier">allocate_dynamic</span> +<span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">mpfr_allocation_type</span> <span class="identifier">AllocateType</span> <span class="special">=</span> <span class="identifier">allocate_dynamic</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">mpfr_float_backend</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_100</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_500</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_1000</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_stack</span><span class="special">></span> <span class="special">></span> <span class="identifier">static_mpfr_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">,</span> <span class="identifier">allocate_stack</span><span class="special">></span> <span class="special">></span> <span class="identifier">static_mpfr_float_100</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> + type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: + It acts as a thin wrapper around the <a href="http://www.mpfr.org" target="_top">MPFR</a> + <code class="computeroutput"><span class="identifier">mpfr_t</span></code> to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision. + </p> +<p> + Type <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> + can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpfr_float provides a variable precision type + whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s + member functions. + </p> +<p> + In addition the second template parameter lets you choose between dynamic + allocation (the default, and uses MPFR's normal allocation routines), or + stack allocation (where all the memory required for the underlying data + types is stored within <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>). + The latter option can result in significantly faster code, at the expense + of growing the size of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>. + It can only be used at fixed precision, and should only be used for lower + digit counts. Note that we can not guarantee that using <code class="computeroutput"><span class="identifier">allocate_stack</span></code> + won't cause any calls to mpfr's allocation routines, as mpfr may call these + inside it's own code. The following table gives an idea of the performance + tradeoff's at 50 decimal digits precision<a href="#ftn.boost_multiprecision.tut.floats.mpfr_float.f0" class="footnote" name="boost_multiprecision.tut.floats.mpfr_float.f0"><sup class="footnote">[2]</sup></a>: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Type + </p> + </th> +<th> + <p> + Bessel function evaluation, relative times + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_static</span><span class="special">>,</span> + <span class="identifier">et_on</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.0 (5.5s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_static</span><span class="special">>,</span> + <span class="identifier">et_off</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.05 (5.8s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_dynamic</span><span class="special">>,</span> + <span class="identifier">et_on</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.05 (5.8s) + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_dynamic</span><span class="special">>,</span> + <span class="identifier">et_off</span><span class="special">></span></code> + </p> + </td> +<td> + <p> + 1.16 (6.4s) + </p> + </td> +</tr> +</tbody> +</table></div> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + This type only provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support when the precision is fixed at compile time. + </p></td></tr> +</table></div> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable + from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>, + <code class="computeroutput"><span class="identifier">mpq_t</span></code>. + </li> +<li class="listitem"> + The <a href="http://www.mpfr.org" target="_top">MPFR</a> native type <code class="computeroutput"><span class="identifier">mpfr_t</span></code>. + </li> +<li class="listitem"> + The <code class="computeroutput"><span class="identifier">number</span></code> wrappers + around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code>. + </li> +</ul></div> +<p> + It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfr_t</span></code> + via the data() member function of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + A default constructed <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> + is set to a NaN (this is the default <a href="http://www.mpfr.org" target="_top">MPFR</a> + behavior). + </li> +<li class="listitem"> + All operations use round to nearest. + </li> +<li class="listitem"> + No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or + <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this + type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a> + or <a href="http://gmplib.org" target="_top">GMP</a> code. + </li> +<li class="listitem"> + The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a> + in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that + is the preferred option on Win32. + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + Division by zero results in an infinity. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.floats.mpfr_float.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.floats.mpfr_float.mpfr_example"></a></span><a class="link" href="mpfr_float.html#boost_multiprecision.tut.floats.mpfr_float.mpfr_example"> MPFR example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at variable precision and no numeric_limits support:</span> + <span class="identifier">mpfr_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">mpfr_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpfr_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span> + + <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> + <span class="identifier">mpfr_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mpfr_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> + <span class="comment">// We can also use any function from Boost.Math:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// These even work when the argument is an expression template:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">// Access the underlying data:</span> + <span class="identifier">mpfr_t</span> <span class="identifier">r</span><span class="special">;</span> + <span class="identifier">mpfr_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> + <span class="identifier">mpfr_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">GMP_RNDN</span><span class="special">);</span> + <span class="identifier">mpfr_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<div class="footnotes"> +<br><hr style="width:100; text-align:left;margin-left: 0"> +<div id="ftn.boost_multiprecision.tut.floats.mpfr_float.f0" class="footnote"><p><a href="#boost_multiprecision.tut.floats.mpfr_float.f0" class="para"><sup class="para">[2] </sup></a> + Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0 + </p></div> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float128.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/gen_int.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/gen_int.html new file mode 100644 index 0000000000..75effaa47f --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/gen_int.html @@ -0,0 +1,180 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Generic Integer Operations</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="mixed.html" title="Mixed Precision Arithmetic"> +<link rel="next" href="serial.html" title="Boost.Serialization Support"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mixed.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="serial.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.gen_int"></a><a class="link" href="gen_int.html" title="Generic Integer Operations">Generic Integer Operations</a> +</h3></div></div></div> +<p> + All of the <a class="link" href="../ref/number.html#boost_multiprecision.ref.number.integer_functions">non-member + integer operations</a> are overloaded for the built in integer types in + <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>. + Where these operations require a temporary increase in precision (such as + for powm), then if no built in type is available, a <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a> + of appropriate precision will be used. + </p> +<p> + Some of these functions are trivial, others use compiler intrinsics (where + available) to ensure optimal evaluation. + </p> +<p> + The overloaded functions are: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Multiplies two <code class="computeroutput"><span class="identifier">I2</span></code> values, + to produce a wider <code class="computeroutput"><span class="identifier">Integer</span></code> + result. + </p> +<p> + Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span> + <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span></code> without overflow or loss of precision + in the multiplication. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Adds two <code class="computeroutput"><span class="identifier">I2</span></code> values, to produce + a wider <code class="computeroutput"><span class="identifier">Integer</span></code> result. + </p> +<p> + Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span> + <span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span></code> without overflow or loss of precision + in the addition. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Subtracts two <code class="computeroutput"><span class="identifier">I2</span></code> values, + to produce a wider <code class="computeroutput"><span class="identifier">Integer</span></code> + result. + </p> +<p> + Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span> + <span class="identifier">a</span> <span class="special">-</span> <span class="identifier">b</span></code> without overflow or loss of precision + in the subtraction. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">m</span><span class="special">);</span> +</pre> +<p> + Returns b<sup>p</sup> % m. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> +</pre> +<p> + Sets <code class="computeroutput"><span class="identifier">q</span> <span class="special">=</span> + <span class="identifier">x</span> <span class="special">/</span> <span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">r</span> + <span class="special">=</span> <span class="identifier">x</span> <span class="special">%</span> <span class="identifier">y</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Integer2</span><span class="special">></span> +<span class="identifier">Integer2</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer1</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer2</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns x % val; + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + Returns the (zero-based) index of the least significant bit of <code class="computeroutput"><span class="identifier">x</span></code>. + </p> +<p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> if <code class="computeroutput"><span class="identifier">x</span> + <span class="special"><=</span> <span class="number">0</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +</pre> +<p> + Returns the (zero-based) index of the most significant bit of <code class="computeroutput"><span class="identifier">x</span></code>. + </p> +<p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> if <code class="computeroutput"><span class="identifier">x</span> + <span class="special"><=</span> <span class="number">0</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if bit <code class="computeroutput"><span class="identifier">index</span></code> is set in <code class="computeroutput"><span class="identifier">val</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Sets the <code class="computeroutput"><span class="identifier">index</span></code> bit in <code class="computeroutput"><span class="identifier">val</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Unsets the <code class="computeroutput"><span class="identifier">index</span></code> bit in + <code class="computeroutput"><span class="identifier">val</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> +</pre> +<p> + Flips the <code class="computeroutput"><span class="identifier">index</span></code> bit in <code class="computeroutput"><span class="identifier">val</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> +<span class="identifier">Integer</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> +</pre> +<p> + Returns the integer square root <code class="computeroutput"><span class="identifier">s</span></code> + of x and sets <code class="computeroutput"><span class="identifier">r</span></code> to the remainder + <span class="emphasis"><em>x - s<sup>2</sup></em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">-</span><span class="keyword">or</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">-</span><span class="identifier">type</span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">-</span><span class="keyword">or</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">-</span><span class="identifier">type</span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> +</pre> +<p> + The regular Miller-Rabin functions in <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">miller_rabin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + are defined in terms of the above generic operations, and so function equally + well for built in and multiprecision types. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="mixed.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="serial.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/input_output.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/input_output.html new file mode 100644 index 0000000000..d58ffe908c --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/input_output.html @@ -0,0 +1,185 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Input Output</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="limits/how_to_tell.html" title="How to Determine the Kind of a Number From std::numeric_limits"> +<link rel="next" href="../ref.html" title="Reference"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="limits/how_to_tell.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.input_output"></a><a class="link" href="input_output.html" title="Input Output">Input Output</a> +</h3></div></div></div> +<h5> +<a name="boost_multiprecision.tut.input_output.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.input_output.loopback_testing"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.loopback_testing">Loopback + testing</a> + </h5> +<p> + <span class="emphasis"><em>Loopback</em></span> or <span class="emphasis"><em>round-tripping</em></span> refers + to writing out a value as a decimal digit string using <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">iostream</span></code>, + usually to a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span></code>, and then reading the string + back in to another value, and confirming that the two values are identical. + A trivial example using <code class="computeroutput"><span class="keyword">float</span></code> + is: + </p> +<pre class="programlisting"><span class="keyword">float</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Value to round-trip.</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span> <span class="comment">// Read and write std::stringstream.</span> +<span class="identifier">ss</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> <span class="comment">// Ensure all potentially significant bits are output.</span> +<span class="identifier">ss</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">fmtflags</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">scientific</span><span class="special">));</span> <span class="comment">// Use scientific format.</span> +<span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Output to string.</span> +<span class="keyword">float</span> <span class="identifier">read</span><span class="special">;</span> <span class="comment">// Expected.</span> +<span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">read</span><span class="special">;</span> <span class="comment">// Read decimal digits string from stringstream.</span> +<span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">write</span><span class="special">,</span> <span class="identifier">read</span><span class="special">);</span> <span class="comment">// Should be the same.</span> +</pre> +<p> + and this can be run in a loop for all possible values of a 32-bit float. + For other floating-point types <code class="computeroutput"><span class="identifier">T</span></code>, + including built-in <code class="computeroutput"><span class="keyword">double</span></code>, it + takes far too long to test all values, so a reasonable test strategy is to + use a large number of random values. + </p> +<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">write</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span> +<span class="identifier">ss</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> <span class="comment">// Ensure all potentially significant bits are output.</span> +<span class="identifier">ss</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> <span class="comment">// Changed from default iostream format flags if desired.</span> +<span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Output to stringstream.</span> + +<span class="identifier">T</span> <span class="identifier">read</span><span class="special">;</span> +<span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">read</span><span class="special">;</span> <span class="comment">// Get read using operator>> from stringstream.</span> +<span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span> + +<span class="identifier">read</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">());</span> <span class="comment">// Get read by converting from decimal digits string representation of write.</span> +<span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span> + +<span class="identifier">read</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">write</span><span class="special">.</span><span class="identifier">str</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">f</span><span class="special">));</span> <span class="comment">// Get read using format specified when written.</span> +<span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span> +</pre> +<p> + The test at <a href="../../../../test/test_cpp_bin_float_io.cpp" target="_top">test_cpp_bin_float_io.cpp</a> + allows any floating-point type to be <span class="emphasis"><em>round_tripped</em></span> using + a wide range of fairly random values. It also includes tests compared a collection + of <a href="../../../../test/string_data.ipp" target="_top">stringdata</a> test cases + in a file. + </p> +<h5> +<a name="boost_multiprecision.tut.input_output.h1"></a> + <span class="phrase"><a name="boost_multiprecision.tut.input_output.comparing_with_output_using_buil"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.comparing_with_output_using_buil">Comparing + with output using Built-in types</a> + </h5> +<p> + One can make some comparisons with the output of + </p> +<pre class="programlisting"><span class="special"><</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">digit_count_2</span><span class="special">></span> <span class="special">></span> +</pre> +<p> + which has the same number of significant bits (53) as 64-bit double precision + floating-point. + </p> +<p> + However, although most outputs are identical, there are differences on some + platforms caused by the implementation-dependent behaviours allowed by the + C99 specification <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf" target="_top">C99 + ISO/IEC 9899:TC2</a>, incorporated by C++. + </p> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>"For e, E, f, F, g, and G conversions, if the number of + significant decimal digits is at most DECIMAL_DIG, then the result should + be correctly rounded. If the number of significant decimal digits is more + than DECIMAL_DIG but the source value is exactly representable with DECIMAL_DIG + digits, then the result should be an exact representation with trailing + zeros. Otherwise, the source value is bounded by two adjacent decimal strings + L < U, both having DECIMAL_DIG significant digits; the value of the + resultant decimal string D should satisfy L<= D <= U, with the extra + stipulation that the error should have a correct sign for the current rounding + direction."</em></span> + </p></blockquote></div> +<p> + So not only is correct rounding for the full number of digits not required, + but even if the <span class="bold"><strong>optional</strong></span> recommended practice + is followed, then the value of these last few digits is unspecified as long + as the value is within certain bounds. + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + Do not expect the output from different platforms to be <span class="bold"><strong>identical</strong></span>, + but <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>, <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> (and other backends) outputs + should be correctly rounded to the number of digits requested by the set + precision and format. + </p></td></tr> +</table></div> +<h5> +<a name="boost_multiprecision.tut.input_output.h2"></a> + <span class="phrase"><a name="boost_multiprecision.tut.input_output.macro_boost_mp_min_exponent_digi"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.macro_boost_mp_min_exponent_digi">Macro + BOOST_MP_MIN_EXPONENT_DIGITS</a> + </h5> +<p> + <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf" target="_top">C99 + Standard</a> for format specifiers, 7.19.6 Formatted input/output functions + requires: + </p> +<p> + "The exponent always contains at least two digits, and only as many + more digits as necessary to represent the exponent." + </p> +<p> + So to conform to the C99 standard (incorporated by C++) + </p> +<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">2</span> +</pre> +<p> + Confusingly, Microsoft (and MinGW) do not conform to this standard and provide + <span class="bold"><strong>at least three digits</strong></span>, for example <code class="computeroutput"><span class="number">1e+001</span></code>. So if you want the output to match + that from built-in floating-point types on compilers that use Microsofts + runtime then use: + </p> +<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">3</span> +</pre> +<p> + Also useful to get the minimum exponent field width is + </p> +<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">1</span> +</pre> +<p> + producing a compact output like <code class="computeroutput"><span class="number">2e+4</span></code>, + useful when conserving space is important. + </p> +<p> + Larger values are also supported, for example, value 4 for <code class="computeroutput"><span class="number">2e+0004</span></code> which may be useful to ensure that + columns line up. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="limits/how_to_tell.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ref.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/interval.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/interval.html new file mode 100644 index 0000000000..8e38ca6072 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/interval.html @@ -0,0 +1,47 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Interval Number Types</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="floats/fp_eg/poly_eg.html" title="Polynomial Evaluation"> +<link rel="next" href="interval/mpfi.html" title="mpfi_float"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="floats/fp_eg/poly_eg.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="interval/mpfi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.interval"></a><a class="link" href="interval.html" title="Interval Number Types">Interval Number Types</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"><dt><span class="section"><a href="interval/mpfi.html">mpfi_float</a></span></dt></dl></div> +<p> + There is one currently only one interval number type supported - <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="floats/fp_eg/poly_eg.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="interval/mpfi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/interval/mpfi.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/interval/mpfi.html new file mode 100644 index 0000000000..fcd2aea9d3 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/interval/mpfi.html @@ -0,0 +1,286 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>mpfi_float</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../interval.html" title="Interval Number Types"> +<link rel="prev" href="../interval.html" title="Interval Number Types"> +<link rel="next" href="../rational.html" title="Rational Number Types"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../interval.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interval.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.interval.mpfi"></a><a class="link" href="mpfi.html" title="mpfi_float">mpfi_float</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">mpfi_float_backend</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float_50</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_100</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_500</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float_1000</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> + type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: + It acts as a thin wrapper around the <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> + <code class="computeroutput"><span class="identifier">mpfi_t</span></code> to provide an real-number + type that is a drop-in replacement for the native C++ floating-point types, + but with much greater precision and implementing interval arithmetic. + </p> +<p> + Type <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> + can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> + template parameter, or at variable precision by setting the template argument + to zero. The typedefs mpfi_float_50, mpfi_float_100, mpfi_float_500, mpfi_float_1000 + provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision + respectively. The typedef mpfi_float provides a variable precision type + whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s + member functions. + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + This type only provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support when the precision is fixed at compile time. + </p></td></tr> +</table></div> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable + from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> + native type <code class="computeroutput"><span class="identifier">mpfi_t</span></code>. + </li> +<li class="listitem"> + The <code class="computeroutput"><span class="identifier">number</span></code> wrappers + around <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> + or <a href="http://www.mpfr.org" target="_top">MPFR</a>: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> + and <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>. + </li> +<li class="listitem"> + There is a two argument constructor taking two <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> + arguments specifying the interval. + </li> +</ul></div> +<p> + It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfi_t</span></code> + via the data() member function of <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + A default constructed <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> + is set to a NaN (this is the default <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> + behavior). + </li> +<li class="listitem"> + No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or + <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this + type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a> + or <a href="http://gmplib.org" target="_top">GMP</a> code. + </li> +<li class="listitem"> + The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a> + in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that + is the preferred option on Win32. + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid floating + point number. + </li> +<li class="listitem"> + Division by zero results in an infinity. + </li> +</ul></div> +<p> + There are some additional non member functions for working on intervals: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">lower</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns the lower end of the interval. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">upper</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns the upper end of the interval. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns the mid point of the interval. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">width</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> +</pre> +<p> + Returns the absolute width of the interval. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">intersect</span><span class="special">(</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns the interval which is the intersection of the <span class="emphasis"><em>a</em></span> + and <span class="emphasis"><em>b</em></span>. Returns an unspecified empty interval if there + is no such intersection. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">hull</span><span class="special">(</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns the interval which is the union of <span class="emphasis"><em>a</em></span> and + <span class="emphasis"><em>b</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">overlap</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the intervals + <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> overlap. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates1</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates2</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates1</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates2</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if point + <span class="emphasis"><em>a</em></span> is contained within the interval <span class="emphasis"><em>b</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">zero_in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the interval + <span class="emphasis"><em>a</em></span> contains the value zero. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> + is a subset of <span class="emphasis"><em>b</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">proper_subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> + is a proper subset of <span class="emphasis"><em>b</em></span>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> + is an empty interval, equivalent to <code class="computeroutput"><span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> + <span class="special"><</span> <span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">singleton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> +</pre> +<p> + Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">==</span> + <span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. + </p> +<h6> +<a name="boost_multiprecision.tut.interval.mpfi.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.interval.mpfi.mpfi_example"></a></span><a class="link" href="mpfi.html#boost_multiprecision.tut.interval.mpfi.mpfi_example"> MPFI + example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="comment">// Operations at variable precision and no numeric_limits support:</span> + <span class="identifier">mpfi_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span> + + <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> + <span class="identifier">mpfi_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mpfi_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">// We can use any C++ std lib function:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> + + <span class="comment">// Access the underlying data:</span> + <span class="identifier">mpfi_t</span> <span class="identifier">r</span><span class="special">;</span> + <span class="identifier">mpfi_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> + <span class="identifier">mpfi_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> + + <span class="comment">// Construct some explicit intervals and perform set operations:</span> + <span class="identifier">mpfi_float_50</span> <span class="identifier">i1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">),</span> <span class="identifier">i2</span><span class="special">(</span><span class="number">1.5</span><span class="special">,</span> <span class="number">2.5</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">hull</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">overlap</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">subset</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">mpfi_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../interval.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interval.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints.html new file mode 100644 index 0000000000..1c606ab903 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints.html @@ -0,0 +1,200 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Integer Types</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="../tut.html" title="Tutorial"> +<link rel="next" href="ints/cpp_int.html" title="cpp_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../tut.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ints/cpp_int.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.ints"></a><a class="link" href="ints.html" title="Integer Types">Integer Types</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="ints/cpp_int.html">cpp_int</a></span></dt> +<dt><span class="section"><a href="ints/gmp_int.html">gmp_int</a></span></dt> +<dt><span class="section"><a href="ints/tom_int.html">tom_int</a></span></dt> +<dt><span class="section"><a href="ints/egs.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="ints/egs/factorials.html">Factorials</a></span></dt> +<dt><span class="section"><a href="ints/egs/bitops.html">Bit Operations</a></span></dt> +</dl></dd> +</dl></div> +<p> + The following back-ends provide integer arithmetic: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend Type + </p> + </th> +<th> + <p> + Header + </p> + </th> +<th> + <p> + Radix + </p> + </th> +<th> + <p> + Dependencies + </p> + </th> +<th> + <p> + Pros + </p> + </th> +<th> + <p> + Cons + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cpp_int</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/cpp_int.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + None + </p> + </td> +<td> + <p> + Very versatile, Boost licensed, all C++ integer type which support + both <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> and fixed precision integer types. + </p> + </td> +<td> + <p> + Slower than <a href="http://gmplib.org" target="_top">GMP</a>, though + typically not as slow as <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a> + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">gmp_int</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/gmp.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://gmplib.org" target="_top">GMP</a> + </p> + </td> +<td> + <p> + Very fast and efficient back-end. + </p> + </td> +<td> + <p> + Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a> + library. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">tom_int</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/tommath.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a> + </p> + </td> +<td> + <p> + Public domain back-end with no licence restrictions. + </p> + </td> +<td> + <p> + Slower than <a href="http://gmplib.org" target="_top">GMP</a>. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../tut.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ints/cpp_int.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/cpp_int.html new file mode 100644 index 0000000000..ab836530fc --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -0,0 +1,385 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>cpp_int</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ints.html" title="Integer Types"> +<link rel="prev" href="../ints.html" title="Integer Types"> +<link rel="next" href="gmp_int.html" title="gmp_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a 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class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">typedef</span> <span class="identifier">unspecified</span><span class="special">-</span><span class="identifier">type</span> <span class="identifier">limb_type</span><span class="special">;</span> + +<span class="keyword">enum</span> <span class="identifier">cpp_integer_type</span> <span class="special">{</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span> <span class="special">};</span> +<span class="keyword">enum</span> <span class="identifier">cpp_int_check_type</span> <span class="special">{</span> <span class="identifier">checked</span><span class="special">,</span> <span class="identifier">unchecked</span> <span class="special">};</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">MinBits</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> + <span class="keyword">unsigned</span> <span class="identifier">MaxBits</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> + <span class="identifier">cpp_integer_type</span> <span class="identifier">SignType</span> <span class="special">=</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> + <span class="identifier">cpp_int_check_type</span> <span class="identifier">Checked</span> <span class="special">=</span> <span class="identifier">unchecked</span><span class="special">,</span> + <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span><span class="special"><</span><span class="identifier">limb_type</span><span class="special">></span> <span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cpp_int_backend</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// Expression templates default to et_off if there is no allocator:</span> +<span class="comment">//</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">MinBits</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">MaxBits</span><span class="special">,</span> <span class="identifier">cpp_integer_type</span> <span class="identifier">SignType</span><span class="special">,</span> <span class="identifier">cpp_int_check_type</span> <span class="identifier">Checked</span><span class="special">></span> +<span class="keyword">struct</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">MinBits</span><span class="special">,</span> <span class="identifier">MaxBits</span><span class="special">,</span> <span class="identifier">SignType</span><span class="special">,</span> <span class="identifier">Checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> +<span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_off</span><span class="special">;</span> <span class="special">};</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><></span> <span class="special">></span> <span class="identifier">cpp_int</span><span class="special">;</span> <span class="comment">// arbitrary precision integer</span> +<span class="keyword">typedef</span> <span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><></span> <span class="special">></span> <span class="identifier">cpp_rational_backend</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_rational_backend</span><span class="special">></span> <span class="identifier">cpp_rational</span><span class="special">;</span> <span class="comment">// arbitrary precision rational number</span> + +<span class="comment">// Fixed precision unsigned types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">uint1024_t</span><span class="special">;</span> + +<span class="comment">// Fixed precision signed types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">unchecked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">int1024_t</span><span class="special">;</span> + +<span class="comment">// Over again, but with checking enabled this time:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_cpp_int</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">0</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_cpp_rational_backend</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_rational_backend</span><span class="special">></span> <span class="identifier">checked_cpp_rational</span><span class="special">;</span> + +<span class="comment">// Checked fixed precision unsigned types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">unsigned_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_uint1024_t</span><span class="special">;</span> + +<span class="comment">// Fixed precision signed types:</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">128</span><span class="special">,</span> <span class="number">128</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int128_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">256</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int256_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">512</span><span class="special">,</span> <span class="number">512</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int512_t</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="number">1024</span><span class="special">,</span> <span class="number">1024</span><span class="special">,</span> <span class="identifier">signed_magnitude</span><span class="special">,</span> <span class="identifier">checked</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> <span class="special">></span> <span class="identifier">checked_int1024_t</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> type + is normally used via one of the convenience typedefs given above. + </p> +<p> + This back-end is the "Swiss Army Knife" of integer types as it + can represent both fixed and <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> integer types, and both signed and unsigned types. There + are five template arguments: + </p> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term">MinBits</span></dt> +<dd><p> + Determines the number of Bits to store directly within the object + before resorting to dynamic memory allocation. When zero, this field + is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value + may improve performance as larger integer values will be stored internally + before memory allocation is required. + </p></dd> +<dt><span class="term">MaxBits</span></dt> +<dd><p> + Determines the maximum number of bits to be stored in the type: resulting + in a fixed precision type. When this value is the same as MinBits, + then the Allocator parameter is ignored, as no dynamic memory allocation + will ever be performed: in this situation the Allocator parameter + should be set to type <code class="computeroutput"><span class="keyword">void</span></code>. + Note that this parameter should not be used simply to prevent large + memory allocations, not only is that role better performed by the + allocator, but fixed precision integers have a tendency to allocate + all of MaxBits of storage more often than one would expect. + </p></dd> +<dt><span class="term">SignType</span></dt> +<dd><p> + Determines whether the resulting type is signed or not. Note that + for <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> types this parameter must be <code class="computeroutput"><span class="identifier">signed_magnitude</span></code>. + For fixed precision types then this type may be either <code class="computeroutput"><span class="identifier">signed_magnitude</span></code> or <code class="computeroutput"><span class="identifier">unsigned_magnitude</span></code>. + </p></dd> +<dt><span class="term">Checked</span></dt> +<dd><p> + This parameter has two values: <code class="computeroutput"><span class="identifier">checked</span></code> + or <code class="computeroutput"><span class="identifier">unchecked</span></code>. See + below. + </p></dd> +<dt><span class="term">Allocator</span></dt> +<dd><p> + The allocator to use for dynamic memory allocation, or type <code class="computeroutput"><span class="keyword">void</span></code> if MaxBits == MinBits. + </p></dd> +</dl> +</div> +<p> + When the template parameter Checked is set to <code class="computeroutput"><span class="identifier">checked</span></code> + then the result is a <span class="emphasis"><em>checked-integer</em></span>, checked and + unchecked integers have the following properties: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Condition + </p> + </th> +<th> + <p> + Checked-Integer + </p> + </th> +<th> + <p> + Unchecked-Integer + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + Numeric overflow in fixed precision arithmetic + </p> + </td> +<td> + <p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>. + </p> + </td> +<td> + <p> + Performs arithmetic modulo 2<sup>MaxBits</sup> + </p> + </td> +</tr> +<tr> +<td> + <p> + Constructing an integer from a value that can not be represented + in the target type + </p> + </td> +<td> + <p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code>. + </p> + </td> +<td> + <p> + Converts the value modulo 2<sup>MaxBits</sup>, signed to unsigned conversions + extract the last MaxBits bits of the 2's complement representation + of the input value. + </p> + </td> +</tr> +<tr> +<td> + <p> + Unsigned subtraction yielding a negative value. + </p> + </td> +<td> + <p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code>. + </p> + </td> +<td> + <p> + Yields the value that would result from treating the unsigned + type as a 2's complement signed type. + </p> + </td> +</tr> +<tr> +<td> + <p> + Attempting a bitwise operation on a negative value. + </p> + </td> +<td> + <p> + Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> + </p> + </td> +<td> + <p> + Yields the value, but not the bit pattern, that would result + from performing the operation on a 2's complement integer type. + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code>s + have the value zero. + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +<li class="listitem"> + Construction from a string that contains invalid non-numeric characters + results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> being thrown. + </li> +<li class="listitem"> + Since the precision of <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> + is necessarily limited when the allocator parameter is void, care should + be taken to avoid numeric overflow when using this type unless you + actually want modulo-arithmetic behavior. + </li> +<li class="listitem"> + The type uses a sign-magnitude representation internally, so type + <code class="computeroutput"><span class="identifier">int128_t</span></code> has 128-bits + of precision plus an extra sign bit. In this respect the behaviour + of these types differs from built-in 2's complement types. In might + be tempting to use a 127-bit type instead, and indeed this does work, + but behaviour is still slightly different from a 2's complement built-in + type as the min and max values are identical (apart from the sign), + where as they differ by one for a true 2's complement type. That said + it should be noted that there's no requirement for built-in types to + be 2's complement either - it's simply that this is the most common + format by far. + </li> +<li class="listitem"> + Attempting to print negative values as either an Octal or Hexadecimal + string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown, this is a direct consequence of the sign-magnitude representation. + </li> +<li class="listitem"> + The fixed precision types <code class="computeroutput"><span class="special">[</span><span class="identifier">checked_</span><span class="special">][</span><span class="identifier">u</span><span class="special">]</span><span class="identifier">intXXX_t</span></code> have expression template + support turned off - it seems to make little difference to the performance + of these types either way - so we may as well have the faster compile + times by turning the feature off. + </li> +<li class="listitem"> + Unsigned types support subtraction - the result is "as if" + a 2's complement operation had been performed as long as they are not + <span class="emphasis"><em>checked-integers</em></span> (see above). In other words they + behave pretty much as a built in integer type would in this situation. + So for example if we were using <code class="computeroutput"><span class="identifier">uint128_t</span></code> + then <code class="computeroutput"><span class="identifier">uint128_t</span><span class="special">(</span><span class="number">1</span><span class="special">)-</span><span class="number">4</span></code> + would result in the value <code class="computeroutput"><span class="number">0</span><span class="identifier">xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD</span></code> + of type <code class="computeroutput"><span class="identifier">uint128_t</span></code>. + However, had this operation been performed on <code class="computeroutput"><span class="identifier">checked_uint128_t</span></code> + then a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> would have been thrown. + </li> +<li class="listitem"> + Unary negation of unsigned types results in a compiler error (static + assertion). + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +<li class="listitem"> + When used at fixed precision, the size of this type is always one machine + word larger than you would expect for an N-bit integer: the extra word + stores both the sign, and how many machine words in the integer are + actually in use. The latter is an optimisation for larger fixed precision + integers, so that a 1024-bit integer has almost the same performance + characteristics as a 128-bit integer, rather than being 4 times slower + for addition and 16 times slower for multiplication (assuming the values + involved would always fit in 128 bits). Typically this means you can + use an integer type wide enough for the "worst case scenario" + with only minor performance degradation even if most of the time the + arithmetic could in fact be done with a narrower type. + </li> +<li class="listitem"> + When used at fixed precision and MaxBits is smaller than the number + of bits in the largest native integer type, then internally <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> switches to a "trivial" + implementation where it is just a thin wrapper around a single integer. + Note that it will still be slightly slower than a bare native integer, + as it emulates a signed-magnitude representation rather than simply + using the platforms native sign representation: this ensures there + is no step change in behavior as a cpp_int grows in size. + </li> +<li class="listitem"> + Fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s + have some support for <code class="computeroutput"><span class="keyword">constexpr</span></code> + values and user-defined literals, see <a class="link" href="../lits.html" title="Literal Types and constexpr Support">here</a> + for the full description. For example <code class="computeroutput"><span class="number">0xfffff</span><span class="identifier">_cppi1024</span></code> specifies a 1024-bit integer + with the value 0xffff. This can be used to generate compile time constants + that are too large to fit into any built in number type. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.ints.cpp_int.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.ints.cpp_int.example"></a></span><a class="link" href="cpp_int.html#boost_multiprecision.tut.ints.cpp_int.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">int128_t</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some fixed precision arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 20!</span> + + <span class="comment">// Repeat at arbitrary precision:</span> + <span class="identifier">cpp_int</span> <span class="identifier">u</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">100</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">u</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">u</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 100!</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../ints.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_int.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs.html new file mode 100644 index 0000000000..f53916fe46 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs.html @@ -0,0 +1,47 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Examples</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ints.html" title="Integer Types"> +<link rel="prev" href="tom_int.html" title="tom_int"> +<link rel="next" href="egs/factorials.html" title="Factorials"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tom_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="egs/factorials.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.ints.egs"></a><a class="link" href="egs.html" title="Examples">Examples</a> +</h4></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="egs/factorials.html">Factorials</a></span></dt> +<dt><span class="section"><a href="egs/bitops.html">Bit Operations</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tom_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="egs/factorials.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/bitops.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/bitops.html new file mode 100644 index 0000000000..7b8cf2d5b8 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/bitops.html @@ -0,0 +1,95 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Bit Operations</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../egs.html" title="Examples"> +<link rel="prev" href="factorials.html" title="Factorials"> +<link rel="next" href="../../floats.html" title="Floating Point Numbers"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="factorials.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../egs.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../floats.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.ints.egs.bitops"></a><a class="link" href="bitops.html" title="Bit Operations">Bit Operations</a> +</h5></div></div></div> +<p> + In this example we'll show how individual bits within an integer may + be manipulated, we'll start with an often needed calculation of <span class="emphasis"><em>2<sup>n</sup> - + 1</em></span>, which we could obviously implement like this: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_int</span><span class="special">;</span> + +<span class="identifier">cpp_int</span> <span class="identifier">b1</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">cpp_int</span> <span class="identifier">r</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> + <span class="keyword">return</span> <span class="special">(</span><span class="identifier">r</span> <span class="special"><<</span> <span class="identifier">n</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Calling: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">b1</span><span class="special">(</span><span class="number">200</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Yields as expected: + </p> +<pre class="programlisting">0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF</pre> +<p> + However, we could equally just set the n'th bit in the result, like this: + </p> +<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">b2</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">cpp_int</span> <span class="identifier">r</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> + <span class="keyword">return</span> <span class="special">--</span><span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">n</span><span class="special">);</span> +<span class="special">}</span> +</pre> +<p> + Note how the <code class="computeroutput"><span class="identifier">bit_set</span></code> + function sets the specified bit in its argument and then returns a reference + to the result - which we can then simply decrement. The result from a + call to <code class="computeroutput"><span class="identifier">b2</span></code> is the same + as that to <code class="computeroutput"><span class="identifier">b1</span></code>. + </p> +<p> + We can equally test bits, so for example the n'th bit of the result returned + from <code class="computeroutput"><span class="identifier">b2</span></code> shouldn't be + set unless we increment it first: + </p> +<pre class="programlisting"><span class="identifier">assert</span><span class="special">(!</span><span class="identifier">bit_test</span><span class="special">(</span><span class="identifier">b1</span><span class="special">(</span><span class="number">200</span><span class="special">),</span> <span class="number">200</span><span class="special">));</span> <span class="comment">// OK</span> +<span class="identifier">assert</span><span class="special">(</span><span class="identifier">bit_test</span><span class="special">(++</span><span class="identifier">b1</span><span class="special">(</span><span class="number">200</span><span class="special">),</span> <span class="number">200</span><span class="special">));</span> <span class="comment">// OK</span> +</pre> +<p> + And of course if we flip the n'th bit after increment, then we should + get back to zero: + </p> +<pre class="programlisting"><span class="identifier">assert</span><span class="special">(!</span><span class="identifier">bit_flip</span><span class="special">(++</span><span class="identifier">b1</span><span class="special">(</span><span class="number">200</span><span class="special">),</span> <span class="number">200</span><span class="special">));</span> <span class="comment">// OK</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="factorials.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../egs.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../floats.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/factorials.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/factorials.html new file mode 100644 index 0000000000..7566f7e4aa --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/egs/factorials.html @@ -0,0 +1,149 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Factorials</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../egs.html" title="Examples"> +<link rel="prev" href="../egs.html" title="Examples"> +<link rel="next" href="bitops.html" title="Bit Operations"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../egs.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../egs.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="bitops.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.ints.egs.factorials"></a><a class="link" href="factorials.html" title="Factorials">Factorials</a> +</h5></div></div></div> +<p> + In this simple example, we'll write a routine to print out all of the + factorials which will fit into a 128-bit integer. At the end of the routine + we do some fancy iostream formatting of the results: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">vector</span><span class="special">></span> + + +<span class="keyword">void</span> <span class="identifier">print_factorials</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_int</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Print all the factorials that will fit inside a 128-bit integer.</span> + <span class="comment">//</span> + <span class="comment">// Begin by building a big table of factorials, once we know just how </span> + <span class="comment">// large the largest is, we'll be able to "pretty format" the results.</span> + <span class="comment">//</span> + <span class="comment">// Calculate the largest number that will fit inside 128 bits, we could</span> + <span class="comment">// also have used numeric_limits<int128_t>::max() for this value:</span> + <span class="identifier">cpp_int</span> <span class="identifier">limit</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span> + <span class="comment">// </span> + <span class="comment">// Our table of values:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">></span> <span class="identifier">results</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Initial values:</span> + <span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + <span class="identifier">cpp_int</span> <span class="identifier">factorial</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Cycle through the factorials till we reach the limit:</span> + <span class="keyword">while</span><span class="special">(</span><span class="identifier">factorial</span> <span class="special"><</span> <span class="identifier">limit</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">results</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">factorial</span><span class="special">);</span> + <span class="special">++</span><span class="identifier">i</span><span class="special">;</span> + <span class="identifier">factorial</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + <span class="special">}</span> + <span class="comment">//</span> + <span class="comment">// Lets see how many digits the largest factorial was:</span> + <span class="keyword">unsigned</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">results</span><span class="special">.</span><span class="identifier">back</span><span class="special">().</span><span class="identifier">str</span><span class="special">().</span><span class="identifier">size</span><span class="special">();</span> + <span class="comment">//</span> + <span class="comment">// Now print them out, using right justification, while we're at it</span> + <span class="comment">// we'll indicate the limit of each integer type, so begin by defining</span> + <span class="comment">// the limits for 16, 32, 64 etc bit integers:</span> + <span class="identifier">cpp_int</span> <span class="identifier">limits</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> + <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">16</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span> + <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">32</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span> + <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">64</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span> + <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span> + <span class="special">};</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">bit_counts</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="string">"16"</span><span class="special">,</span> <span class="string">"32"</span><span class="special">,</span> <span class="string">"64"</span><span class="special">,</span> <span class="string">"128"</span> <span class="special">};</span> + <span class="keyword">unsigned</span> <span class="identifier">current_limit</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">j</span> <span class="special"><</span> <span class="identifier">results</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">j</span><span class="special">)</span> + <span class="special">{</span> + <span class="keyword">if</span><span class="special">(</span><span class="identifier">limits</span><span class="special">[</span><span class="identifier">current_limit</span><span class="special">]</span> <span class="special"><</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">])</span> + <span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Limit of "</span> <span class="special">+</span> <span class="identifier">bit_counts</span><span class="special">[</span><span class="identifier">current_limit</span><span class="special">]</span> <span class="special">+</span> <span class="string">" bit integers"</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setfill</span><span class="special">(</span><span class="char">'.'</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">digits</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">message</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setfill</span><span class="special">(</span><span class="char">' '</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="special">++</span><span class="identifier">current_limit</span><span class="special">;</span> + <span class="special">}</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">digits</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">]</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="special">}</span> +<span class="special">}</span> +</pre> +<p> + The output from this routine is: + </p> +<pre class="programlisting"> 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 +................Limit of 16 bit integers + 362880 + 3628800 + 39916800 + 479001600 +................Limit of 32 bit integers + 6227020800 + 87178291200 + 1307674368000 + 20922789888000 + 355687428096000 + 6402373705728000 + 121645100408832000 + 2432902008176640000 +................Limit of 64 bit integers + 51090942171709440000 + 1124000727777607680000 + 25852016738884976640000 + 620448401733239439360000 + 15511210043330985984000000 + 403291461126605635584000000 + 10888869450418352160768000000 + 304888344611713860501504000000 + 8841761993739701954543616000000 + 265252859812191058636308480000000 + 8222838654177922817725562880000000 + 263130836933693530167218012160000000 + 8683317618811886495518194401280000000 + 295232799039604140847618609643520000000 +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../egs.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../egs.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="bitops.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/gmp_int.html new file mode 100644 index 0000000000..e27cdf7c59 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -0,0 +1,148 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>gmp_int</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ints.html" title="Integer Types"> +<link rel="prev" href="cpp_int.html" title="cpp_int"> +<link rel="next" href="tom_int.html" title="tom_int"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tom_int.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.ints.gmp_int"></a><a class="link" href="gmp_int.html" title="gmp_int">gmp_int</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">gmp_int</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span> <span class="special">></span> <span class="identifier">mpz_int</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">gmp_int</span></code> back-end is + used via the typedef <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">mpz_int</span></code>. + It acts as a thin wrapper around the <a href="http://gmplib.org" target="_top">GMP</a> + <code class="computeroutput"><span class="identifier">mpz_t</span></code> to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. + </p> +<p> + As well as the usual conversions from arithmetic and string types, type + <code class="computeroutput"><span class="identifier">mpz_int</span></code> is copy constructible + and assignable from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The <a href="http://gmplib.org" target="_top">GMP</a> native types: <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>, + <code class="computeroutput"><span class="identifier">mpq_t</span></code>. + </li> +<li class="listitem"> + Instances of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> that are wrappers around those + types: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code>. + </li> +</ul></div> +<p> + It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpz_t</span></code> + via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> + member function of <code class="computeroutput"><span class="identifier">gmp_int</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + No changes are made to the GMP library's global settings - so you can + safely mix this type with existing code that uses <a href="http://gmplib.org" target="_top">GMP</a>. + </li> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">gmp_int</span></code>s + have the value zero (this is GMP's default behavior). + </li> +<li class="listitem"> + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">oct</span></code> or <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">hex</span></code> + are set, will result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + will be thrown. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid integer. + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +<li class="listitem"> + Although this type is a wrapper around <a href="http://gmplib.org" target="_top">GMP</a> + it will work equally well with <a href="http://mpir.org/" target="_top">MPIR</a>. + Indeed use of <a href="http://mpir.org/" target="_top">MPIR</a> is recommended + on Win32. + </li> +<li class="listitem"> + This backend supports rvalue-references and is move-aware, making instantiations + of <code class="computeroutput"><span class="identifier">number</span></code> on this backend + move aware. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.ints.gmp_int.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.ints.gmp_int.example"></a></span><a class="link" href="gmp_int.html#boost_multiprecision.tut.ints.gmp_int.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">mpz_int</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">1000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000!</span> + + <span class="comment">// Access the underlying representation:</span> + <span class="identifier">mpz_t</span> <span class="identifier">z</span><span class="special">;</span> + <span class="identifier">mpz_init</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span> + <span class="identifier">mpz_set</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">v</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> + <span class="identifier">mpz_clear</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tom_int.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/tom_int.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/tom_int.html new file mode 100644 index 0000000000..265acbde50 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/ints/tom_int.html @@ -0,0 +1,134 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>tom_int</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../ints.html" title="Integer Types"> +<link rel="prev" href="gmp_int.html" title="gmp_int"> +<link rel="next" href="egs.html" title="Examples"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="egs.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.ints.tom_int"></a><a class="link" href="tom_int.html" title="tom_int">tom_int</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">tommath</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">tommath_int</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">tommath_int</span> <span class="special">></span> <span class="identifier">tom_int</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">tommath_int</span></code> back-end + is used via the typedef <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">tom_int</span></code>. + It acts as a thin wrapper around the <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a> + <code class="computeroutput"><span class="identifier">tom_int</span></code> to provide an integer + type that is a drop-in replacement for the native C++ integer types, but + with unlimited precision. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed objects have the value zero (this is <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a>'s + default behavior). + </li> +<li class="listitem"> + Although <code class="computeroutput"><span class="identifier">tom_int</span></code> is + mostly a drop in replacement for the builtin integer types, it should + be noted that it is a rather strange beast as it's a signed type that + is not a 2's complement type. As a result the bitwise operations <code class="computeroutput"><span class="special">|</span> <span class="special">&</span> <span class="special">^</span></code> will throw a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + exception if either of the arguments is negative. Similarly the complement + operator<code class="computeroutput"><span class="special">~</span></code> is deliberately + not implemented for this type. + </li> +<li class="listitem"> + Formatted IO for this type does not support octal or hexadecimal notation + for negative values, as a result performing formatted output on this + type when the argument is negative and either of the flags <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">oct</span></code> or <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">hex</span></code> + are set, will result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + will be thrown. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid integer. + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.ints.tom_int.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.ints.tom_int.example"></a></span><a class="link" href="tom_int.html#boost_multiprecision.tut.ints.tom_int.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">tommath</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">tom_int</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">1000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000!</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000! in hex format</span> + + <span class="keyword">try</span><span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="special">-</span><span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Ooops! can't print a negative value in hex format!</span> + <span class="special">}</span> + <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span><span class="special">&</span> <span class="identifier">e</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="special">}</span> + + <span class="keyword">try</span><span class="special">{</span> + <span class="comment">// v is not a 2's complement type, bitwise operations are only supported</span> + <span class="comment">// on positive values:</span> + <span class="identifier">v</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">v</span> <span class="special">&</span> <span class="number">2</span><span class="special">;</span> + <span class="special">}</span> + <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span><span class="special">&</span> <span class="identifier">e</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="special">}</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_int.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ints.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="egs.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/limits.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits.html new file mode 100644 index 0000000000..5cd48aaced --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits.html @@ -0,0 +1,100 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Numeric Limits</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="serial.html" title="Boost.Serialization Support"> +<link rel="next" href="limits/constants.html" title="std::numeric_limits<> constants"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="serial.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="limits/constants.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.limits"></a><a class="link" href="limits.html" title="Numeric Limits">Numeric Limits</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="limits/constants.html">std::numeric_limits<> + constants</a></span></dt> +<dt><span class="section"><a href="limits/functions.html">std::numeric_limits<> + functions</a></span></dt> +<dt><span class="section"><a href="limits/limits32.html">Numeric limits + for 32-bit platform</a></span></dt> +<dt><span class="section"><a href="limits/how_to_tell.html">How to + Determine the Kind of a Number From <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code></a></span></dt> +</dl></div> +<p> + Boost.Multiprecision tries hard to implement <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> + for all types as far as possible and meaningful because experience with Boost.Math + has shown that this aids portability. + </p> +<p> + The <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3690.pdf" target="_top">C++ + standard library</a> defines <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> + in section 18.3.2. + </p> +<p> + This in turn refers to the C standard <a href="http://www.open-std.org/jtc1/sc22/wg11/docs/n507.pdf" target="_top">SC22/WG11 + N507 DRAFT INTERNATIONAL ISO/IEC STANDARD WD 10967-1</a> Information + technology Language independent arithmetic Part 1: Integer and Floating point + arithmetic. + </p> +<p> + That C Standard in turn refers to + </p> +<p> + <a href="http://754r.ucbtest.org/standards/754.pdf" target="_top">IEEE754 IEEE Standard + for Binary Floating-Point Arithmetic</a> + </p> +<p> + There is a useful summary at <a href="http://www.cplusplus.com/reference/limits/numeric_limits/" target="_top">C++ + reference</a>. + </p> +<p> + The chosen backend often determines how completely <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> + is available. + </p> +<p> + Compiler options, processor type, and definition of macros or assembler instructions + to control denormal numbers will alter the values in the tables given below. + </p> +<div class="warning"><table border="0" summary="Warning"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../doc/src/images/warning.png"></td> +<th align="left">Warning</th> +</tr> +<tr><td align="left" valign="top"><p> + GMP's <code class="computeroutput"><span class="identifier">mpf_t</span></code> does not have + a concept of overflow: operations that lead to overflow eventually run + of out of resources and terminate with stack overflow (often after several + seconds). + </p></td></tr> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="serial.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="limits/constants.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/constants.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/constants.html new file mode 100644 index 0000000000..2a085c9ad8 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/constants.html @@ -0,0 +1,705 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; 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For example floating + point types with runtime-variable precision such as <code class="computeroutput"><span class="identifier">mpfr_float</span></code> + have no <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + specialization as it would be impossible to define all the members at compile + time. In contrast the precision of a type such as <code class="computeroutput"><span class="identifier">mpfr_float_50</span></code> + is known at compile time, and so it <span class="emphasis"><em>does</em></span> have a <code class="computeroutput"><span class="identifier">numeric_limits</span></code> specialization. + </p> +<p> + Note that not all the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> + member constants and functions are meaningful for all user-defined types + (UDT), such as the decimal and binary multiprecision types provided here. + More information on this is given in the sections below. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h1"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.infinity"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.infinity">infinity</a> + </h5> +<p> + For floating-point types, ∞ is defined wherever possible, but clearly infinity + is meaningless for __arbitrary_precision arithmetic backends, and there + is one floating point type (GMP's <code class="computeroutput"><span class="identifier">mpf_t</span></code>, + see <a class="link" href="../floats/gmp_float.html" title="gmp_float">gmp_float</a>) + which has no notion of infinity or NaN at all. + </p> +<p> + A typical test whether infinity is implemented is + </p> +<pre class="programlisting"><span class="keyword">if</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_infinity</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + and using tests like this is strongly recommended to improve portability. + </p> +<p> + If the backend is switched to a type that does not support infinity then, + without checks like this, there will be trouble. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h2"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.is_signed"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.is_signed">is_signed</a> + </h5> +<p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_signed</span> <span class="special">==</span> + <span class="keyword">true</span></code> if the type <code class="computeroutput"><span class="identifier">T</span></code> + is signed. + </p> +<p> + For built-in binary types, the sign is held in a single bit, but for other + types (cpp_dec_float and cpp_bin_float) it may be a separate storage element, + usually <code class="computeroutput"><span class="keyword">bool</span></code>. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h3"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.is_exact"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.is_exact">is_exact</a> + </h5> +<p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_exact</span> <span class="special">==</span> + <span class="keyword">true</span></code> if type T uses exact representations. + </p> +<p> + This is defined as <code class="computeroutput"><span class="keyword">true</span></code> for + all integer types and <code class="computeroutput"><span class="keyword">false</span></code> + for floating-point types. + </p> +<p> + <a href="http://stackoverflow.com/questions/14203654/stdnumeric-limitsis-exact-what-is-a-usable-definition" target="_top">A + usable definition</a> has been discussed. + </p> +<p> + ISO/IEC 10967-1, Language independent arithmetic, noted by the C++ Standard + defines + </p> +<pre class="programlisting"><span class="identifier">A</span> <span class="identifier">floating</span> <span class="identifier">point</span> <span class="identifier">type</span> <span class="identifier">F</span> <span class="identifier">shall</span> <span class="identifier">be</span> <span class="identifier">a</span> <span class="identifier">finite</span> <span class="identifier">subset</span> <span class="identifier">of</span> <span class="special">[</span><span class="identifier">real</span><span class="special">].</span> +</pre> +<p> + The important practical distinction is that all integers (up to <code class="computeroutput"><span class="identifier">max</span><span class="special">()</span></code>) + can be stored exactly. + </p> +<p> + <a href="http://en.wikipedia.org/wiki/Rational_number" target="_top">Rational</a> + types using two integer types are also exact. + </p> +<p> + Floating-point types <span class="bold"><strong>cannot store all real values</strong></span> + (those in the set of ℜ) <span class="bold"><strong>exactly</strong></span>. For example, + 0.5 can be stored exactly in a binary floating-point, but 0.1 cannot. What + is stored is the nearest representable real value, that is, rounded to + nearest. + </p> +<p> + Fixed-point types (usually decimal) are also defined as exact, in that + they only store a <span class="bold"><strong>fixed precision</strong></span>, so + half cents or pennies (or less) cannot be stored. The results of computations + are rounded up or down, just like the result of integer division stored + as an integer result. + </p> +<p> + There are number of proposals to <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html" target="_top">add + Decimal Floating Point Support to C++</a>. + </p> +<p> + <a href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2849.pdf" target="_top">Decimal + TR</a>. + </p> +<p> + And also <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html" target="_top">C++ + Binary Fixed-Point Arithmetic</a>. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h4"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.is_bounded"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.is_bounded">is_bounded</a> + </h5> +<p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_bounded</span> <span class="special">==</span> + <span class="keyword">true</span></code> if the set of values represented + by the type <code class="computeroutput"><span class="identifier">T</span></code> is finite. + </p> +<p> + This is <code class="computeroutput"><span class="keyword">true</span></code> for all built-in + integer, fixed and floating-point types, and most multi-precision types. + </p> +<p> + It is only <code class="computeroutput"><span class="keyword">false</span></code> for a few + __arbitrary_precision types like <code class="computeroutput"><span class="identifier">cpp_int</span></code>. + </p> +<p> + Rational and fixed-exponent representations are exact but not integer. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h5"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.is_modulo"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.is_modulo">is_modulo</a> + </h5> +<p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_modulo</span></code> is defined as <code class="computeroutput"><span class="keyword">true</span></code> if adding two positive values of type + T can yield a result less than either value. + </p> +<p> + <code class="computeroutput"><span class="identifier">is_modulo</span> <span class="special">==</span> + <span class="keyword">true</span></code> means that the type does not + overflow, but, for example, 'wraps around' to zero, when adding one to + the <code class="computeroutput"><span class="identifier">max</span><span class="special">()</span></code> + value. + </p> +<p> + For most built-in integer types, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><>::</span><span class="identifier">is_modulo</span></code> + is <code class="computeroutput"><span class="keyword">true</span></code>. + </p> +<p> + <code class="computeroutput"><span class="keyword">bool</span></code> is the only exception. + </p> +<p> + The modulo behaviour is sometimes useful, but also can be unexpected, and + sometimes undesired, behaviour. + </p> +<p> + Overflow of signed integers can be especially unexpected, possibly causing + change of sign. + </p> +<p> + Boost.Multiprecision integer type <code class="computeroutput"><span class="identifier">cpp_int</span></code> + is not modulo because as an __arbitrary_precision types, it expands to + hold any value that the machine resources permit. + </p> +<p> + However fixed precision <a class="link" href="../ints/cpp_int.html" title="cpp_int">cpp_int</a>'s + may be modulo if they are unchecked (i.e. they behave just like built in + integers), but not if they are checked (overflow causes an exception to + be raised). + </p> +<p> + Built-in and multi-precision floating-point types are normally not modulo. + </p> +<p> + Where possible, overflow is to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><>::</span><span class="identifier">infinity</span><span class="special">()</span></code>, provided <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><>::</span><span class="identifier">has_infinity</span> + <span class="special">==</span> <span class="keyword">true</span></code>. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h6"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.radix"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.radix">radix</a> + </h5> +<p> + Constant <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">radix</span></code> returns either 2 (for built-in + and binary types) or 10 (for decimal types). + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h7"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.digits"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.digits">digits</a> + </h5> +<p> + The number of <code class="computeroutput"><span class="identifier">radix</span></code> digits + that be represented without change: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + for integer types, the number of <span class="bold"><strong>non-sign bits</strong></span> + in the significand. + </li> +<li class="listitem"> + for floating types, the number of <span class="bold"><strong>radix digits</strong></span> + in the significand. + </li> +</ul></div> +<p> + The values include any implicit bit, so for example, for the ubiquious + <code class="computeroutput"><span class="keyword">double</span></code> using 64 bits (<a href="http://en.wikipedia.org/wiki/Double_precision_floating-point_format" target="_top">IEEE + binary64 </a>), <code class="computeroutput"><span class="identifier">digits</span></code> + == 53, even though there are only 52 actual bits of the significand stored + in the representation. The value of <code class="computeroutput"><span class="identifier">digits</span></code> + reflects the fact that there is one implicit bit which is always set to + 1. + </p> +<p> + The Boost.Multiprecision binary types do not use an implicit bit, so the + <code class="computeroutput"><span class="identifier">digits</span></code> member reflects + exactly how many bits of precision were requested: + </p> +<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> <span class="identifier">digit_base_2</span><span class="special">></span> <span class="special">></span> <span class="identifier">float64</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="number">113</span><span class="special">,</span> <span class="identifier">digit_base_2</span><span class="special">></span> <span class="special">></span> <span class="identifier">float128</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float64</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">53.</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">113.</span> +</pre> +<p> + For the most common case of <code class="computeroutput"><span class="identifier">radix</span> + <span class="special">==</span> <span class="number">2</span></code>, + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span></code> is the number of bits in the representation, + not counting any sign bit. + </p> +<p> + For a decimal integer type, when <code class="computeroutput"><span class="identifier">radix</span> + <span class="special">==</span> <span class="number">10</span></code>, + it is the number of decimal digits. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h8"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.digits10"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.digits10">digits10</a> + </h5> +<p> + Constant <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits10</span></code> returns the number of decimal + digits that can be represented without change or loss. + </p> +<p> + For example, <code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">char</span><span class="special">>::</span><span class="identifier">digits10</span></code> is 2. + </p> +<p> + This somewhat inscrutable definition means that an <code class="computeroutput"><span class="keyword">unsigned</span> + <span class="keyword">char</span></code> can hold decimal values <code class="computeroutput"><span class="number">0.</span><span class="special">.</span><span class="number">99</span></code> + without loss of precision or accuracy, usually from truncation. + </p> +<p> + Had the definition been 3 then that would imply it could hold 0..999, but + as we all know, an 8-bit <code class="computeroutput"><span class="keyword">unsigned</span> + <span class="keyword">char</span></code> can only hold 0..255, and an + attempt to store 256 or more will involve loss or change. + </p> +<p> + For bounded integers, it is thus <span class="bold"><strong>one less</strong></span> + than number of decimal digits you need to display the biggest integer + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code>. + This value can be used to predict the layout width required for + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">short</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special">+</span><span class="number">1</span> <span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="comment">// digits10+1, and +1 for sign.</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpos</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">short</span><span class="special">>::</span><span class="identifier">max</span><span class="special">)()</span> <span class="comment">// +32767</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">short</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special">+</span><span class="number">1</span> <span class="special">+</span><span class="number">1</span><span class="special">)</span> + <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">short</span><span class="special">>::</span><span class="identifier">min</span><span class="special">)()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// -32767</span> +</pre> +<p> + For example, <code class="computeroutput"><span class="keyword">unsigned</span> <span class="keyword">short</span></code> + is often stored in 16 bits, so the maximum value is 0xFFFF or 65535. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special">+</span><span class="number">1</span> <span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="comment">// digits10+1, and +1 for sign.</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpos</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">>::</span><span class="identifier">max</span><span class="special">)()</span> <span class="comment">// 65535</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special">+</span><span class="number">1</span> <span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="comment">// digits10+1, and +1 for sign.</span> + <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">>::</span><span class="identifier">min</span><span class="special">)()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0</span> +</pre> +<p> + For bounded floating-point types, if we create a <code class="computeroutput"><span class="keyword">double</span></code> + with a value with <code class="computeroutput"><span class="identifier">digits10</span></code> + (usually 15) decimal digits, <code class="computeroutput"><span class="number">1e15</span></code> + or <code class="computeroutput"><span class="number">1000000000000000</span></code> : + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">1e15</span><span class="special">;</span> +<span class="keyword">double</span> <span class="identifier">dp1</span> <span class="special">=</span> <span class="identifier">d</span><span class="special">+</span><span class="number">1</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="special"><<</span> <span class="identifier">dp1</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="comment">// 1000000000000000</span> +<span class="comment">// 1000000000000001</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">dp1</span> <span class="special">-</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1</span> +</pre> +<p> + and we can increment this value to <code class="computeroutput"><span class="number">1000000000000001</span></code> + as expected and show the difference too. + </p> +<p> + But if we try to repeat this with more than <code class="computeroutput"><span class="identifier">digits10</span></code> + digits, + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">1e16</span><span class="special">;</span> +<span class="keyword">double</span> <span class="identifier">dp1</span> <span class="special">=</span> <span class="identifier">d</span><span class="special">+</span><span class="number">1</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="special"><<</span> <span class="identifier">dp1</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="comment">// 10000000000000000</span> +<span class="comment">// 10000000000000000</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">dp1</span> <span class="special">-</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0 !!!</span> +</pre> +<p> + then we find that when we add one it has no effect, and display show that + there is loss of precision. See <a href="http://en.wikipedia.org/wiki/Loss_of_significance" target="_top">Loss + of significance or cancellation error</a>. + </p> +<p> + So <code class="computeroutput"><span class="identifier">digits10</span></code> is the number + of decimal digits <span class="bold"><strong>guaranteed</strong></span> to be correct. + </p> +<p> + For example, 'round-tripping' for <code class="computeroutput"><span class="keyword">double</span></code>: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + If a decimal string with at most <code class="computeroutput"><span class="identifier">digits10</span></code>( + == 15) significant decimal digits is converted to <code class="computeroutput"><span class="keyword">double</span></code> + and then converted back to the same number of significant decimal digits, + then the final string will match the original 15 decimal digit string. + </li> +<li class="listitem"> + If a <code class="computeroutput"><span class="keyword">double</span></code> floating-point + number is converted to a decimal string with at least 17 decimal digits + and then converted back to <code class="computeroutput"><span class="keyword">double</span></code>, + then the result will be binary identical to the original <code class="computeroutput"><span class="keyword">double</span></code> value. + </li> +</ul></div> +<p> + For most purposes, you will much more likely want <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><>::</span><span class="identifier">max_digits10</span></code>, + the number of decimal digits that ensure that a change of one least significant + bit (ULP) produces a different decimal digits string. + </p> +<p> + For nearly all floating-point types, <code class="computeroutput"><span class="identifier">max_digits10</span></code> + is <code class="computeroutput"><span class="identifier">digits10</span><span class="special">+</span><span class="number">2</span></code>, but you should use <code class="computeroutput"><span class="identifier">max_digits10</span></code> + where possible. + </p> +<p> + If <code class="computeroutput"><span class="identifier">max_digits10</span></code> is not + available, you should using the <a href="http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF" target="_top">Kahan + formula for floating-point type T</a> + </p> +<pre class="programlisting"><span class="identifier">max_digits10</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">3010U</span><span class="special">/</span><span class="number">10000U</span><span class="special">;</span> +</pre> +<p> + The factor is log<sub>10</sub>(2) = 0.3010 but must be evaluated at compile time using + only integers. + </p> +<p> + (See also <a href="http://www.loria.fr/~zimmerma/mca/mca-cup-0.5.9.pdf" target="_top">Richard + P. Brent and Paul Zimmerman, Modern Computer Arithmetic</a> Equation + 3.8 on page 116.). + </p> +<p> + The extra two (or 3) least significant digits are 'noisy' and may be junk, + but if you want to 'round-trip' - printing a value out and reading it back + in - you must use <code class="computeroutput"><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span></code>. + For at least one popular compiler, you must also use <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span></code> + format. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h9"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.max_digits10"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.max_digits10">max_digits10</a> + </h5> +<p> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_digits10</span></code> was added for floating-point + because <code class="computeroutput"><span class="identifier">digits10</span></code> decimal + digits are insufficient to show a least significant bit (ULP) change giving + puzzling displays like + </p> +<pre class="programlisting"><span class="number">0.666666666666667</span> <span class="special">!=</span> <span class="number">0.666666666666667</span> +</pre> +<p> + from failure to 'round-trip', for example: + </p> +<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">write</span> <span class="special">=</span> <span class="number">2.</span><span class="special">/</span><span class="number">3</span><span class="special">;</span> <span class="comment">// Any arbitrary value that cannot be represented exactly.</span> +<span class="keyword">double</span> <span class="identifier">read</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">s</span><span class="special">;</span> +<span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span> <span class="comment">// or `float64_t` for 64-bit IEE754 double.</span> +<span class="identifier">s</span> <span class="special"><<</span> <span class="identifier">write</span><span class="special">;</span> +<span class="identifier">s</span> <span class="special">>></span> <span class="identifier">read</span><span class="special">;</span> +<span class="keyword">if</span><span class="special">(</span><span class="identifier">read</span> <span class="special">!=</span> <span class="identifier">write</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">read</span> <span class="special"><<</span> <span class="string">" != "</span> <span class="special"><<</span> <span class="identifier">write</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + If you wish to ensure that a change of one least significant bit (ULP) + produces a different decimal digits string, then <code class="computeroutput"><span class="identifier">max_digits10</span></code> + is the precision to use. + </p> +<p> + For example: + </p> +<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">double_constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">pi</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 3.1415926535897931</span> +</pre> +<p> + will display π to the maximum possible precision using a <code class="computeroutput"><span class="keyword">double</span></code>. + </p> +<p> + and similarly for a much higher precision type: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">cpp_dec_float_50</span><span class="special">;</span> <span class="comment">// 50 decimal digits.</span> + +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">;</span> + +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>();</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">pi</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="comment">// 3.141592653589793238462643383279502884197169399375105820974944592307816406</span> +</pre> +<p> + For integer types, <code class="computeroutput"><span class="identifier">max_digits10</span></code> + is implementation-dependant, but is usually <code class="computeroutput"><span class="identifier">digits10</span> + <span class="special">+</span> <span class="number">2</span></code>. + This is the output field width required for the maximum value of the type + T <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code> + including a sign and a space. + </p> +<p> + So this will produce neat columns. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> <span class="special">...</span> +</pre> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + For Microsoft Visual Studio 2010, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">float</span><span class="special">>::</span><span class="identifier">max_digits10</span></code> + is wrongly defined as 8. It should be 9. + </p></td></tr> +</table></div> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"> +<p> + For Microsoft Visual Studio, and default float format, a small range + of values approximately 0.0001 to 0.004, with exponent values of 3f2 + to 3f6, are wrongly input by one least significant bit, probably every + third value of significand. + </p> +<p> + A workaround is using scientific or exponential format <code class="computeroutput"><span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span></code>. + </p> +</td></tr> +</table></div> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + BOOST_NO_CXX11_NUMERIC_LIMITS is a suitable feature-test macro to determine + if <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">float</span><span class="special">>::</span><span class="identifier">max_digits10</span></code> is implemented on any + platform. If <code class="computeroutput"><span class="identifier">max_digits10</span></code> + is not available, you should using the <a href="http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF" target="_top">Kahan + formula for floating-point type T</a>. See above. + </p></td></tr> +</table></div> +<p> + For example, to be portable, including older platforms: + </p> +<pre class="programlisting"> <span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">T</span><span class="special">;</span> <span class="comment">// Any type: `double`, cpp_dec_float_50, bin_128bit_double_type ...</span> + +<span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_NO_CXX11_NUMERIC_LIMITS</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">2</span> <span class="special">+</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">3010U</span><span class="special">/</span><span class="number">10000U</span><span class="special">);</span> +<span class="preprocessor">#else</span> +<span class="preprocessor"># if</span> <span class="special">(</span><span class="identifier">_MSC_VER</span> <span class="special"><=</span> <span class="number">1600</span><span class="special">)</span> <span class="comment">// Correct wrong value for float.</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">2</span> <span class="special">+</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">3010U</span><span class="special">/</span><span class="number">10000U</span><span class="special">);</span> +<span class="preprocessor"># else</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="preprocessor"># endif</span> +<span class="preprocessor">#endif</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"std::cout.precision = "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">1.2345678901234567889</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"x = "</span> <span class="special"><<</span> <span class="identifier">x</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">//</span> +</pre> +<p> + which should output: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span> <span class="special">=</span> <span class="number">9</span> +<span class="identifier">x</span> <span class="special">=</span> <span class="number">1.23456789</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h10"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.round_style"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.round_style">round_style</a> + </h5> +<p> + The rounding style determines how the result of floating-point operations + is treated when the result cannot be <span class="bold"><strong>exactly represented</strong></span> + in the significand. Various rounding modes may be provided: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + round to nearest up or down (default for floating-point types). + </li> +<li class="listitem"> + round up (toward positive infinity). + </li> +<li class="listitem"> + round down (toward negative infinity). + </li> +<li class="listitem"> + round toward zero (integer types). + </li> +<li class="listitem"> + no rounding (if decimal radix). + </li> +<li class="listitem"> + rounding mode is not determinable. + </li> +</ul></div> +<p> + For integer types, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">round_style</span></code> + is always towards zero, so + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">round_style</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">round_to_zero</span><span class="special">;</span> +</pre> +<p> + A decimal type, <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + rounds in no particular direction, which is to say it doesn't round at + all. And since there are several guard digits, it's not really the same + as truncation (round toward zero) either. + </p> +<p> + For floating-point types, it is normal to round to nearest. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">round_style</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">round_to_nearest</span><span class="special">;</span> +</pre> +<p> + See function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">round_error</span></code> for the maximum error (in + ULP) that rounding can cause. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h11"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.has_denorm_loss"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.has_denorm_loss">has_denorm_loss</a> + </h5> +<p> + <code class="computeroutput"><span class="keyword">true</span></code> if a loss of precision + is detected as a <a href="http://en.wikipedia.org/wiki/Denormalization" target="_top">denormalization</a> + loss, rather than an inexact result. + </p> +<p> + Always <code class="computeroutput"><span class="keyword">false</span></code> for integer types. + </p> +<p> + <code class="computeroutput"><span class="keyword">false</span></code> for all types which + do not have <code class="computeroutput"><span class="identifier">has_denorm</span></code> + == <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_present</span></code>. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h12"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.denorm_style"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.denorm_style">denorm_style</a> + </h5> +<p> + <a href="http://en.wikipedia.org/wiki/Denormal_number" target="_top">Denormalized + values</a> are representations with a variable number of exponent bits + that can permit gradual underflow, so that, if type T is <code class="computeroutput"><span class="keyword">double</span></code>. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">denorm_min</span><span class="special">()</span> <span class="special"><</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span> +</pre> +<p> + A type may have any of the following <code class="computeroutput"><span class="keyword">enum</span> + <span class="identifier">float_denorm_style</span></code> values: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_absent</span></code>, if it does not allow + denormalized values. (Always used for all integer and exact types). + </li> +<li class="listitem"> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_present</span></code>, if the floating-point + type allows denormalized values. + </li> +<li class="listitem"> + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_indeterminate</span></code>, if indeterminate + at compile time. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.tut.limits.constants.h13"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.constants.tinyness_before_rounding"></a></span><a class="link" href="constants.html#boost_multiprecision.tut.limits.constants.tinyness_before_rounding">Tinyness + before rounding</a> + </h5> +<p> + <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">tinyness_before</span></code> + </p> +<p> + <code class="computeroutput"><span class="keyword">true</span></code> if a type can determine + that a value is too small to be represent as a normalized value before + rounding it. + </p> +<p> + Generally true for <code class="computeroutput"><span class="identifier">is_iec559</span></code> + floating-point built-in types, but false for integer types. + </p> +<p> + Standard-compliant IEEE 754 floating-point implementations may detect the + floating-point underflow at three predefined moments: + </p> +<div class="orderedlist"><ol class="orderedlist" type="1"> +<li class="listitem"> + After computation of a result with absolute value smaller than <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span></code>, + such implementation detects <span class="emphasis"><em>tinyness before rounding</em></span> + (e.g. UltraSparc). + </li> +<li class="listitem"> + After rounding of the result to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span></code> + bits, if the result is tiny, such implementation detects <span class="emphasis"><em>tinyness + after rounding</em></span> (e.g. SuperSparc). + </li> +<li class="listitem"> + If the conversion of the rounded tiny result to subnormal form resulted + in the loss of precision, such implementation detects <span class="emphasis"><em>denorm + loss</em></span>. + </li> +</ol></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../limits.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="functions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/functions.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/functions.html new file mode 100644 index 0000000000..7e8cbc7c67 --- /dev/null +++ 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name="boost_multiprecision.tut.limits.functions"></a><a class="link" href="functions.html" title="std::numeric_limits<> functions">std::numeric_limits<> + functions</a> +</h4></div></div></div> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.max_function"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.max_function">max function</a> + </h5> +<p> + Function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code> + returns the largest finite value that can be represented by the type T. + If there is no such value (and <code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">bounded</span></code> + is <code class="computeroutput"><span class="keyword">false</span></code>) then returns <code class="computeroutput"><span class="identifier">T</span><span class="special">()</span></code>. + </p> +<p> + For built-in types there is usually a corresponding MACRO value TYPE_MAX, + where TYPE is CHAR, INT, FLOAT etc. + </p> +<p> + Other types, including those provided by a typedef, for example <code class="computeroutput"><span class="identifier">INT64_T_MAX</span></code> for <code class="computeroutput"><span class="identifier">int64_t</span></code>, + may provide a macro definition. + </p> +<p> + To cater for situations where no <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + specialization is available (for example because the precision of the type + varies at runtime), packaged versions of this (and other functions) are + provided using + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">precision</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="identifier">T</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">max_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>();</span> +</pre> +<p> + Of course, these simply use <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code> if available, but otherwise 'do something + sensible'. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h1"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.lowest_function"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.lowest_function">lowest + function</a> + </h5> +<p> + Since C++11: <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">lowest</span><span class="special">()</span></code> + is + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + For integral types, the same as function <code class="computeroutput"><span class="identifier">min</span><span class="special">()</span></code>. + </li> +<li class="listitem"> + For floating-point types, generally the negative of <code class="computeroutput"><span class="identifier">max</span><span class="special">()</span></code> (but implementation-dependent). + </li> +</ul></div> +<pre class="programlisting"><span class="special">-(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max</span><span class="special">)()</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">lowest</span><span class="special">();</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h2"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.min_function"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.min_function">min function</a> + </h5> +<p> + Function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span></code> + returns the minimum finite value that can be represented by the type T. + </p> +<p> + For built-in types there is usually a corresponding MACRO value TYPE_MIN, + where TYPE is CHAR, INT, FLOAT etc. + </p> +<p> + Other types, including those provided by a typedef, for example <code class="computeroutput"><span class="identifier">INT64_T_MIN</span></code> for <code class="computeroutput"><span class="identifier">int64_t</span></code>, + may provide a macro definition. + </p> +<p> + For floating-point types, it is more fully defined as the <span class="emphasis"><em>minimum + positive normalized value</em></span>. + </p> +<p> + See <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">denorm_min</span><span class="special">()</span></code> + for the smallest denormalized value, provided + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_denorm</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_present</span> +</pre> +<p> + To cater for situations where no <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + specialization is available (for example because the precision of the type + varies at runtime), packaged versions of this (and other functions) are + provided using + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">precision</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="identifier">T</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">min_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>();</span> +</pre> +<p> + Of course, these simply use <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span></code> if available. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h3"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.denorm_min_function"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.denorm_min_function">denorm_min + function</a> + </h5> +<p> + Function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">denorm_min</span><span class="special">()</span></code> + returns the smallest <a href="http://en.wikipedia.org/wiki/Denormal_number" target="_top">denormalized + value</a>, provided + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_denorm</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_present</span> +</pre> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="keyword">if</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">has_denorm</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_present</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">denorm_min</span><span class="special">();</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 4.9406564584124654e-324</span> + + <span class="keyword">int</span> <span class="identifier">exponent</span><span class="special">;</span> + + <span class="keyword">double</span> <span class="identifier">significand</span> <span class="special">=</span> <span class="identifier">frexp</span><span class="special">(</span><span class="identifier">d</span><span class="special">,</span> <span class="special">&</span><span class="identifier">exponent</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"exponent = "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">exponent</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// fffffbcf</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"significand = "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">significand</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.50000000000000000</span> +<span class="special">}</span> +<span class="keyword">else</span> +<span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"No denormalization. "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + The exponent is effectively reduced from -308 to -324 (though it remains + encoded as zero and leading zeros appear in the significand, thereby losing + precision until the significand reaches zero). + </p> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h4"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.round_error"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.round_error">round_error</a> + </h5> +<p> + Function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">round_error</span><span class="special">()</span></code> + returns the maximum error (in units of <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">ULP</a>) + that can be caused by any basic arithmetic operation. + </p> +<pre class="programlisting"><span class="identifier">round_style</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">round_indeterminate</span><span class="special">;</span> +</pre> +<p> + The rounding style is indeterminable at compile time. + </p> +<p> + For floating-point types, when rounding is to nearest, only half a bit + is lost by rounding, and <code class="computeroutput"><span class="identifier">round_error</span> + <span class="special">==</span> <span class="number">0.5</span></code>. + In contrast when rounding is towards zero, or plus/minus infinity, we can + loose up to one bit from rounding, and <code class="computeroutput"><span class="identifier">round_error</span> + <span class="special">==</span> <span class="number">1</span></code>. + </p> +<p> + For integer types, rounding always to zero, so at worst almost one bit + can be rounded, so <code class="computeroutput"><span class="identifier">round_error</span> + <span class="special">==</span> <span class="number">1</span></code>. + </p> +<p> + <code class="computeroutput"><span class="identifier">round_error</span><span class="special">()</span></code> + can be used with <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span></code> + to estimate the maximum potential error caused by rounding. For typical + floating-point types, <code class="computeroutput"><span class="identifier">round_error</span><span class="special">()</span> <span class="special">=</span> <span class="number">1</span><span class="special">/</span><span class="number">2</span></code>, so half + epsilon is the maximum potential error. + </p> +<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">round_err</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span> <span class="comment">// 2.2204460492503131e-016</span> + <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">round_error</span><span class="special">();</span> <span class="comment">// 1/2</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">round_err</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1.1102230246251565e-016</span> +</pre> +<p> + There are, of course, many occasions when much bigger loss of precision + occurs, for example, caused by <a href="http://en.wikipedia.org/wiki/Loss_of_significance" target="_top">Loss + of significance or cancellation error</a> or very many iterations. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h5"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.epsilon"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.epsilon">epsilon</a> + </h5> +<p> + Function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span></code> + is meaningful only for non-integral types. + </p> +<p> + It returns the difference between <code class="computeroutput"><span class="number">1.0</span></code> + and the next value representable by the floating-point type T. So it is + a one least-significant-bit change in this floating-point value. + </p> +<p> + For <code class="computeroutput"><span class="keyword">double</span></code> (<code class="computeroutput"><span class="identifier">float_64t</span></code>) it is <code class="computeroutput"><span class="number">2.2204460492503131e-016</span></code> + showing all possibly significant 17 decimal digits. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> +<span class="keyword">double</span> <span class="identifier">eps</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> +<span class="keyword">double</span> <span class="identifier">dpeps</span> <span class="special">=</span> <span class="identifier">d</span><span class="special">+</span><span class="identifier">eps</span><span class="special">;</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpoint</span> <span class="comment">// Ensure all trailing zeros are shown.</span> + <span class="special"><<</span> <span class="identifier">d</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="comment">// 1.0000000000000000</span> + <span class="special"><<</span> <span class="identifier">dpeps</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 2.2204460492503131e-016</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">dpeps</span> <span class="special">-</span> <span class="identifier">d</span> <span class="comment">// 1.0000000000000002</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + We can explicitly increment by one bit using the function <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">float_next</span><span class="special">()</span></code> + and the result is the same as adding <code class="computeroutput"><span class="identifier">epsilon</span></code>. + </p> +<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">one</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> +<span class="keyword">double</span> <span class="identifier">nad</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">float_next</span><span class="special">(</span><span class="identifier">one</span><span class="special">);</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">nad</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="comment">// 1.0000000000000002</span> + <span class="special"><<</span> <span class="identifier">nad</span> <span class="special">-</span> <span class="identifier">one</span> <span class="comment">// 2.2204460492503131e-016</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + Adding any smaller value, like half <code class="computeroutput"><span class="identifier">epsilon</span></code>, + will have no effect on this value. + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> +<span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> +<span class="keyword">double</span> <span class="identifier">eps</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> +<span class="keyword">double</span> <span class="identifier">dpeps</span> <span class="special">=</span> <span class="identifier">d</span> <span class="special">+</span> <span class="identifier">eps</span><span class="special">/</span><span class="number">2</span><span class="special">;</span> + +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpoint</span> <span class="comment">// Ensure all trailing zeros are shown.</span> + <span class="special"><<</span> <span class="identifier">dpeps</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="comment">// 1.0000000000000000</span> + <span class="special"><<</span> <span class="identifier">eps</span><span class="special">/</span><span class="number">2</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1.1102230246251565e-016</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">dpeps</span> <span class="special">-</span> <span class="identifier">d</span> <span class="comment">// 0.00000000000000000</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +</pre> +<p> + So this cancellation error leaves the values equal, despite adding half + <code class="computeroutput"><span class="identifier">epsilon</span></code>. + </p> +<p> + To achieve greater portability over platform and floating-point type, Boost.Math + and Boost.Multiprecion provide a package of functions that 'do something + sensible' if the standard <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + is not available. To use these <code class="computeroutput"><span class="preprocessor">#include</span> + <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">precision</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>. + </p> +<p> + A tolerance might be defined using this version of epsilon thus: + </p> +<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">tolerance</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">epsilon</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>()</span> <span class="special">*</span> <span class="number">2</span><span class="special">;</span> +</pre> +<h6> +<a name="boost_multiprecision.tut.limits.functions.h6"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.tolerance_for_floating_point_com"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.tolerance_for_floating_point_com">Tolerance + for Floating-point Comparisons</a> + </h6> +<p> + <code class="computeroutput"><span class="identifier">epsilon</span></code> is very useful + to compute a tolerance when comparing floating-point values, a much more + difficult task than is commonly imagined. + </p> +<p> + For more information you probably want (but still need) see <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">What + Every Computer Scientist Should Know About Floating-Point Arithmetic</a> + </p> +<p> + The naive test comparing the absolute difference between two values and + a tolerance does not give useful results if the values are too large or + too small. + </p> +<p> + So Boost.Test uses an algorithm first devised by Knuth for reliably checking + if floating-point values are close enough. + </p> +<p> + See Donald. E. Knuth. The art of computer programming (vol II). Copyright + 1998 Addison-Wesley Longman, Inc., 0-201-89684-2. Addison-Wesley Professional; + 3rd edition. + </p> +<p> + See also: + </p> +<p> + <a href="http://adtmag.com/articles/2000/03/15/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx" target="_top">Alberto + Squassia, Comparing floats</a> + </p> +<p> + <a href="http://adtmag.com/articles/2000/03/16/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx" target="_top">Alberto + Squassia, Comparing floats code</a> + </p> +<p> + <a href="../../../../../../../libs/test/doc/html/utf/testing-tools/floating_point_comparison.html" target="_top">floating-point + comparison</a>. + </p> +<p> + For example, if we want a tolerance that might suit about 9 arithmetical + operations, say sqrt(9) = 3, we could define: + </p> +<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">tolerance</span> <span class="special">=</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> +</pre> +<p> + This is very widely used in Boost.Math testing with Boost.Test's macro + <code class="computeroutput"><span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span></code> + </p> +<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> +<span class="identifier">T</span> <span class="identifier">calculated</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">+</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> + +<span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">expected</span><span class="special">,</span> <span class="identifier">calculated</span><span class="special">,</span> <span class="identifier">tolerance</span><span class="special">);</span> +</pre> +<p> + used thus: + </p> +<pre class="programlisting"><span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">expected</span><span class="special">,</span> <span class="identifier">calculated</span><span class="special">,</span> <span class="identifier">tolerance</span><span class="special">);</span> +</pre> +<p> + (There is also a version using tolerance as a percentage rather than a + fraction). + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</span><span class="special">;</span> +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float</span><span class="special">;</span> +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_off</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">>,</span> <span class="identifier">et_off</span> <span class="special">></span> <span class="identifier">cpp_dec_float_50</span><span class="special">;</span> <span class="comment">// 50 decimal digits.</span> +</pre> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + that Boost.Test does not yet allow floating-point comparisons with expression + templates on, so the default expression template parameter has been replaced + by <code class="computeroutput"><span class="identifier">et_off</span></code>. + </p></td></tr> +</table></div> +<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">tolerance</span> <span class="special">=</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">two_pi</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>();</span> +<span class="identifier">cpp_dec_float_50</span> <span class="identifier">calculated</span> <span class="special">=</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>();</span> + +<span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">expected</span><span class="special">,</span> <span class="identifier">calculated</span><span class="special">,</span> <span class="identifier">tolerance</span><span class="special">);</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h7"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.infinity_positive_and_negative"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.infinity_positive_and_negative">Infinity + - positive and negative</a> + </h5> +<p> + For floating-point types only, for which <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_infinity</span> + <span class="special">==</span> <span class="keyword">true</span></code>, + function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">()</span></code> + provides an implementation-defined representation for ∞. + </p> +<p> + The 'representation' is a particular bit pattern reserved for infinity. + For IEEE754 system (for which <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_iec559</span> + <span class="special">==</span> <span class="keyword">true</span></code>) + <a href="http://en.wikipedia.org/wiki/IEEE_754-1985#Positive_and_negative_infinity" target="_top">positive + and negative infinity</a> are assigned bit patterns for all defined + floating-point types. + </p> +<p> + Confusingly, the string resulting from outputting this representation, + is also implementation-defined. And the string that can be input to generate + the representation is also implementation-defined. + </p> +<p> + For example, the output is <code class="computeroutput"><span class="number">1.</span><span class="special">#</span><span class="identifier">INF</span></code> + on Microsoft systems, but <code class="computeroutput"><span class="identifier">inf</span></code> + on most *nix platforms. + </p> +<p> + This implementation-defined-ness has hampered use of infinity (and NaNs) + but Boost.Math and Boost.Multiprecision work hard to provide a sensible + representation for <span class="bold"><strong>all</strong></span> floating-point + types, not just the built-in types, which with the use of suitable facets + to define the input and output strings, makes it possible to use these + useful features portably and including Boost.Serialization. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.functions.h8"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.not_a_number_nan"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.not_a_number_nan">Not-A-Number + NaN</a> + </h5> +<h6> +<a name="boost_multiprecision.tut.limits.functions.h9"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.quiet_nan"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.quiet_nan">Quiet_NaN</a> + </h6> +<p> + For floating-point types only, for which <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_quiet_NaN</span> + <span class="special">==</span> <span class="keyword">true</span></code>, + function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code> + provides an implementation-defined representation for NaN. + </p> +<p> + <a href="http://en.wikipedia.org/wiki/NaN" target="_top">NaNs</a> are values to + indicate that the result of an assignment or computation is meaningless. + A typical example is <code class="computeroutput"><span class="number">0</span><span class="special">/</span><span class="number">0</span></code> but there are many others. + </p> +<p> + NaNs may also be used, to represent missing values: for example, these + could, by convention, be ignored in calculations of statistics like means. + </p> +<p> + Many of the problems with a representation for <a href="http://en.wikipedia.org/wiki/NaN" target="_top">Not-A-Number</a> + has hampered portable use, similar to those with infinity. + </p> +<p> + NaN can be used with binary multiprecision types like <code class="computeroutput"><span class="identifier">cpp_bin_float_quad</span></code>: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_float_quad</span><span class="special">;</span> + +<span class="keyword">if</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_quad</span><span class="special">>::</span><span class="identifier">has_quiet_NaN</span> <span class="special">==</span> <span class="keyword">true</span><span class="special">)</span> +<span class="special">{</span> + <span class="identifier">cpp_bin_float_quad</span> <span class="identifier">tolerance</span> <span class="special">=</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_quad</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">();</span> + + <span class="identifier">cpp_bin_float_quad</span> <span class="identifier">NaN</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_quad</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">();</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cpp_bin_float_quad NaN is "</span> <span class="special"><<</span> <span class="identifier">NaN</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// cpp_bin_float_quad NaN is nan</span> + + <span class="identifier">cpp_bin_float_quad</span> <span class="identifier">expected</span> <span class="special">=</span> <span class="identifier">NaN</span><span class="special">;</span> + <span class="identifier">cpp_bin_float_quad</span> <span class="identifier">calculated</span> <span class="special">=</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">NaN</span><span class="special">;</span> + <span class="comment">// Comparisons of NaN's always fail:</span> + <span class="keyword">bool</span> <span class="identifier">b</span> <span class="special">=</span> <span class="identifier">expected</span> <span class="special">==</span> <span class="identifier">calculated</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">b</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">BOOST_CHECK_NE</span><span class="special">(</span><span class="identifier">expected</span><span class="special">,</span> <span class="identifier">expected</span><span class="special">);</span> + <span class="identifier">BOOST_CHECK_NE</span><span class="special">(</span><span class="identifier">expected</span><span class="special">,</span> <span class="identifier">calculated</span><span class="special">);</span> +<span class="special">}</span> +<span class="keyword">else</span> +<span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Type "</span> <span class="special"><<</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">cpp_bin_float_quad</span><span class="special">).</span><span class="identifier">name</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" does not have NaNs!"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + But using Boost.Math and suitable facets can permit portable use of both + NaNs and positive and negative infinity. + </p> +<p> + See <a href="../../../../../../../libs/math/example/nonfinite_facet_sstream.cpp" target="_top">boost:/libs/math/example/nonfinite_facet_sstream.cpp</a> + and we also need + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">nonfinite_num_facets</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +</pre> +<p> + Then we can equally well use a multiprecision type cpp_bin_float_quad: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_bin_float_quad</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">cpp_bin_float_quad</span> <span class="identifier">T</span><span class="special">;</span> + +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_put</span><span class="special">;</span> +<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_get</span><span class="special">;</span> +<span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">old_locale</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">tmp_locale</span><span class="special">(</span><span class="identifier">old_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_put</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">new_locale</span><span class="special">(</span><span class="identifier">tmp_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_get</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span> + <span class="identifier">ss</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">new_locale</span><span class="special">);</span> + <span class="identifier">T</span> <span class="identifier">inf</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">();</span> + <span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">inf</span><span class="special">;</span> <span class="comment">// Write out.</span> + <span class="identifier">assert</span><span class="special">(</span><span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special">==</span> <span class="string">"inf"</span><span class="special">);</span> + <span class="identifier">T</span> <span class="identifier">r</span><span class="special">;</span> + <span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">r</span><span class="special">;</span> <span class="comment">// Read back in.</span> + <span class="identifier">assert</span><span class="special">(</span><span class="identifier">inf</span> <span class="special">==</span> <span class="identifier">r</span><span class="special">);</span> <span class="comment">// Confirms that the floating-point values really are identical.</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity output was "</span> <span class="special"><<</span> <span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity input was "</span> <span class="special"><<</span> <span class="identifier">r</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<pre class="programlisting"><span class="identifier">infinity</span> <span class="identifier">output</span> <span class="identifier">was</span> <span class="identifier">inf</span> +<span class="identifier">infinity</span> <span class="identifier">input</span> <span class="identifier">was</span> <span class="identifier">inf</span> +</pre> +<p> + Similarly we can do the same with NaN (except that we cannot use <code class="computeroutput"><span class="identifier">assert</span></code>) + </p> +<pre class="programlisting"><span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">old_locale</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">tmp_locale</span><span class="special">(</span><span class="identifier">old_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_put</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">new_locale</span><span class="special">(</span><span class="identifier">tmp_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_get</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span> + <span class="identifier">ss</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">new_locale</span><span class="special">);</span> + <span class="identifier">T</span> <span class="identifier">n</span><span class="special">;</span> + <span class="identifier">T</span> <span class="identifier">NaN</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">quiet_NaN</span><span class="special">();</span> + <span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">NaN</span><span class="special">;</span> <span class="comment">// Write out.</span> + <span class="identifier">assert</span><span class="special">(</span><span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special">==</span> <span class="string">"nan"</span><span class="special">);</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"NaN output was "</span> <span class="special"><<</span> <span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">n</span><span class="special">;</span> <span class="comment">// Read back in.</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"NaN input was "</span> <span class="special"><<</span> <span class="identifier">n</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + NaN output was nan NaN input was nan + </p> +<h6> +<a name="boost_multiprecision.tut.limits.functions.h10"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.functions.signaling_nan"></a></span><a class="link" href="functions.html#boost_multiprecision.tut.limits.functions.signaling_nan">Signaling + NaN</a> + </h6> +<p> + For floating-point types only, for which <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">has_signaling_NaN</span> + <span class="special">==</span> <span class="keyword">true</span></code>, + function <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">signaling_NaN</span><span class="special">()</span></code> + provides an implementation-defined representation for NaN that causes a + hardware trap. It should be noted however, that at least one implementation + of this function causes a hardware trap to be triggered simply by calling + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">signaling_NaN</span><span class="special">()</span></code>, + and not only by using the value returned. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="constants.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="limits32.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/how_to_tell.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/how_to_tell.html new file mode 100644 index 0000000000..6efd4f80af --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/how_to_tell.html @@ -0,0 +1,168 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>How to Determine the Kind of a Number From std::numeric_limits</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../limits.html" title="Numeric Limits"> +<link rel="prev" href="limits32.html" title="Numeric limits for 32-bit platform"> +<link rel="next" href="../input_output.html" title="Input Output"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="limits32.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../input_output.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.limits.how_to_tell"></a><a class="link" href="how_to_tell.html" title="How to Determine the Kind of a Number From std::numeric_limits">How to + Determine the Kind of a Number From <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code></a> +</h4></div></div></div> +<p> + Based on the information above, one can see that different kinds of numbers + can be differentiated based on the information stored in <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>. This is in addition to + the traits class <a class="link" href="../../ref/number.html#boost_multiprecision.ref.number.traits_class_support">number_category</a> + provided by this library. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.integer_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.integer_types">Integer + Types</a> + </h5> +<p> + For an integer type T, all of the following conditions hold: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_specialized</span> <span class="special">==</span> <span class="keyword">true</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">true</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">true</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min_exponent</span> <span class="special">==</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_exponent</span> <span class="special">==</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min_exponent10</span> <span class="special">==</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_exponent10</span> <span class="special">==</span> <span class="number">0</span> +</pre> +<p> + In addition the type is <span class="emphasis"><em>signed</em></span> if: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_signed</span> <span class="special">==</span> <span class="keyword">true</span> +</pre> +<p> + If the type is arbitrary precision then: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_bounded</span> <span class="special">==</span> <span class="keyword">false</span> +</pre> +<p> + Otherwise the type is bounded, and returns a non zero value from: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span> +</pre> +<p> + and has: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_modulo</span> <span class="special">==</span> <span class="keyword">true</span> +</pre> +<p> + if the type implements modulo arithmetic on overflow. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h1"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.rational_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.rational_types">Rational + Types</a> + </h5> +<p> + Rational types are just like integers except that: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">false</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h2"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.fixed_precision_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.fixed_precision_types">Fixed + Precision Types</a> + </h5> +<p> + There appears to be no way to tell these apart from rational types, unless + they set: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">false</span> +</pre> +<p> + This is because these types are in essence a rational type with a fixed + denominator. + </p> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h3"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.floating_point_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.floating_point_types">Floating + Point Types</a> + </h5> +<p> + For a floating point type T, all of the following conditions hold: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_specialized</span> <span class="special">==</span> <span class="keyword">true</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">false</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">false</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min_exponent</span> <span class="special">!=</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_exponent</span> <span class="special">!=</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min_exponent10</span> <span class="special">!=</span> <span class="number">0</span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max_exponent10</span> <span class="special">!=</span> <span class="number">0</span> +</pre> +<p> + In addition the type is <span class="emphasis"><em>signed</em></span> if: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_signed</span> <span class="special">==</span> <span class="keyword">true</span> +</pre> +<p> + And the type may be decimal or binary depending on the value of: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">radix</span> +</pre> +<p> + In general, there are no arbitrary precision floating point types, and + so: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_bounded</span> <span class="special">==</span> <span class="keyword">false</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h4"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.exact_floating_point_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.exact_floating_point_types">Exact + Floating Point Types</a> + </h5> +<p> + Exact floating point types are a <a href="http://en.wikipedia.org/wiki/Field_%28mathematics%29" target="_top">field</a> + composed of an arbitrary precision integer scaled by an exponent. Such + types have no division operator and are the same as floating point types + except: + </p> +<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">true</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.limits.how_to_tell.h5"></a> + <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.complex_numbers"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.complex_numbers">Complex + Numbers</a> + </h5> +<p> + For historical reasons, complex numbers do not specialize <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>, instead you must inspect + <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">></span></code>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="limits32.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../input_output.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/limits32.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/limits32.html new file mode 100644 index 0000000000..40d4570d5d --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/limits/limits32.html @@ -0,0 +1,2049 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Numeric limits for 32-bit platform</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../limits.html" title="Numeric Limits"> +<link rel="prev" href="functions.html" title="std::numeric_limits<> functions"> +<link rel="next" href="how_to_tell.html" title="How to Determine the Kind of a Number From std::numeric_limits"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="functions.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="how_to_tell.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.limits.limits32"></a><a class="link" href="limits32.html" title="Numeric limits for 32-bit platform">Numeric limits + for 32-bit platform</a> +</h4></div></div></div> +<p> + These tables were generated using the following program and options: + </p> +<pre class="programlisting"> +Program: + numeric_limits_qbk.cpp +Mon Nov 4 18:09:06 2013 +BuildInfo: + Platform Win32 + Compiler Microsoft Visual C++ version 10.0 + MSVC version 160040219. + STL Dinkumware standard library version 520 + Boost version 1.55.0 +</pre> +<div class="table"> +<a name="boost_multiprecision.tut.limits.limits32.integral_constants"></a><p class="title"><b>Table 1.4. Integer types constants (<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> + <span class="special">==</span> <span class="keyword">true</span></code> + && is_exact == true)</b></p> +<div class="table-contents"><table class="table" summary="Integer types constants (std::numeric_limits<T>::is_integer + == true + && is_exact == true)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + type + </p> + </th> +<th> + <p> + signed + </p> + </th> +<th> + <p> + bound + </p> + </th> +<th> + <p> + modulo + </p> + </th> +<th> + <p> + round + </p> + </th> +<th> + <p> + radix + </p> + </th> +<th> + <p> + digits + </p> + </th> +<th> + <p> + digits10 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + bool + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + no + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 1 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + char + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 7 + </p> + </td> +<td> + <p> + 2 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned char + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 8 + </p> + </td> +<td> + <p> + 2 + </p> + </td> +</tr> +<tr> +<td> + <p> + char16_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 16 + </p> + </td> +<td> + <p> + 4 + </p> + </td> +</tr> +<tr> +<td> + <p> + char32_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 32 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + short + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 15 + </p> + </td> +<td> + <p> + 4 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned short + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 16 + </p> + </td> +<td> + <p> + 4 + </p> + </td> +</tr> +<tr> +<td> + <p> + int + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 31 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 32 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + long + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 31 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned long + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 32 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + long long + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 63 + </p> + </td> +<td> + <p> + 18 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned long long + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 64 + </p> + </td> +<td> + <p> + 19 + </p> + </td> +</tr> +<tr> +<td> + <p> + int32_t + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 31 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + uint32_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 32 + </p> + </td> +<td> + <p> + 9 + </p> + </td> +</tr> +<tr> +<td> + <p> + int64_t + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 63 + </p> + </td> +<td> + <p> + 18 + </p> + </td> +</tr> +<tr> +<td> + <p> + uint64_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 64 + </p> + </td> +<td> + <p> + 19 + </p> + </td> +</tr> +<tr> +<td> + <p> + int128_t + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 128 + </p> + </td> +<td> + <p> + 38 + </p> + </td> +</tr> +<tr> +<td> + <p> + uint128_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 128 + </p> + </td> +<td> + <p> + 38 + </p> + </td> +</tr> +<tr> +<td> + <p> + int256_t + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 256 + </p> + </td> +<td> + <p> + 77 + </p> + </td> +</tr> +<tr> +<td> + <p> + uint256_t + </p> + </td> +<td> + <p> + unsigned + </p> + </td> +<td> + <p> + bound + </p> + </td> +<td> + <p> + modulo + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 256 + </p> + </td> +<td> + <p> + 77 + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_int + </p> + </td> +<td> + <p> + signed + </p> + </td> +<td> + <p> + unbounded + </p> + </td> +<td> + <p> + no + </p> + </td> +<td> + <p> + to zero + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 2147483647 + </p> + </td> +<td> + <p> + 646392383 + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.tut.limits.limits32.integral_functions"></a><p class="title"><b>Table 1.5. Integer types functions (<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> + <span class="special">==</span> <span class="keyword">true</span> + <span class="special">&&</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">lowest</span><span class="special">()</span></code> )</b></p> +<div class="table-contents"><table class="table" summary="Integer types functions (std::numeric_limits<T>::is_integer + == true + && std::numeric_limits<T>::min() == std::numeric_limits<T>::lowest() )"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + function + </p> + </th> +<th> + <p> + max + </p> + </th> +<th> + <p> + min + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + bool + </p> + </td> +<td> + <p> + 1 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + char + </p> + </td> +<td> + <p> + 127 + </p> + </td> +<td> + <p> + -128 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned char + </p> + </td> +<td> + <p> + 255 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + char16_t + </p> + </td> +<td> + <p> + 65535 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + char32_t + </p> + </td> +<td> + <p> + 4294967295 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + short + </p> + </td> +<td> + <p> + 32767 + </p> + </td> +<td> + <p> + -32768 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned short + </p> + </td> +<td> + <p> + 65535 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + int + </p> + </td> +<td> + <p> + 2147483647 + </p> + </td> +<td> + <p> + -2147483648 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned int + </p> + </td> +<td> + <p> + 4294967295 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + long + </p> + </td> +<td> + <p> + 2147483647 + </p> + </td> +<td> + <p> + -2147483648 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned long + </p> + </td> +<td> + <p> + 4294967295 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + long long + </p> + </td> +<td> + <p> + 9223372036854775807 + </p> + </td> +<td> + <p> + -9223372036854775808 + </p> + </td> +</tr> +<tr> +<td> + <p> + unsigned long long + </p> + </td> +<td> + <p> + 18446744073709551615 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + int32_t + </p> + </td> +<td> + <p> + 2147483647 + </p> + </td> +<td> + <p> + -2147483648 + </p> + </td> +</tr> +<tr> +<td> + <p> + int64_t + </p> + </td> +<td> + <p> + 9223372036854775807 + </p> + </td> +<td> + <p> + -9223372036854775808 + </p> + </td> +</tr> +<tr> +<td> + <p> + int128_t + </p> + </td> +<td> + <p> + 340282366920938463463374607431768211455 + </p> + </td> +<td> + <p> + -340282366920938463463374607431768211455 + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.tut.limits.limits32.float_functions"></a><p class="title"><b>Table 1.6. Floating-point types constants (<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span><span class="special">==</span><span class="keyword">false</span> <span class="special">&&</span> <span class="identifier">is_signed</span><span class="special">==</span><span class="keyword">true</span> <span class="special">&&</span> <span class="identifier">is_modulo</span><span class="special">==</span><span class="keyword">false</span> <span class="special">&&</span> <span class="identifier">is_exact</span><span class="special">==</span><span class="keyword">false</span> <span class="special">&&</span> <span class="identifier">is_bound</span><span class="special">==</span><span class="keyword">true</span></code>)</b></p> +<div class="table-contents"><table class="table" summary="Floating-point types constants (std::numeric_limits<T>::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + type + </p> + </th> +<th> + <p> + round + </p> + </th> +<th> + <p> + radix + </p> + </th> +<th> + <p> + digits + </p> + </th> +<th> + <p> + digits10 + </p> + </th> +<th> + <p> + max_digits10 + </p> + </th> +<th> + <p> + min_exp + </p> + </th> +<th> + <p> + min_exp10 + </p> + </th> +<th> + <p> + max_exp + </p> + </th> +<th> + <p> + max_exp10 + </p> + </th> +<th> + <p> + tiny + </p> + </th> +<th> + <p> + trap + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + float + </p> + </td> +<td> + <p> + to nearest + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 24 + </p> + </td> +<td> + <p> + 6 + </p> + </td> +<td> + <p> + 8 + </p> + </td> +<td> + <p> + -125 + </p> + </td> +<td> + <p> + -37 + </p> + </td> +<td> + <p> + 128 + </p> + </td> +<td> + <p> + 38 + </p> + </td> +<td> + <p> + tiny + </p> + </td> +<td> + <p> + traps + </p> + </td> +</tr> +<tr> +<td> + <p> + double + </p> + </td> +<td> + <p> + to nearest + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 53 + </p> + </td> +<td> + <p> + 15 + </p> + </td> +<td> + <p> + 17 + </p> + </td> +<td> + <p> + -1021 + </p> + </td> +<td> + <p> + -307 + </p> + </td> +<td> + <p> + 1024 + </p> + </td> +<td> + <p> + 308 + </p> + </td> +<td> + <p> + tiny + </p> + </td> +<td> + <p> + traps + </p> + </td> +</tr> +<tr> +<td> + <p> + long double + </p> + </td> +<td> + <p> + to nearest + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 53 + </p> + </td> +<td> + <p> + 15 + </p> + </td> +<td> + <p> + 17 + </p> + </td> +<td> + <p> + -1021 + </p> + </td> +<td> + <p> + -307 + </p> + </td> +<td> + <p> + 1024 + </p> + </td> +<td> + <p> + 308 + </p> + </td> +<td> + <p> + tiny + </p> + </td> +<td> + <p> + traps + </p> + </td> +</tr> +<tr> +<td> + <p> + cpp_dec_float_50 + </p> + </td> +<td> + <p> + indeterminate + </p> + </td> +<td> + <p> + 10 + </p> + </td> +<td> + <p> + 50 + </p> + </td> +<td> + <p> + 50 + </p> + </td> +<td> + <p> + 80 + </p> + </td> +<td> + <p> + -222953000 + </p> + </td> +<td> + <p> + -67108864 + </p> + </td> +<td> + <p> + 222953000 + </p> + </td> +<td> + <p> + 67108864 + </p> + </td> +<td> + <p> + no + </p> + </td> +<td> + <p> + no + </p> + </td> +</tr> +<tr> +<td> + <p> + bin_128bit_double_type + </p> + </td> +<td> + <p> + to nearest + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + 377 + </p> + </td> +<td> + <p> + 113 + </p> + </td> +<td> + <p> + 115 + </p> + </td> +<td> + <p> + -2147482894 + </p> + </td> +<td> + <p> + -646392082 + </p> + </td> +<td> + <p> + 2147482893 + </p> + </td> +<td> + <p> + 646392082 + </p> + </td> +<td> + <p> + no + </p> + </td> +<td> + <p> + traps + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"><div class="table"> +<a name="boost_multiprecision.tut.limits.limits32.float_functions0"></a><p class="title"><b>Table 1.7. Floating-point types functions (<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">is_integer</span> + <span class="special">==</span> <span class="keyword">false</span></code>)</b></p> +<div class="table-contents"><table class="table" summary="Floating-point types functions (std::numeric_limits<T>::is_integer + == false)"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + function + </p> + </th> +<th> + <p> + float + </p> + </th> +<th> + <p> + double + </p> + </th> +<th> + <p> + long double + </p> + </th> +<th> + <p> + cpp_dec_50 + </p> + </th> +<th> + <p> + cpp_bin_128 + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + max + </p> + </td> +<td> + <p> + 3.40282e+038 + </p> + </td> +<td> + <p> + 1.79769e+308 + </p> + </td> +<td> + <p> + 1.79769e+308 + </p> + </td> +<td> + <p> + 1e+67108865 + </p> + </td> +<td> + <p> + 1.85906e+646456766 + </p> + </td> +</tr> +<tr> +<td> + <p> + min + </p> + </td> +<td> + <p> + 1.17549e-038 + </p> + </td> +<td> + <p> + 2.22507e-308 + </p> + </td> +<td> + <p> + 2.22507e-308 + </p> + </td> +<td> + <p> + 1e-67108864 + </p> + </td> +<td> + <p> + 5.37906e-646456767 + </p> + </td> +</tr> +<tr> +<td> + <p> + epsilon + </p> + </td> +<td> + <p> + 1.19209e-007 + </p> + </td> +<td> + <p> + 2.22045e-016 + </p> + </td> +<td> + <p> + 2.22045e-016 + </p> + </td> +<td> + <p> + 1e-49 + </p> + </td> +<td> + <p> + 6.49713e-114 + </p> + </td> +</tr> +<tr> +<td> + <p> + round_error + </p> + </td> +<td> + <p> + 0.5 + </p> + </td> +<td> + <p> + 0.5 + </p> + </td> +<td> + <p> + 0.5 + </p> + </td> +<td> + <p> + 0.5 + </p> + </td> +<td> + <p> + 0.5 + </p> + </td> +</tr> +<tr> +<td> + <p> + infinity + </p> + </td> +<td> + <p> + 1.#INF + </p> + </td> +<td> + <p> + 1.#INF + </p> + </td> +<td> + <p> + 1.#INF + </p> + </td> +<td> + <p> + inf + </p> + </td> +<td> + <p> + inf + </p> + </td> +</tr> +<tr> +<td> + <p> + quiet_NaN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + nan + </p> + </td> +<td> + <p> + nan + </p> + </td> +</tr> +<tr> +<td> + <p> + signaling_NaN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + 1.#QNAN + </p> + </td> +<td> + <p> + 0 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +<tr> +<td> + <p> + denorm_min + </p> + </td> +<td> + <p> + 1.4013e-045 + </p> + </td> +<td> + <p> + 4.94066e-324 + </p> + </td> +<td> + <p> + 4.94066e-324 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +<td> + <p> + 0 + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<br class="table-break"> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="functions.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="how_to_tell.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/lits.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/lits.html new file mode 100644 index 0000000000..6971ffc88d --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/lits.html @@ -0,0 +1,210 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Literal Types and constexpr Support</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="primetest.html" title="Primality Testing"> +<link rel="next" href="rounding.html" title="Rounding Rules for Conversions"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="primetest.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rounding.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.lits"></a><a class="link" href="lits.html" title="Literal Types and constexpr Support">Literal Types and <code class="computeroutput"><span class="keyword">constexpr</span></code> Support</a> +</h3></div></div></div> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + The features described in this section make heavy use of C++11 language + features, currently (as of May 2013) only GCC-4.7 and later, and Clang + 3.3 and later have the support required to make these features work. + </p></td></tr> +</table></div> +<p> + There is limited support for <code class="computeroutput"><span class="keyword">constexpr</span></code> + and user-defined literals in the library, currently the <code class="computeroutput"><span class="identifier">number</span></code> + front end supports <code class="computeroutput"><span class="keyword">constexpr</span></code> + on default construction and all forwarding constructors, but not on any of + the non-member operators. So if some type <code class="computeroutput"><span class="identifier">B</span></code> + is a literal type, then <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">B</span><span class="special">></span></code> + is also a literal type, and you will be able to compile-time-construct such + a type from any literal that <code class="computeroutput"><span class="identifier">B</span></code> + is compile-time-constructible from. However, you will not be able to perform + compile-time arithmetic on such types. + </p> +<p> + Currently the only backend type provided by the library that is also a literal + type are instantiations of <code class="computeroutput"><span class="identifier">cpp_int_backend</span></code> + where the Allocator parameter is type <code class="computeroutput"><span class="keyword">void</span></code>, + and the Checked parameter is <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">unchecked</span></code>. + </p> +<p> + For example: + </p> +<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + +<span class="keyword">constexpr</span> <span class="identifier">int128_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="comment">// OK, fixed precision int128_t has no allocator.</span> +<span class="keyword">constexpr</span> <span class="identifier">uint1024_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">xFFFFFFFF00000000uLL</span><span class="special">;</span> <span class="comment">// OK, fixed precision uint1024_t has no allocator.</span> + +<span class="keyword">constexpr</span> <span class="identifier">checked_uint128_t</span> <span class="identifier">k</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="comment">// Error, checked type is not a literal type as we need runtime error checking.</span> +<span class="keyword">constexpr</span> <span class="identifier">cpp_int</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="comment">// Error, type is not a literal as it performs memory management.</span> +</pre> +<p> + There is also limited support for user defined-literals - these are limited + to unchecked, fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s + which are specified in hexadecimal notation. The suffixes supported are: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Suffix + </p> + </th> +<th> + <p> + Meaning + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + _cppi + </p> + </td> +<td> + <p> + Specifies a value of type: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">signed_magnitude</span><span class="special">,</span><span class="identifier">unchecked</span><span class="special">,</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span></code>, + where N is chosen to contain just enough digits to hold the number + specified. + </p> + </td> +</tr> +<tr> +<td> + <p> + _cppui + </p> + </td> +<td> + <p> + Specifies a value of type: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">unsigned_magnitude</span><span class="special">,</span><span class="identifier">unchecked</span><span class="special">,</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span></code>, + where N is chosen to contain just enough digits to hold the number + specified. + </p> + </td> +</tr> +<tr> +<td> + <p> + _cppi<span class="emphasis"><em>N</em></span> + </p> + </td> +<td> + <p> + Specifies a value of type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">signed_magnitude</span><span class="special">,</span><span class="identifier">unchecked</span><span class="special">,</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + _cppui<span class="emphasis"><em>N</em></span> + </p> + </td> +<td> + <p> + Specifies a value of type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">signed_magnitude</span><span class="special">,</span><span class="identifier">unchecked</span><span class="special">,</span><span class="keyword">void</span><span class="special">></span> <span class="special">></span></code>. + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + In each case, use of these suffixes with hexadecimal values produces a <code class="computeroutput"><span class="keyword">constexpr</span></code> result. + </p> +<p> + Examples: + </p> +<pre class="programlisting"><span class="comment">//</span> +<span class="comment">// Any use of user defined literals requires that we import the literal-operators</span> +<span class="comment">// into current scope first:</span> +<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">literals</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// To keep things simple in the example, we'll make our types used visible to this scope as well:</span> +<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// The value zero as a number<cpp_int_backend<4,4,signed_magnitude,unchecked,void> >:</span> +<span class="keyword">constexpr</span> <span class="keyword">auto</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">0x0</span><span class="identifier">_cppi</span><span class="special">;</span> +<span class="comment">// The type of each constant has 4 bits per hexadecimal digit,</span> +<span class="comment">// so this is of type uint256_t (ie number<cpp_int_backend<256,256,unsigned_magnitude,unchecked,void> >):</span> +<span class="keyword">constexpr</span> <span class="keyword">auto</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// Smaller values can be assigned to larger values:</span> +<span class="identifier">int256_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">0x1234</span><span class="identifier">_cppi</span><span class="special">;</span> <span class="comment">// OK</span> +<span class="comment">//</span> +<span class="comment">// However, this does not currently work in constexpr contexts:</span> +<span class="keyword">constexpr</span> <span class="identifier">int256_t</span> <span class="identifier">d</span> <span class="special">=</span> <span class="number">0x1</span><span class="identifier">_cppi</span><span class="special">;</span> <span class="comment">// Compiler error</span> +<span class="comment">//</span> +<span class="comment">// Constants can be padded out with leading zeros to generate wider types:</span> +<span class="keyword">constexpr</span> <span class="identifier">uint256_t</span> <span class="identifier">e</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">x0000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFF_cppui</span><span class="special">;</span> <span class="comment">// OK</span> +<span class="comment">//</span> +<span class="comment">// However, specific width types are best produced with specific-width suffixes,</span> +<span class="comment">// ones supported by default are `_cpp[u]i128`, `_cpp[u]i256`, `_cpp[u]i512`, `_cpp[u]i1024`.</span> +<span class="comment">//</span> +<span class="keyword">constexpr</span> <span class="identifier">int128_t</span> <span class="identifier">f</span> <span class="special">=</span> <span class="number">0x1234</span><span class="identifier">_cppi128</span><span class="special">;</span> <span class="comment">// OK, always produces an int128_t as the result.</span> +<span class="keyword">constexpr</span> <span class="identifier">uint1024_t</span> <span class="identifier">g</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccc_cppui1024</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// If other specific width types are required, then there is a macro for generating the operators</span> +<span class="comment">// for these. The macro can be used at namespace scope only:</span> +<span class="comment">//</span> +<span class="identifier">BOOST_MP_DEFINE_SIZED_CPP_INT_LITERAL</span><span class="special">(</span><span class="number">2048</span><span class="special">);</span> +<span class="comment">//</span> +<span class="comment">// Now we can create 2048-bit literals as well:</span> +<span class="keyword">constexpr</span> <span class="keyword">auto</span> <span class="identifier">h</span> <span class="special">=</span> <span class="number">0xff</span><span class="identifier">_cppi2048</span><span class="special">;</span> <span class="comment">// h is of type number<cpp_int_backend<2048,2048,signed_magnitude,unchecked,void> ></span> +<span class="comment">//</span> +<span class="comment">// Finally negative values are handled via the unary minus operator:</span> +<span class="comment">//</span> +<span class="keyword">constexpr</span> <span class="identifier">int1024_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="special">-</span><span class="number">0</span><span class="identifier">xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui1024</span><span class="special">;</span> +<span class="comment">//</span> +<span class="comment">// Which means this also works:</span> +<span class="keyword">constexpr</span> <span class="identifier">int1024_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">g</span><span class="special">;</span> <span class="comment">// OK: unary minus operator is constexpr.</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="primetest.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rounding.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/misc.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc.html new file mode 100644 index 0000000000..7438ba6ea1 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc.html @@ -0,0 +1,52 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Miscellaneous Number Types.</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="rational/rational_adaptor.html" title="rational_adaptor"> +<link rel="next" href="misc/logged_adaptor.html" title="logged_adaptor"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rational/rational_adaptor.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="misc/logged_adaptor.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.misc"></a><a class="link" href="misc.html" title="Miscellaneous Number Types.">Miscellaneous Number Types.</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="misc/logged_adaptor.html">logged_adaptor</a></span></dt> +<dt><span class="section"><a href="misc/debug_adaptor.html">debug_adaptor</a></span></dt> +<dt><span class="section"><a href="misc/visualizers.html">Visual C++ + Debugger Visualizers</a></span></dt> +</dl></div> +<p> + Backend types listed in this section are predominantly designed to aid debugging. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rational/rational_adaptor.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="misc/logged_adaptor.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html new file mode 100644 index 0000000000..5b7f0c3972 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html @@ -0,0 +1,99 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>debug_adaptor</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="prev" href="logged_adaptor.html" title="logged_adaptor"> +<link rel="next" href="visualizers.html" title="Visual C++ Debugger Visualizers"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="logged_adaptor.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="visualizers.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.misc.debug_adaptor"></a><a class="link" href="debug_adaptor.html" title="debug_adaptor">debug_adaptor</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">debug_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">debug_adaptor</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">debug_adaptor</span></code> type + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code> + and some other backend type: it acts as a thin wrapper around some other + backend to class <code class="computeroutput"><span class="identifier">number</span></code> + and intercepts all operations on that object storing the result as a string + within itself. + </p> +<p> + This type provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support whenever the template argument Backend does so. + </p> +<p> + This type is particularly useful when your debugger provides a good view + of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>: when this is the case multiprecision + values can easily be inspected in the debugger by looking at the <code class="computeroutput"><span class="identifier">debug_value</span></code> member of <code class="computeroutput"><span class="identifier">debug_adaptor</span></code>. + The down side of this approach is that runtimes are much slower when using + this type. Set against that it can make debugging very much easier, certainly + much easier than sprinkling code with <code class="computeroutput"><span class="identifier">printf</span></code> + statements. + </p> +<p> + When used in conjunction with the Visual C++ debugger visualisers, the + value of a multiprecision type that uses this backend is displayed in the + debugger just a builtin value would be, here we're inspecting a value of + type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">debug_adaptor</span><span class="special"><</span><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> + <span class="special">></span></code>: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger1.png"></span> + </p> +<p> + Otherwise you will need to expand out the view and look at the "debug_value" + member: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger2.png"></span> + </p> +<p> + It works for all the backend types equally too, here it is inspecting a + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">debug_adaptor</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span> + <span class="special">></span></code>: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger3.png"></span> + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="logged_adaptor.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="visualizers.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adapter.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adapter.html new file mode 100644 index 0000000000..91b44abd6f --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adapter.html @@ -0,0 +1,223 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>logged_adaptor</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="prev" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="next" href="../conversions.html" title="Constructing and Interconverting Between Number Types"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../misc.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../conversions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section boost_multiprecision_tut_misc_logged_adaptor"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.misc.logged_adaptor"></a><a class="link" href="logged_adaptor.html" title="logged_adaptor">logged_adaptor</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">result1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">result2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">arg4</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">logged_adaptor</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">logged_adaptor</span></code> type + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code> + and some other backend type: it acts as a thin wrapper around some other + backend to class <code class="computeroutput"><span class="identifier">number</span></code> + and logs all the events that take place on that object. Before any number + operation takes place, it calls <code class="computeroutput"><span class="identifier">log_prefix_event</span></code> + with the arguments to the operation (up to 4), plus a string describing + the operation. Then after the operation it calls <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + with the result of the operation, plus a string describing the operation. + Optionally, <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + takes a second result argument: this occurs when the result of the operation + is not a <code class="computeroutput"><span class="identifier">number</span></code>, for example + when <code class="computeroutput"><span class="identifier">fpclassify</span></code> is called, + <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> will + be called with <code class="computeroutput"><span class="identifier">result1</span></code> + being the argument to the function, and <code class="computeroutput"><span class="identifier">result2</span></code> + being the integer result of <code class="computeroutput"><span class="identifier">fpclassify</span></code>. + </p> +<p> + The default versions of <code class="computeroutput"><span class="identifier">log_prefix_event</span></code> + and <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> do + nothing, it is therefore up to the user to overload these for the particular + backend being observed. + </p> +<p> + This type provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support whenever the template argument Backend does so. + </p> +<p> + This type is particularly useful when combined with an interval number + type - in this case we can use <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + to monitor the error accumulated after each operation. We could either + set some kind of trap whenever the accumulated error exceeds some threshold, + or simply print out diagnostic information. Using this technique we can + quickly locate the cause of numerical instability in a particular routine. + The following example demonstrates this technique in a trivial algorithm + that deliberately introduces cancellation error: + </p> +<p> +</p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> +<span class="comment">//</span> +<span class="comment">// Begin by overloading log_postfix_event so we can capture each arithmetic event as it happens:</span> +<span class="comment">//</span> +<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">></span> +<span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// Print out the (relative) diameter of the interval:</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">></span> <span class="special">></span> <span class="identifier">diam</span><span class="special">;</span> + <span class="identifier">mpfi_diam</span><span class="special">(</span><span class="identifier">diam</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">val</span><span class="special">.</span><span class="identifier">data</span><span class="special">());</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Diameter was "</span> <span class="special"><<</span> <span class="identifier">diam</span> <span class="special"><<</span> <span class="string">" after operation: "</span> <span class="special"><<</span> <span class="identifier">event_description</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">>&,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// This version is never called in this example.</span> +<span class="special">}</span> + +<span class="special">}}</span> + + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">logged_adaptor</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">17</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">logged_type</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Test case deliberately introduces cancellation error, relative size of interval</span> + <span class="comment">// gradually gets larger after each operation:</span> + <span class="comment">//</span> + <span class="identifier">logged_type</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + <span class="identifier">a</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">13</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">logged_type</span> <span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="number">9</span><span class="special">;</span> + <span class="identifier">b</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + <span class="identifier">a</span> <span class="special">-=</span> <span class="identifier">b</span><span class="special">;</span> + <span class="special">}</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Final value was: "</span> <span class="special"><<</span> <span class="identifier">a</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + </p> +<p> + When we examine program output we can clearly see that the diameter of + the interval increases after each subtraction: + </p> +<p> +</p> +<pre class="programlisting"><span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Assignment</span> <span class="identifier">from</span> <span class="identifier">arithmetic</span> <span class="identifier">type</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.33681e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">7.70988e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.63735e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.38537e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54863e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84221e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19966e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.296861</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Final</span> <span class="identifier">value</span> <span class="identifier">was</span><span class="special">:</span> <span class="special">{</span><span class="number">8.51569e-15</span><span class="special">,</span><span class="number">1.14843e-14</span><span class="special">}</span> +</pre> +<p> + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2012 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../misc.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../conversions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html new file mode 100644 index 0000000000..278e2ab068 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html @@ -0,0 +1,215 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>logged_adaptor</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="prev" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="next" href="debug_adaptor.html" title="debug_adaptor"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a 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name="boost_multiprecision.tut.misc.logged_adaptor"></a><a class="link" href="logged_adaptor.html" title="logged_adaptor">logged_adaptor</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">result1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">result2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> +<span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">arg4</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="identifier">Backend</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">logged_adaptor</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">logged_adaptor</span></code> type + is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code> + and some other backend type: it acts as a thin wrapper around some other + backend to class <code class="computeroutput"><span class="identifier">number</span></code> + and logs all the events that take place on that object. Before any number + operation takes place, it calls <code class="computeroutput"><span class="identifier">log_prefix_event</span></code> + with the arguments to the operation (up to 4), plus a string describing + the operation. Then after the operation it calls <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + with the result of the operation, plus a string describing the operation. + Optionally, <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + takes a second result argument: this occurs when the result of the operation + is not a <code class="computeroutput"><span class="identifier">number</span></code>, for example + when <code class="computeroutput"><span class="identifier">fpclassify</span></code> is called, + <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> will + be called with <code class="computeroutput"><span class="identifier">result1</span></code> + being the argument to the function, and <code class="computeroutput"><span class="identifier">result2</span></code> + being the integer result of <code class="computeroutput"><span class="identifier">fpclassify</span></code>. + </p> +<p> + The default versions of <code class="computeroutput"><span class="identifier">log_prefix_event</span></code> + and <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> do + nothing, it is therefore up to the user to overload these for the particular + backend being observed. + </p> +<p> + This type provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> + support whenever the template argument Backend does so. + </p> +<p> + This type is particularly useful when combined with an interval number + type - in this case we can use <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> + to monitor the error accumulated after each operation. We could either + set some kind of trap whenever the accumulated error exceeds some threshold, + or simply print out diagnostic information. Using this technique we can + quickly locate the cause of numerical instability in a particular routine. + The following example demonstrates this technique in a trivial algorithm + that deliberately introduces cancellation error: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> +<span class="comment">//</span> +<span class="comment">// Begin by overloading log_postfix_event so we can capture each arithmetic event as it happens:</span> +<span class="comment">//</span> +<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">></span> +<span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// Print out the (relative) diameter of the interval:</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">></span> <span class="special">></span> <span class="identifier">diam</span><span class="special">;</span> + <span class="identifier">mpfi_diam</span><span class="special">(</span><span class="identifier">diam</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">val</span><span class="special">.</span><span class="identifier">data</span><span class="special">());</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Diameter was "</span> <span class="special"><<</span> <span class="identifier">diam</span> <span class="special"><<</span> <span class="string">" after operation: "</span> <span class="special"><<</span> <span class="identifier">event_description</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> +<span class="special">}</span> +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">D</span><span class="special">>&,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span> +<span class="special">{</span> + <span class="comment">// This version is never called in this example.</span> +<span class="special">}</span> + +<span class="special">}}</span> + + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">logged_adaptor</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">17</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">logged_type</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Test case deliberately introduces cancellation error, relative size of interval</span> + <span class="comment">// gradually gets larger after each operation:</span> + <span class="comment">//</span> + <span class="identifier">logged_type</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + <span class="identifier">a</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">13</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">logged_type</span> <span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="number">9</span><span class="special">;</span> + <span class="identifier">b</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + <span class="identifier">a</span> <span class="special">-=</span> <span class="identifier">b</span><span class="special">;</span> + <span class="special">}</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Final value was: "</span> <span class="special"><<</span> <span class="identifier">a</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + When we examine program output we can clearly see that the diameter of + the interval increases after each subtraction: + </p> +<pre class="programlisting"><span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Assignment</span> <span class="identifier">from</span> <span class="identifier">arithmetic</span> <span class="identifier">type</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.33681e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">7.70988e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.63735e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.38537e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54863e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84221e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19966e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span> +<span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.296861</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span> +<span class="identifier">Final</span> <span class="identifier">value</span> <span class="identifier">was</span><span class="special">:</span> <span class="special">{</span><span class="number">8.51569e-15</span><span class="special">,</span><span class="number">1.14843e-14</span><span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../misc.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="debug_adaptor.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/visualizers.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/visualizers.html new file mode 100644 index 0000000000..8b77d657b3 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/visualizers.html @@ -0,0 +1,106 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Visual C++ Debugger Visualizers</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../misc.html" title="Miscellaneous Number Types."> +<link rel="prev" href="debug_adaptor.html" title="debug_adaptor"> +<link rel="next" href="../conversions.html" title="Constructing and Interconverting Between Number Types"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="debug_adaptor.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../conversions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.misc.visualizers"></a><a class="link" href="visualizers.html" title="Visual C++ Debugger Visualizers">Visual C++ + Debugger Visualizers</a> +</h4></div></div></div> +<p> + Let's face it debugger multiprecision numbers is hard - simply because + we can't easily inspect the value of the numbers. Visual C++ provides a + partial solution in the shape of "visualizers" which provide + improved views of complex data structures, these visualizers need to be + added to the <code class="computeroutput"><span class="special">[</span><span class="identifier">Visualizer</span><span class="special">]</span></code> section of <code class="computeroutput"><span class="identifier">autoexp</span><span class="special">.</span><span class="identifier">dat</span></code> + located in the <code class="computeroutput"><span class="identifier">Common7</span><span class="special">/</span><span class="identifier">Packages</span><span class="special">/</span><span class="identifier">Debugger</span></code> + directory of your Visual Studio installation. The actual visualizer code + is in the sandbox <a href="https://svn.boost.org/svn/boost/sandbox/boost_docs/subprojects/DebuggerVisualizers/multiprecision.vis.txt" target="_top">here</a> + - just cut and paste the code into your <code class="computeroutput"><span class="identifier">autoexp</span><span class="special">.</span><span class="identifier">dat</span></code> + file. + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"><p> + These visualizers have only been tested with VC10, also given the ability + of buggy visualizers to crash your Visual C++ debugger, make sure you + back up <code class="computeroutput"><span class="identifier">autoexp</span><span class="special">.</span><span class="identifier">dat</span></code> file before using these!! + </p></td></tr> +</table></div> +<p> + The first visualizer provides improved views of <code class="computeroutput"><span class="identifier">debug_adaptor</span></code>: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger1.png"></span> + </p> +<p> + The next visualizer provides improved views of cpp_int: small numbers are + displayed as actual values, while larger numbers are displayed as an array + of hexadecimal parts, with the most significant part first. + </p> +<p> + Here's what it looks like for small values: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger4.png"></span> + </p> +<p> + And for larger values: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger5.png"></span> + </p> +<p> + There is also a <code class="computeroutput"><span class="special">~</span><span class="identifier">raw</span></code> + child member that lets you see the actual members of the class: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger6.png"></span> + </p> +<p> + The visualizer for <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> + shows the first few digits of the value in the preview field, and the full + array of digits when you expand the view. As before the <code class="computeroutput"><span class="special">~</span><span class="identifier">raw</span></code> child gives you access to the actual + data members: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../debugger7.png"></span> + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="debug_adaptor.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../misc.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../conversions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/mixed.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/mixed.html new file mode 100644 index 0000000000..4eb40a8c7f --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/mixed.html @@ -0,0 +1,177 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Mixed Precision Arithmetic</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="rounding.html" title="Rounding Rules for Conversions"> +<link rel="next" href="gen_int.html" title="Generic Integer Operations"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rounding.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gen_int.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.mixed"></a><a class="link" href="mixed.html" title="Mixed Precision Arithmetic">Mixed Precision Arithmetic</a> +</h3></div></div></div> +<p> + Mixed precision arithmetic is fully supported by the library. + </p> +<p> + There are two different forms: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Where the operands are of different precision. + </li> +<li class="listitem"> + Where the operands are of the same precision, but yield a higher precision + result. + </li> +</ul></div> +<h5> +<a name="boost_multiprecision.tut.mixed.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.mixed.mixing_operands_of_differing_pre"></a></span><a class="link" href="mixed.html#boost_multiprecision.tut.mixed.mixing_operands_of_differing_pre">Mixing + Operands of Differing Precision</a> + </h5> +<p> + If the arguments to a binary operator are of different precision, then the + operation is allowed as long as there is an unambiguous implicit conversion + from one argument type to the other. In all cases the arithmetic is performed + "as if" the lower precision type is promoted to the higher precision + type before applying the operator. However, particular backends may optimise + this and avoid actually creating a temporary if they are able to do so. + </p> +<p> + For example: + </p> +<pre class="programlisting"><span class="identifier">mpfr_float_50</span> <span class="identifier">a</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">b</span><span class="special">;</span> +<span class="identifier">mpfr_float_100</span> <span class="identifier">c</span><span class="special">(</span><span class="number">3</span><span class="special">),</span> <span class="identifier">d</span><span class="special">;</span> +<span class="identifier">static_mpfr_float_50</span> <span class="identifier">e</span><span class="special">(</span><span class="number">5</span><span class="special">),</span> <span class="identifier">f</span><span class="special">;</span> +<span class="identifier">mpz_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">20</span><span class="special">);</span> + +<span class="identifier">d</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">c</span><span class="special">;</span> <span class="comment">// OK, result of operand is an mpfr_float_100.</span> +<span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">c</span><span class="special">;</span> <span class="comment">// Error, can't convert the result to an mpfr_float_50 as it will lose digits.</span> +<span class="identifier">f</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">e</span><span class="special">;</span> <span class="comment">// Error, operator is ambiguous, result could be of either type.</span> +<span class="identifier">f</span> <span class="special">=</span> <span class="identifier">e</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// OK, unambiguous conversion from mpz_int to static_mpfr_float_50</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.mixed.h1"></a> + <span class="phrase"><a name="boost_multiprecision.tut.mixed.operands_of_the_same_precision"></a></span><a class="link" href="mixed.html#boost_multiprecision.tut.mixed.operands_of_the_same_precision">Operands + of the Same Precision</a> + </h5> +<p> + Sometimes you want to apply an operator to two arguments of the same precision + in such a way as to obtain a result of higher precision. The most common + situation occurs with fixed precision integers, where you want to multiply + two N-bit numbers to obtain a 2N-bit result. This is supported in this library + by the following free functions: + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> +<span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> +</pre> +<p> + These functions apply the named operator to the arguments <span class="emphasis"><em>a</em></span> + and <span class="emphasis"><em>b</em></span> and store the result in <span class="emphasis"><em>result</em></span>, + returning <span class="emphasis"><em>result</em></span>. In all cases they behave "as + if" arguments <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> were + first promoted to type <code class="computeroutput"><span class="identifier">ResultType</span></code> + before applying the operator, though particular backends may well avoid that + step by way of an optimization. + </p> +<p> + The type <code class="computeroutput"><span class="identifier">ResultType</span></code> must + be an instance of class <code class="computeroutput"><span class="identifier">number</span></code>, + and the types <code class="computeroutput"><span class="identifier">Source1</span></code> and + <code class="computeroutput"><span class="identifier">Source2</span></code> may be either instances + of class <code class="computeroutput"><span class="identifier">number</span></code> or native + integer types. The latter is an optimization that allows arithmetic to be + performed on native integer types producing an extended precision result. + </p> +<p> + For example: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint64_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint64_t</span><span class="special">>::</span><span class="identifier">max</span><span class="special">)();</span> + <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uint64_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="identifier">uint128_t</span> <span class="identifier">ui128</span><span class="special">;</span> + <span class="identifier">uint256_t</span> <span class="identifier">ui256</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Start by performing arithmetic on 64-bit integers to yield 128-bit results:</span> + <span class="comment">//</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">i</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ui128</span><span class="special">,</span> <span class="identifier">i</span><span class="special">,</span> <span class="identifier">j</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ui128</span><span class="special">,</span> <span class="identifier">i</span><span class="special">,</span> <span class="identifier">i</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// The try squaring a 128-bit integer to yield a 256-bit result:</span> + <span class="comment">//</span> + <span class="identifier">ui128</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">uint128_t</span><span class="special">>::</span><span class="identifier">max</span><span class="special">)();</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ui256</span><span class="special">,</span> <span class="identifier">ui128</span><span class="special">,</span> <span class="identifier">ui128</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Produces the output: + </p> +<pre class="programlisting"><span class="number">0</span><span class="identifier">xffffffffffffffff</span> +<span class="number">0</span><span class="identifier">x10000000000000000</span> +<span class="number">0</span><span class="identifier">xFFFFFFFFFFFFFFFE0000000000000001</span> +<span class="number">0</span><span class="identifier">xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE00000000000000000000000000000001</span> +</pre> +<h5> +<a name="boost_multiprecision.tut.mixed.h2"></a> + <span class="phrase"><a name="boost_multiprecision.tut.mixed.backends_with_optimized_mixed_pr"></a></span><a class="link" href="mixed.html#boost_multiprecision.tut.mixed.backends_with_optimized_mixed_pr">Backends + With Optimized Mixed Precision Arithmetic</a> + </h5> +<p> + The following backends have at least some direct support for mixed precision + arithmetic, and therefore avoid creating unnecessary temporaries when using + the interfaces above. Therefore when using these types it's more efficient + to use mixed precision arithmetic, than it is to explicitly cast the operands + to the result type: + </p> +<p> + <a class="link" href="floats/mpfr_float.html" title="mpfr_float">mpfr_float</a>, + <a class="link" href="floats/gmp_float.html" title="gmp_float">gmp_float</a>, + <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rounding.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gen_int.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/primetest.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/primetest.html new file mode 100644 index 0000000000..a4186e6bb4 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/primetest.html @@ -0,0 +1,116 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Primality Testing</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="random.html" title="Generating Random Numbers"> +<link rel="next" href="lits.html" title="Literal Types and constexpr Support"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="random.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="lits.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.primetest"></a><a class="link" href="primetest.html" title="Primality Testing">Primality Testing</a> +</h3></div></div></div> +<p> + The library implements a Miller-Rabin test for primality: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">miller_rabin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> +<span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> +</pre> +<p> + These functions perform a Miller-Rabin test for primality, if the result + is <code class="computeroutput"><span class="keyword">false</span></code> then <span class="emphasis"><em>n</em></span> + is definitely composite, while if the result is true then n is probably prime. + The probability to declare a composite n as probable prime is at most 0.25<sup>trials</sup>. + Note that this does not allow a statement about the probability of n being + actually prime (for that, the prior probability would have to be known). + The algorithm used performs some trial divisions to exclude small prime factors, + does one Fermat test to exclude many more composites, and then uses the Miller-Rabin + algorithm straight out of Knuth Vol 2, which recommends 25 trials for a pretty + strong likelihood that <span class="emphasis"><em>n</em></span> is prime. + </p> +<p> + The third optional argument is for a Uniform Random Number Generator from + Boost.Random. When not provided the <code class="computeroutput"><span class="identifier">mt19937</span></code> + generator is used. Note that when producing random primes then you should + probably use a different random number generator to produce candidate prime + numbers for testing, than is used internally by <code class="computeroutput"><span class="identifier">miller_rabin_test</span></code> + for determining whether the value is prime. It also helps of course to seed + the generators with some source of randomness. + </p> +<p> + The following example searches for a prime <code class="computeroutput"><span class="identifier">p</span></code> + for which <code class="computeroutput"><span class="special">(</span><span class="identifier">p</span><span class="special">-</span><span class="number">1</span><span class="special">)/</span><span class="number">2</span></code> is also probably prime: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">miller_rabin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">;</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="keyword">typedef</span> <span class="identifier">cpp_int</span> <span class="identifier">int_type</span><span class="special">;</span> + <span class="identifier">mt11213b</span> <span class="identifier">base_gen</span><span class="special">(</span><span class="identifier">clock</span><span class="special">());</span> + <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt11213b</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">int_type</span><span class="special">></span> <span class="identifier">gen</span><span class="special">(</span><span class="identifier">base_gen</span><span class="special">);</span> + <span class="comment">//</span> + <span class="comment">// We must use a different generator for the tests and number generation, otherwise</span> + <span class="comment">// we get false positives.</span> + <span class="comment">//</span> + <span class="identifier">mt19937</span> <span class="identifier">gen2</span><span class="special">(</span><span class="identifier">clock</span><span class="special">());</span> + + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="special">{</span> + <span class="identifier">int_type</span> <span class="identifier">n</span> <span class="special">=</span> <span class="identifier">gen</span><span class="special">();</span> + <span class="keyword">if</span><span class="special">(</span><span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="number">25</span><span class="special">,</span> <span class="identifier">gen2</span><span class="special">))</span> + <span class="special">{</span> + <span class="comment">// Value n is probably prime, see if (n-1)/2 is also prime:</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"We have a probable prime with value: "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">n</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">if</span><span class="special">(</span><span class="identifier">miller_rabin_test</span><span class="special">((</span><span class="identifier">n</span><span class="special">-</span><span class="number">1</span><span class="special">)/</span><span class="number">2</span><span class="special">,</span> <span class="number">25</span><span class="special">,</span> <span class="identifier">gen2</span><span class="special">))</span> + <span class="special">{</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"We have a safe prime with value: "</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">n</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> + <span class="special">}</span> + <span class="special">}</span> + <span class="special">}</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Ooops, no safe primes were found"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="random.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="lits.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/random.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/random.html new file mode 100644 index 0000000000..fa113f9669 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/random.html @@ -0,0 +1,167 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Generating Random Numbers</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="conversions.html" title="Constructing and Interconverting Between Number Types"> +<link rel="next" href="primetest.html" title="Primality Testing"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="conversions.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="primetest.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.random"></a><a class="link" href="random.html" title="Generating Random Numbers">Generating Random Numbers</a> +</h3></div></div></div> +<p> + Random numbers are generated in conjunction with Boost.Random. However, since + Boost.Random is unaware of <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary + precision</a> numbers, it's necessary to include the header: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +</pre> +<p> + In order to act as a bridge between the two libraries. + </p> +<p> + Integers with <span class="emphasis"><em>N</em></span> random bits are generated using <code class="computeroutput"><span class="identifier">independent_bits_engine</span></code>: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">;</span> + + <span class="comment">//</span> + <span class="comment">// Declare our random number generator type, the underlying generator</span> + <span class="comment">// is the Mersenne twister mt19937 engine, and 256 bits are generated:</span> + <span class="comment">//</span> + <span class="keyword">typedef</span> <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">generator_type</span><span class="special">;</span> + <span class="identifier">generator_type</span> <span class="identifier">gen</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Generate some values:</span> + <span class="comment">//</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span><span class="special">;</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">gen</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Alternatively we can generate integers in a given range using <code class="computeroutput"><span class="identifier">uniform_int_distribution</span></code>, this will invoke + the underlying engine multiple times to build up the required number of bits + in the result: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">;</span> + + <span class="comment">//</span> + <span class="comment">// Generate integers in a given range using uniform_int,</span> + <span class="comment">// the underlying generator is invoked multiple times</span> + <span class="comment">// to generate enough bits:</span> + <span class="comment">//</span> + <span class="identifier">mt19937</span> <span class="identifier">mt</span><span class="special">;</span> + <span class="identifier">uniform_int_distribution</span><span class="special"><</span><span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">ui</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">256</span><span class="special">);</span> + <span class="comment">//</span> + <span class="comment">// Generate the numbers:</span> + <span class="comment">//</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span><span class="special">;</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">ui</span><span class="special">(</span><span class="identifier">mt</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Floating point values in [0,1) are generated using <code class="computeroutput"><span class="identifier">uniform_01</span></code>, + the trick here is to ensure that the underlying generator produces as many + random bits as there are digits in the floating point type. As above <code class="computeroutput"><span class="identifier">independent_bits_engine</span></code> can be used for + this purpose, note that we also have to convert decimal digits (in the floating + point type) to bits (in the random number generator): + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// We need an underlying generator with at least as many bits as the</span> + <span class="comment">// floating point type to generate numbers in [0, 1) with all the bits</span> + <span class="comment">// in the floating point type randomly filled:</span> + <span class="comment">//</span> + <span class="identifier">uniform_01</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">uf</span><span class="special">;</span> + <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">50L</span><span class="special">*</span><span class="number">1000L</span><span class="special">/</span><span class="number">301L</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">gen</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Generate the values:</span> + <span class="comment">//</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">);</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">uf</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + Finally, we can modify the above example to produce numbers distributed according + to some distribution: + </p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// We can repeat the above example, with other distributions:</span> + <span class="comment">//</span> + <span class="identifier">uniform_real_distribution</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">ur</span><span class="special">(-</span><span class="number">20</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> + <span class="identifier">gamma_distribution</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">gd</span><span class="special">(</span><span class="number">20</span><span class="special">);</span> + <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">50L</span><span class="special">*</span><span class="number">1000L</span><span class="special">/</span><span class="number">301L</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">gen</span><span class="special">;</span> + <span class="comment">//</span> + <span class="comment">// Generate some values:</span> + <span class="comment">//</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">);</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">ur</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">gd</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="conversions.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="primetest.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational.html new file mode 100644 index 0000000000..f29486d993 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational.html @@ -0,0 +1,261 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Rational Number Types</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="interval/mpfi.html" title="mpfi_float"> +<link rel="next" href="rational/cpp_rational.html" title="cpp_rational"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="interval/mpfi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational/cpp_rational.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.rational"></a><a class="link" href="rational.html" title="Rational Number Types">Rational Number Types</a> +</h3></div></div></div> +<div class="toc"><dl class="toc"> +<dt><span class="section"><a href="rational/cpp_rational.html">cpp_rational</a></span></dt> +<dt><span class="section"><a href="rational/gmp_rational.html">gmp_rational</a></span></dt> +<dt><span class="section"><a href="rational/tommath_rational.html">tommath_rational</a></span></dt> +<dt><span class="section"><a href="rational/br.html">Use With Boost.Rational</a></span></dt> +<dt><span class="section"><a href="rational/rational_adaptor.html">rational_adaptor</a></span></dt> +</dl></div> +<p> + The following back-ends provide rational number arithmetic: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend Type + </p> + </th> +<th> + <p> + Header + </p> + </th> +<th> + <p> + Radix + </p> + </th> +<th> + <p> + Dependencies + </p> + </th> +<th> + <p> + Pros + </p> + </th> +<th> + <p> + Cons + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">cpp_rational</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/cpp_int.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + None + </p> + </td> +<td> + <p> + An all C++ Boost-licensed implementation. + </p> + </td> +<td> + <p> + Slower than <a href="http://gmplib.org" target="_top">GMP</a>. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">gmp_rational</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/gmp.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://gmplib.org" target="_top">GMP</a> + </p> + </td> +<td> + <p> + Very fast and efficient back-end. + </p> + </td> +<td> + <p> + Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a> + library. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">tommath_rational</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/tommath.hpp + </p> + </td> +<td> + <p> + 2 + </p> + </td> +<td> + <p> + <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a> + </p> + </td> +<td> + <p> + All C/C++ implementation that's Boost Software Licence compatible. + </p> + </td> +<td> + <p> + Slower than <a href="http://gmplib.org" target="_top">GMP</a>. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">rational_adaptor</span></code> + </p> + </td> +<td> + <p> + boost/multiprecision/rational_adaptor.hpp + </p> + </td> +<td> + <p> + N/A + </p> + </td> +<td> + <p> + none + </p> + </td> +<td> + <p> + All C++ adaptor that allows any integer back-end type to be used + as a rational type. + </p> + </td> +<td> + <p> + Requires an underlying integer back-end type. + </p> + </td> +</tr> +<tr> +<td> + <p> + <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code> + </p> + </td> +<td> + <p> + boost/rational.hpp + </p> + </td> +<td> + <p> + N/A + </p> + </td> +<td> + <p> + None + </p> + </td> +<td> + <p> + A C++ rational number type that can used with any <code class="computeroutput"><span class="identifier">number</span></code> integer type. + </p> + </td> +<td> + <p> + The expression templates used by <code class="computeroutput"><span class="identifier">number</span></code> + end up being "hidden" inside <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>: + performance may well suffer as a result. + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="interval/mpfi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational/cpp_rational.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/br.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/br.html new file mode 100644 index 0000000000..2f331f6f9b --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/br.html @@ -0,0 +1,51 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Use With Boost.Rational</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../rational.html" title="Rational Number Types"> +<link rel="prev" href="tommath_rational.html" title="tommath_rational"> +<link rel="next" href="rational_adaptor.html" title="rational_adaptor"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tommath_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational_adaptor.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.br"></a><a class="link" href="br.html" title="Use With Boost.Rational">Use With Boost.Rational</a> +</h4></div></div></div> +<p> + All of the integer types in this library can be used as template arguments + to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span><span class="special"><</span><span class="identifier">IntType</span><span class="special">></span></code>. + </p> +<p> + Note that using the library in this way largely negates the effect of the + expression templates in <code class="computeroutput"><span class="identifier">number</span></code>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="tommath_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rational_adaptor.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/cpp_rational.html new file mode 100644 index 0000000000..6a5756867a --- /dev/null +++ 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+<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.cpp_rational"></a><a class="link" href="cpp_rational.html" title="cpp_rational">cpp_rational</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">typedef</span> <span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">cpp_int_backend</span><span class="special"><></span> <span class="special">></span> <span class="identifier">cpp_rational_backend</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_rational_backend</span><span class="special">></span> <span class="identifier">cpp_rational</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">cpp_rational_backend</span></code> + type is used via the typedef <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_rational</span></code>. + It provides a rational number type that is a drop-in replacement for the + native C++ number types, but with unlimited precision. + </p> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">cpp_rational</span></code> are copy + constructible and assignable from type <code class="computeroutput"><span class="identifier">cpp_int</span></code>. + </p> +<p> + There is also a two argument constructor that accepts a numerator and denominator: + both of type <code class="computeroutput"><span class="identifier">cpp_int</span></code>. + </p> +<p> + There are also non-member functions: + </p> +<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">numerator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">cpp_rational</span><span class="special">&);</span> +<span class="identifier">cpp_int</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">cpp_rational</span><span class="special">&);</span> +</pre> +<p> + which return the numerator and denominator of the number. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">cpp_rational</span></code>s + have the value zero. + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid rational + number. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.rational.cpp_rational.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.rational.cpp_rational.example"></a></span><a class="link" href="cpp_rational.html#boost_multiprecision.tut.rational.cpp_rational.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">cpp_rational</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">1000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + <span class="identifier">v</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000! / 10</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">numerator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">denominator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="identifier">cpp_rational</span> <span class="identifier">w</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// component wise constructor</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">w</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 2/3</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gmp_rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/gmp_rational.html new file mode 100644 index 0000000000..6800cc4264 --- /dev/null +++ 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+<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tommath_rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.gmp_rational"></a><a class="link" href="gmp_rational.html" title="gmp_rational">gmp_rational</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">class</span> <span class="identifier">gmp_rational</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span> <span class="special">></span> <span class="identifier">mpq_rational</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">gmp_rational</span></code> back-end + is used via the typedef <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">mpq_rational</span></code>. + It acts as a thin wrapper around the <a href="http://gmplib.org" target="_top">GMP</a> + <code class="computeroutput"><span class="identifier">mpq_t</span></code> to provide a rational + number type that is a drop-in replacement for the native C++ number types, + but with unlimited precision. + </p> +<p> + As well as the usual conversions from arithmetic and string types, instances + of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code> + are copy constructible and assignable from: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + The <a href="http://gmplib.org" target="_top">GMP</a> native types: <code class="computeroutput"><span class="identifier">mpz_t</span></code>, <code class="computeroutput"><span class="identifier">mpq_t</span></code>. + </li> +<li class="listitem"> + <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>. + </li> +</ul></div> +<p> + There is also a two-argument constructor that accepts a numerator and denominator + (both of type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>). + </p> +<p> + There are also non-member functions: + </p> +<pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">numerator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpq_rational</span><span class="special">&);</span> +<span class="identifier">mpz_int</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpq_rational</span><span class="special">&);</span> +</pre> +<p> + which return the numerator and denominator of the number. + </p> +<p> + It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpq_t</span></code> + via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> + member function of <code class="computeroutput"><span class="identifier">mpq_rational</span></code>. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">mpq_rational</span></code>s + have the value zero (this is the <a href="http://gmplib.org" target="_top">GMP</a> + default behavior). + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid rational + number. + </li> +<li class="listitem"> + No changes are made to the <a href="http://gmplib.org" target="_top">GMP</a> + library's global settings, so this type can coexist with existing + <a href="http://gmplib.org" target="_top">GMP</a> code. + </li> +<li class="listitem"> + The code can equally be used with <a href="http://mpir.org/" target="_top">MPIR</a> + as the underlying library - indeed that is the preferred option on + Win32. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.rational.gmp_rational.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.rational.gmp_rational.example"></a></span><a class="link" href="gmp_rational.html#boost_multiprecision.tut.rational.gmp_rational.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">mpq_rational</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">1000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + <span class="identifier">v</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000! / 10</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">numerator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">denominator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="identifier">mpq_rational</span> <span class="identifier">w</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// component wise constructor</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">w</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 2/3</span> + + <span class="comment">// Access the underlying data:</span> + <span class="identifier">mpq_t</span> <span class="identifier">q</span><span class="special">;</span> + <span class="identifier">mpq_init</span><span class="special">(</span><span class="identifier">q</span><span class="special">);</span> + <span class="identifier">mpq_set</span><span class="special">(</span><span class="identifier">q</span><span class="special">,</span> <span class="identifier">v</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> + <span class="identifier">mpq_clear</span><span class="special">(</span><span class="identifier">q</span><span class="special">);</span> + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cpp_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tommath_rational.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adapter.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adapter.html new file mode 100644 index 0000000000..8ef5da4274 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adapter.html @@ -0,0 +1,67 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>rational_adaptor</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../rational.html" title="Rational Number Types"> +<link rel="prev" href="br.html" title="Use With Boost.Rational"> +<link rel="next" href="../misc.html" title="Miscellaneous Number Types."> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="br.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../misc.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section boost_multiprecision_tut_rational_rational_adaptor"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.rational_adaptor"></a><a class="link" href="rational_adaptor.html" title="rational_adaptor">rational_adaptor</a> +</h4></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">IntBackend</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">rational_adpater</span><span class="special">;</span> + +<span class="special">}}</span> +</pre> +<p> + The class template <code class="computeroutput"><span class="identifier">rational_adaptor</span></code> + is a back-end for <code class="computeroutput"><span class="identifier">number</span></code> + which converts any existing integer back-end into a rational-number back-end. + </p> +<p> + So for example, given an integer back-end type <code class="computeroutput"><span class="identifier">MyIntegerBackend</span></code>, + the use would be something like: + </p> +<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">MyIntegerBackend</span><span class="special">></span> <span class="identifier">MyInt</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">MyIntegerBackend</span><span class="special">></span> <span class="special">></span> <span class="identifier">MyRational</span><span class="special">;</span> + +<span class="identifier">MyRational</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> +<span class="identifier">r</span> <span class="special">/=</span> <span class="number">3</span><span class="special">;</span> +<span class="identifier">MyInt</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">numerator</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> +<span class="identifier">assert</span><span class="special">(</span><span class="identifier">i</span> <span class="special">==</span> <span class="number">2</span><span class="special">);</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2012 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="br.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../misc.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html new file mode 100644 index 0000000000..26623160ee --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html @@ -0,0 +1,67 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>rational_adaptor</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../rational.html" title="Rational Number Types"> +<link rel="prev" href="br.html" title="Use With Boost.Rational"> +<link rel="next" href="../misc.html" title="Miscellaneous Number Types."> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="br.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../misc.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.rational_adaptor"></a><a class="link" href="rational_adaptor.html" title="rational_adaptor">rational_adaptor</a> +</h4></div></div></div> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">IntBackend</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">rational_adpater</span><span class="special">;</span> + +<span class="special">}}</span> +</pre> +<p> + The class template <code class="computeroutput"><span class="identifier">rational_adaptor</span></code> + is a back-end for <code class="computeroutput"><span class="identifier">number</span></code> + which converts any existing integer back-end into a rational-number back-end. + </p> +<p> + So for example, given an integer back-end type <code class="computeroutput"><span class="identifier">MyIntegerBackend</span></code>, + the use would be something like: + </p> +<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">MyIntegerBackend</span><span class="special">></span> <span class="identifier">MyInt</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">rational_adaptor</span><span class="special"><</span><span class="identifier">MyIntegerBackend</span><span class="special">></span> <span class="special">></span> <span class="identifier">MyRational</span><span class="special">;</span> + +<span class="identifier">MyRational</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> +<span class="identifier">r</span> <span class="special">/=</span> <span class="number">3</span><span class="special">;</span> +<span class="identifier">MyInt</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">numerator</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> +<span class="identifier">assert</span><span class="special">(</span><span class="identifier">i</span> <span class="special">==</span> <span class="number">2</span><span class="special">);</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="br.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../misc.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/tommath_rational.html new file mode 100644 index 0000000000..5df03879e5 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rational/tommath_rational.html @@ -0,0 +1,130 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>tommath_rational</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../rational.html" title="Rational Number Types"> +<link rel="prev" href="gmp_rational.html" title="gmp_rational"> +<link rel="next" href="br.html" title="Use With Boost.Rational"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="br.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h4 class="title"> +<a name="boost_multiprecision.tut.rational.tommath_rational"></a><a class="link" href="tommath_rational.html" title="tommath_rational">tommath_rational</a> +</h4></div></div></div> +<p> + <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">tommath</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> + +<span class="keyword">typedef</span> <span class="identifier">rational_adpater</span><span class="special"><</span><span class="identifier">tommath_int</span><span class="special">></span> <span class="identifier">tommath_rational</span><span class="special">;</span> +<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">tommath_rational</span> <span class="special">></span> <span class="identifier">tom_rational</span><span class="special">;</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The <code class="computeroutput"><span class="identifier">tommath_rational</span></code> back-end + is used via the typedef <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">tom_rational</span></code>. + It acts as a thin wrapper around <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span><span class="special"><</span><span class="identifier">tom_int</span><span class="special">></span></code> to provide a rational number type that + is a drop-in replacement for the native C++ number types, but with unlimited + precision. + </p> +<p> + The advantage of using this type rather than <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span><span class="special"><</span><span class="identifier">tom_int</span><span class="special">></span></code> directly, is that it is expression-template + enabled, greatly reducing the number of temporaries created in complex + expressions. + </p> +<p> + There are also non-member functions: + </p> +<pre class="programlisting"><span class="identifier">tom_int</span> <span class="identifier">numerator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">tom_rational</span><span class="special">&);</span> +<span class="identifier">tom_int</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">tom_rational</span><span class="special">&);</span> +</pre> +<p> + which return the numerator and denominator of the number. + </p> +<p> + Things you should know when using this type: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Default constructed <code class="computeroutput"><span class="identifier">tom_rational</span></code>s + have the value zero (this the inherited Boost.Rational behavior). + </li> +<li class="listitem"> + Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> + being thrown. + </li> +<li class="listitem"> + Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> + being thrown if the string can not be interpreted as a valid rational + number. + </li> +<li class="listitem"> + No changes are made to <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a>'s + global state, so this type can safely coexist with other <a href="http://libtom.org/?page=features&newsitems=5&whatfile=ltm" target="_top">libtommath</a> + code. + </li> +<li class="listitem"> + Performance of this type has been found to be pretty poor - this need + further investigation - but it appears that Boost.Rational needs some + improvement in this area. + </li> +</ul></div> +<h6> +<a name="boost_multiprecision.tut.rational.tommath_rational.h0"></a> + <span class="phrase"><a name="boost_multiprecision.tut.rational.tommath_rational.example"></a></span><a class="link" href="tommath_rational.html#boost_multiprecision.tut.rational.tommath_rational.example">Example:</a> + </h6> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">tommath</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> + +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> + + <span class="identifier">tom_rational</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> + + <span class="comment">// Do some arithmetic:</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><=</span> <span class="number">1000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> + <span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span> + <span class="identifier">v</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span> + + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">v</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1000! / 10</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">numerator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">denominator</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="identifier">tom_rational</span> <span class="identifier">w</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Component wise constructor</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">w</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 2/3</span> + + <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> +<span class="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gmp_rational.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rational.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="br.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/rounding.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/rounding.html new file mode 100644 index 0000000000..9626a37b66 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/rounding.html @@ -0,0 +1,191 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Rounding Rules for Conversions</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="lits.html" title="Literal Types and constexpr Support"> +<link rel="next" href="mixed.html" title="Mixed Precision Arithmetic"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="lits.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mixed.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.rounding"></a><a class="link" href="rounding.html" title="Rounding Rules for Conversions">Rounding Rules for + Conversions</a> +</h3></div></div></div> +<p> + As a general rule, all conversions between unrelated types are performed + using basic arithmetic operations, therefore conversions are either exact, + or follow the same rounding rules as arithmetic for the type in question. + </p> +<p> + The following table summarises the situation for conversions from native + types: + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Backend + </p> + </th> +<th> + <p> + Rounding Rules + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a> + </p> + </td> +<td> + <p> + Conversions from integer types are exact if the target has sufficient + precision, otherwise they truncate to the first 2^MaxBits bits + (modulo arithmetic). Conversions from floating point types are + truncating to the nearest integer. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a> + </p> + </td> +<td> + <p> + Conversions are performed by the GMP library except for conversion + from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code> + which is truncating. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a> + </p> + </td> +<td> + <p> + Conversions from floating point types are truncating, all others + are performed by libtommath and are exact. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="floats/gmp_float.html" title="gmp_float">gmp_float</a> + </p> + </td> +<td> + <p> + Conversions are performed by the GMP library except for conversion + from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code> + which should be exact provided the target type has as much precision + as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="floats/mpfr_float.html" title="mpfr_float">mpfr_float</a> + </p> + </td> +<td> + <p> + All conversions are performed by the underlying MPFR library. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> + </p> + </td> +<td> + <p> + All conversions are performed using basic arithmetic operations + and are truncating. + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="rational/gmp_rational.html" title="gmp_rational">gmp_rational</a> + </p> + </td> +<td> + <p> + See <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a> + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="rational/cpp_rational.html" title="cpp_rational">cpp_rational</a> + </p> + </td> +<td> + <p> + See <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a> + </p> + </td> +</tr> +<tr> +<td> + <p> + <a class="link" href="rational/tommath_rational.html" title="tommath_rational">tommath_rational</a> + </p> + </td> +<td> + <p> + See <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="lits.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mixed.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/serial.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/serial.html new file mode 100644 index 0000000000..667dcea832 --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/serial.html @@ -0,0 +1,64 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Boost.Serialization Support</title> +<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../tut.html" title="Tutorial"> +<link rel="prev" href="gen_int.html" title="Generic Integer Operations"> +<link rel="next" href="limits.html" title="Numeric Limits"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gen_int.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="limits.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_multiprecision.tut.serial"></a><a class="link" href="serial.html" title="Boost.Serialization Support">Boost.Serialization + Support</a> +</h3></div></div></div> +<p> + Support for serialization comes in two forms: + </p> +<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> +<li class="listitem"> + Classes <a class="link" href="../ref/number.html" title="number">number</a>, + <a class="link" href="misc/debug_adaptor.html" title="debug_adaptor">debug_adaptor</a>, + <a class="link" href="misc/logged_adaptor.html" title="logged_adaptor">logged_adaptor</a> + and <a class="link" href="rational/rational_adaptor.html" title="rational_adaptor">rational_adaptor</a> + have "pass through" serialization support which requires the + underlying backend to be serializable. + </li> +<li class="listitem"> + Backends <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>, + <a class="link" href="floats/cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a>, + <a class="link" href="floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> + and <a class="link" href="floats/float128.html" title="float128">float128</a> + have full support for Boost.Serialization. + </li> +</ul></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="gen_int.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="limits.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/multiprecision/doc/html/index.html b/libs/multiprecision/doc/html/index.html new file mode 100644 index 0000000000..c39180a691 --- /dev/null +++ b/libs/multiprecision/doc/html/index.html @@ -0,0 +1,172 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Chapter 1. Boost.Multiprecision</title> +<link rel="stylesheet" href="../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="next" href="boost_multiprecision/intro.html" title="Introduction"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td> +<td align="center"><a href="../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"><a accesskey="n" href="boost_multiprecision/intro.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a></div> +<div class="chapter"> +<div class="titlepage"><div> +<div><h2 class="title"> +<a name="boost_multiprecision"></a>Chapter 1. Boost.Multiprecision</h2></div> +<div><div class="author"><h3 class="author"> +<span class="firstname">John</span> <span class="surname">Maddock</span> +</h3></div></div> +<div><div class="author"><h3 class="author"> +<span class="firstname">Christopher</span> <span class="surname">Kormanyos</span> +</h3></div></div> +<div><p class="copyright">Copyright © 2002-2013 John Maddock and Christopher Kormanyos</p></div> +<div><div class="legalnotice"> +<a name="boost_multiprecision.legal"></a><p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></div> +</div></div> +<div class="toc"> +<p><b>Table of Contents</b></p> +<dl class="toc"> +<dt><span class="section"><a href="boost_multiprecision/intro.html">Introduction</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut.html">Tutorial</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/ints.html">Integer Types</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/cpp_int.html">cpp_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/gmp_int.html">gmp_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/tom_int.html">tom_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/egs.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/egs/factorials.html">Factorials</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/ints/egs/bitops.html">Bit Operations</a></span></dt> +</dl></dd> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/floats.html">Floating Point Numbers</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/cpp_bin_float.html">cpp_bin_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/cpp_dec_float.html">cpp_dec_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/gmp_float.html">gmp_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/mpfr_float.html">mpfr_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/float128.html">float128</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg.html">Examples</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg/aos.html">Area of + Circle</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg/jel.html">Defining + a Special Function.</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg/nd.html">Calculating + a Derivative</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg/gi.html">Calculating + an Integral</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/floats/fp_eg/poly_eg.html">Polynomial + Evaluation</a></span></dt> +</dl></dd> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/interval.html">Interval Number Types</a></span></dt> +<dd><dl><dt><span class="section"><a href="boost_multiprecision/tut/interval/mpfi.html">mpfi_float</a></span></dt></dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/rational.html">Rational Number Types</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/rational/cpp_rational.html">cpp_rational</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/rational/gmp_rational.html">gmp_rational</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/rational/tommath_rational.html">tommath_rational</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/rational/br.html">Use With Boost.Rational</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/rational/rational_adaptor.html">rational_adaptor</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/misc.html">Miscellaneous Number Types.</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/misc/logged_adaptor.html">logged_adaptor</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/misc/debug_adaptor.html">debug_adaptor</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/misc/visualizers.html">Visual C++ + Debugger Visualizers</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/conversions.html">Constructing and + Interconverting Between Number Types</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/random.html">Generating Random Numbers</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/primetest.html">Primality Testing</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/lits.html">Literal Types and <code class="computeroutput"><span class="keyword">constexpr</span></code> Support</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/rounding.html">Rounding Rules for + Conversions</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/mixed.html">Mixed Precision Arithmetic</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/gen_int.html">Generic Integer Operations</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/serial.html">Boost.Serialization + Support</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/limits.html">Numeric Limits</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/tut/limits/constants.html">std::numeric_limits<> + constants</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/limits/functions.html">std::numeric_limits<> + functions</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/limits/limits32.html">Numeric limits + for 32-bit platform</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/tut/limits/how_to_tell.html">How to + Determine the Kind of a Number From <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code></a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/tut/input_output.html">Input Output</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/ref.html">Reference</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/ref/number.html">number</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/cpp_int_ref.html">cpp_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/gmp_int_ref.html">gmp_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/tom_int_ref.html">tom_int</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/mpf_ref.html">gmp_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/mpfr_ref.html">mpfr_float_backend</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/cpp_bin_float_ref.html">cpp_bin_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/cpp_dec_ref.html">cpp_dec_float</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/internals.html">Internal Support + Code</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/backendconc.html">Backend Requirements</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/ref/headers.html">Header File Structure</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/perf.html">Performance Comparison</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/perf/overhead.html">The Overhead in the + Number Class Wrapper</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/perf/realworld.html">Floating-Point Real + World Tests</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/perf/int_real_world.html">Integer Real + World Tests</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/perf/float_performance.html">Float Algorithm + Performance</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/perf/integer_performance.html">Integer + Algorithm Performance</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/perf/rational_performance.html">Rational + Type Performance</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/map.html">Roadmap</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/map/hist.html">History</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/map/todo.html">TODO</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/map/faq.html">FAQ</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/map/ack.html">Acknowledgements</a></span></dt> +</dl></dd> +<dt><span class="section"><a href="boost_multiprecision/indexes.html">Indexes</a></span></dt> +<dd><dl> +<dt><span class="section"><a href="boost_multiprecision/indexes/s01.html">Function Index</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/indexes/s02.html">Class Index</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/indexes/s03.html">Typedef Index</a></span></dt> +<dt><span class="section"><a href="boost_multiprecision/indexes/s04.html">Index</a></span></dt> +</dl></dd> +</dl> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"><p><small>Last revised: October 17, 2014 at 17:53:54 GMT</small></p></td> +<td align="right"><div class="copyright-footer"></div></td> +</tr></table> +<hr> +<div class="spirit-nav"><a accesskey="n" href="boost_multiprecision/intro.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a></div> +</body> +</html> diff --git a/libs/multiprecision/doc/html4_symbols.qbk b/libs/multiprecision/doc/html4_symbols.qbk new file mode 100644 index 0000000000..3462e30fa0 --- /dev/null +++ b/libs/multiprecision/doc/html4_symbols.qbk @@ -0,0 +1,215 @@ +[/ Symbols and Greek letters (about 120) from HTML4.] +[/ File HTML4_symbols.qbk] +[/ See http://www.htmlhelp.com/reference/html40/entities/symbols.html] +[/ See also http://en.wikipedia.org/wiki/List_of_XML_and_HTML_character_entity_references] +[/ http://www.alanwood.net/demos/ent4_frame.html] +[/ http://www.unicode.org/charts/PDF/U2200.pdf and others] +[/ All (except 2 angle brackets) show OK on Firefox 2.0] + +[/ See also Latin-1 aka Western (ISO-8859-1) in latin1_symbols.qbk] +[/ http://www.htmlhelp.com/reference/html40/entities/latin1.html] +[/Unicode Latin extended http://www.unicode.org/charts/U0080.pdf] + +[/ Also some miscellaneous math characters added to this list - see the end.] +[/ For others see also math_symbols.qbk] + +[/ To use, enclose the template name in square brackets.] + +[template fnof[]'''ƒ'''] [/ ƒ Latin small f with hook = function = florin] +[/ Capital Greek start with capital letter, lower case all small.] +[template Alpha[]'''Α'''] [/ ? Greek capital letter alpha] +[template Beta[]'''Β'''] [/ ? Greek capital letter beta] +[template Gamma[]'''Γ'''] [/ G Greek capital letter gamma] +[template Delta[]'''Δ'''] [/ ? Greek capital letter delta] +[template Epsilon[]'''Ε'''] [/ ? Greek capital letter epsilon] +[template Zeta[]'''Ζ'''] [/ ? Greek capital letter zeta] +[template Eta[]'''Η'''] [/ ? Greek capital letter eta] +[template Theta[]'''Θ'''] [/ T Greek capital letter theta] +[template Iota[]'''Ι'''] [/ ? Greek capital letter iota] +[template Kappa[]'''Κ'''] [/ ? Greek capital letter kappa] +[template Lambda[]'''Λ'''] [/ ? Greek capital letter lambda] +[template Mu[]'''Μ'''] [/ ? Greek capital letter mu] +[template Nu[]'''Ν'''] [/ ? Greek capital letter nu] +[template Xi[]'''Ξ'''] [/ ? Greek capital letter xi] +[template Omicron[]'''Ο'''] [/ ? Greek capital letter omicron] +[template Pi[]'''Π'''] [/ ? Greek capital letter pi] +[template Rho[]'''Ρ'''] [/ ? Greek capital letter rho] +[template Sigma[]'''Σ'''] [/ S Greek capital letter sigma] +[template Tau[]'''Τ'''] [/ ? Greek capital letter tau] +[template Upsilon[]'''Υ'''] [/ ? Greek capital letter upsilon] +[template Phi[]'''Φ'''] [/ F Greek capital letter phi] +[template Chi[]'''Χ'''] [/ ? Greek capital letter chi] +[template Psi[]'''Ψ'''] [/ ? Greek capital letter psi] +[template Omega[]'''Ω'''] [/ O Greek capital letter omega] +[template alpha[]'''α'''] [/ a Greek small letter alpha] +[template beta[]'''β'''] [/ ß Greek small letter beta] +[template gamma[]'''γ'''] [/ ? Greek small letter gamma] +[template delta[]'''δ'''] [/ d Greek small letter delta] +[template epsilon[]'''ε'''] [/ e Greek small letter epsilon] +[template zeta[]'''ζ'''] [/ ? Greek small letter zeta] +[template eta[]'''η'''] [/ ? Greek small letter eta] +[template theta[]'''θ'''] [/ ? Greek small letter theta] +[template iota[]'''ι'''] [/ ? Greek small letter iota] +[template kappa[]'''κ'''] [/ ? Greek small letter kappa] +[template lambda[]'''λ'''] [/ ? Greek small letter lambda] +[template mu[]'''μ'''] [/ µ Greek small letter mu] +[template nu[]'''ν'''] [/ ? Greek small letter nu] +[template xi[]'''ξ'''] [/ ? Greek small letter xi] +[template omicron[]'''ο'''] [/ ? Greek small letter omicron] +[template pi[]'''π'''] [/ p Greek small letter pi] +[template rho[]'''ρ'''] [/ ? Greek small letter rho] +[template sigmaf[]'''ς'''] [/ ? Greek small letter final sigma] +[template sigma[]'''σ'''] [/ s Greek small letter sigma] +[template tau[]'''τ'''] [/ t Greek small letter tau] +[template upsilon[]'''υ'''] [/ ? Greek small letter upsilon] +[template phi[]'''φ'''] [/ f Greek small letter phi] +[template chi[]'''χ'''] [/ ? Greek small letter chi] +[template psi[]'''ψ'''] [/ ? Greek small letter psi] +[template omega[]'''ω'''] [/ ? Greek small letter omega] +[template thetasym[]'''ϑ'''] [/ ? Greek small letter theta symbol] +[template upsih[]'''ϒ'''] [/ ? Greek upsilon with hook symbol] +[template piv[]'''ϖ'''] [/ ? Greek pi symbol] + +[template bull[]'''•'''] [/ • bullet = black small circle] +[template hellip[]'''…'''] [/ … horizontal ellipsis = three dot leader] +[template prime[]'''′'''] [/ ' prime = minutes = feet] +[template Prime[]'''″'''] [/ ? double prime = seconds = inches] +[template oline[]'''‾'''] [/ ? overline = spacing overscore] +[template frasl[]'''⁄'''] [/ / fraction slash] +[template weierp[]'''℘'''] [/ P script capital P = power set = Weierstrass p] +[template image[]'''ℑ'''] [/ I blackletter capital I = imaginary part] +[template real[]'''ℜ'''] [/ R blackletter capital R = real part symbol] +[template trade[]'''™'''] [/ ™ trade mark sign] +[template alefsym[]'''ℵ'''] [/ ? alef symbol = first transfinite cardinal] +[template larr[]'''←'''] [/ ? leftwards arrow] +[template uarr[]'''↑'''] [/ ? upwards arrow] +[template rarr[]'''→'''] [/ ? rightwards arrow] +[template darr[]'''↓'''] [/ ? downwards arrow] +[template harr[]'''↔'''] [/ ? left right arrow] +[template crarr[]'''↵'''] [/ ? downwards arrow with corner leftwards = CR] +[template lArr[]'''⇐'''] [/ ? leftwards double arrow] +[template uArr[]'''⇑'''] [/ ? upwards double arrow] +[template rArr[]'''⇒'''] [/ ? rightwards double arrow] +[template dArr[]'''⇓'''] [/ ? downwards double arrow] +[template hArr[]'''⇔'''] [/ ? left right double arrow] +[template forall[]'''∀'''] [/ ? for all] +[template part[]'''∂'''] [/ ? partial differential] +[template exist[]'''∃'''] [/ ? there exists] +[template empty[]'''∅'''] [/ Ø empty set = null set = diameter] +[template nabla[]'''∇'''] [/ ? nabla = backward difference] +[template isin[]'''∈'''] [/ ? element of] +[template notin[]'''∉'''] [/ ? not an element of] +[template ni[]'''∋'''] [/ ? contains as member] +[template prod[]'''∏'''] [/ ? n-ary product = product sign] +[template sum[]'''∑'''] [/ ? n-ary sumation] +[template minus[]'''−'''] [/ - minus sign] +[template lowast[]'''∗'''] [/ * asterisk operator] +[template radic[]'''√'''] [/ v square root = radical sign] +[template prop[]'''∝'''] [/ ? proportional to] +[template infin[]'''∞'''] [/ 8 infinity] +[template ang[]'''∠'''] [/ ? angle] +[template and[]'''∧'''] [/ ? logical and = wedge] +[template or[]'''∨'''] [/ ? logical or = vee] +[template cap[]'''∩'''] [/ n intersection = cap] +[template cup[]'''∪'''] [/ ? union = cup] +[template int[]'''∫'''] [/ ? integral] +[template there4[]'''∴'''] [/ ? therefore] +[template sim[]'''∼'''] [/ ~ tilde operator = varies with = similar to] +[template cong[]'''≅'''] [/ ? approximately equal to] +[template asymp[]'''≈'''] [/ ˜ almost equal to = asymptotic to] +[template ne[]'''≠'''] [/ ? not equal to] +[template equiv[]'''≡'''] [/ = identical to] +[template le[]'''≤'''] [/ = less-than or equal to] +[template ge[]'''≥'''] [/ = greater-than or equal to] +[template subset[]'''⊂'''] [/ ? subset of] +[template superset[]'''⊃'''] [/ ? superset of] +[template nsubset[]'''⊄'''] [/ ? not a subset of] +[template sube[]'''⊆'''] [/ ? subset of or equal to] +[template supe[]'''⊇'''] [/ ? superset of or equal to] +[template oplus[]'''⊕'''] [/ ? circled plus = direct sum] +[template otimes[]'''⊗'''] [/ ? circled times = vector product] +[template perp[]'''⊥'''] [/ ? up tack = orthogonal to = perpendicular] +[template sdot[]'''⋅'''] [/ · dot operator] +[template lceil[]'''⌈'''] [/ ? left ceiling = APL upstile] +[template rceil[]'''⌉'''] [/ ? right ceiling] +[template lfloor[]'''⌊'''] [/ ? left floor = APL downstile] +[template rfloor[]'''⌋'''] [/ ? right floor] +[template lang[]'''〈'''] [/ < left-pointing angle bracket = bra (Firefox shows ?)] +[template rang[]'''〉'''] [/ > right-pointing angle bracket = ket (Firefox shows ?)] +[template loz[]'''◊'''] [/ ? lozenge] +[template spades[]'''♠'''] [/ ? black spade suit] +[template clubs[]'''♣'''] [/ ? black club suit = shamrock] +[template hearts[]'''♥'''] [/ ? black heart suit = valentine] +[template diams[]'''♦'''] [/ ? black diamond suit] +[template euro[]'''€'''] [/ ? Euro currency symbol] +[template lchev[]'''⟨'''] [/ ? left chevron] +[template rchev[]'''⟩'''] [/ right chevron] +[template rflat[]'''⟮'''] [/ right flat bracket Misc Math Symbol A] +[template lflat[]'''⟮'''] [/ left flat bracket] +[/ U2000.pdf punctuation] +[template endash[]'''–'''] [/ em width dash] +[template emdash[]'''—'''] [/ en width dash] +[template hbar[]'''―'''] [/ ? horizontal bar - introducing quoted text] +[template vert2bar[]'''‖'''] [/ ? double vertical bar] +[template line2[]'''‖'''] [/ ? double low line bar] +[template dagger[]'''†'''] [/ ? dagger] +[template dagger2[]'''‡'''] [/ ? double dagger] +[template dot[]'''․'''] [/ dot leader] +[template dot2[]'''‥'''] [/ ? dots leader] +[template ellipsis[]'''…'''] [/ horizontal ellipsis] + +[template dotover[]'''̇'''] [/ dot over symbol] +[template recur[]''' ̇'''] [/ math recurring symbol, eg after 0.333] +[/ Note use of a thin space before digit, so that dot isn't placed directly over the digit.] +[/ Use:1[recur]] + +[/ Other symbols, not in the HTML4 list:] +[template enquad[] ''' '''] [/ en quad space] +[template emquad[] ''' '''] [/ em quad space] +[template enspace[] ''' '''] [/ em half en space] +[template emspace[] ''' '''] [/ em space type size in points] +[template thickspace[] ''' '''] [/ 3 per em space] +[template midspace[] ''' '''] [/ 4 per em space] +[template sixemspace[] ''' '''] [/ 6 em space] +[template figspace[] ''' '''] [/ space = width fixed font digit] +[template punctspace[] ''' '''] [/ space = width punctuation] +[template thin[] ''' '''] [/ thin space ] +[template hair[] ''' '''] [/ hair space] +[template nbsp[] ''' '''] [/ non-breaking space] +[template space[] ''' '''] [/ plain non-breaking space] + +[template nospace[] '''​'''] [/ zero width space] +[template wordjoin[] '''⁠'''] [/ word joiner - no line break either side] +[template narrownbsp[] ''' '''] [/ narrow non-breaking space] +[template hyphen[] '''‐'''] [/ soft hyphen] +[template nbhyphen[] '''‑'''] [/ non-breaking hyphen] + +[template plusminus[]'''±'''] [/ ? plus or minus sign] +[template sqrt[]'''√'''] [/ ? square root sqrt symbol] +[/template pow2[]'''⁳'''] [/ 2073 is NOT superscript 2 character] +[template pow2[]'''²'''] [/ superscript 2 character] +[template pow3[]'''³'''] [/ superscript 3 character] +[template pown[]'''ⁿ'''] [/ superscript n character] +[template frac12[]'''½'''] [/ fraction half] +[template frac14[]'''¼'''] [/ fraction quarter] +[template frac34[]'''¾'''] [/ fraction three quarter] +[template sup1[]'''¹'''] [/ superscript one = superscript digit one ] +[template sup2[]'''²'''] [/ superscript two = superscript digit two = squared ] +[template cubed[]'''³'''] [/ superscript three = superscript digit three = cubed ] +[template macron[]'''¯'''] [/ macron = spacing macron = overline = APL overbar ] +[template deg[]'''°'''] [/ degree sign ] +[template plusmn[]'''±'''] [/ plus-minus sign = plus-or-minus sign ] +[template micro[]'''µ'''] [/ micro sign ] +[template cedil[]'''¸'''] [/ cedilla = spacing cedilla ] +[template ordm[]'''º'''] [/ masculine ordinal indicator ] +[template ordf[]'''ª'''] [/ feminine ordinal indicator ] +[template laquo[]'''«'''] [/ left-pointing double angle quotation mark = left pointing guillemet ] +[template raquo[]'''»'''] [/ right-pointing double angle quotation mark = right pointing guillemet ] + +[/ +Copyright 2007, 2010 Paul A. Bristow. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/libs/multiprecision/doc/index.idx b/libs/multiprecision/doc/index.idx new file mode 100644 index 0000000000..629072a409 --- /dev/null +++ b/libs/multiprecision/doc/index.idx @@ -0,0 +1,18 @@ +# Copyright 2011 John Maddock. Distributed under the Boost +# Software License, Version 1.0. (See accompanying file +# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +# +# Rewrite the class scanner to accept declarations, not just definitions, +# as the docs don't include full definitions. +# +!define-scanner class_name "^[[:space:]]*(template[[:space:]]*<[^;:{]+>[[:space:]]*)?(class|struct)[[:space:]]*(\<\w+\>([[:blank:]]*\([^)]*\))?[[:space:]]*)*(\<\w*\>)[[:space:]]*(<[^;:{]+>)?[[:space:]]*(\{|:[^;\{()]*\{)" "(?:class|struct)[^;{]+\\<\5\\>\\s*[;{]" \5 + +!scan-path boost/multiprecision .*\.hpp true + + + + + + + + diff --git a/libs/multiprecision/doc/multiprecision.qbk b/libs/multiprecision/doc/multiprecision.qbk new file mode 100644 index 0000000000..274302bda7 --- /dev/null +++ b/libs/multiprecision/doc/multiprecision.qbk @@ -0,0 +1,5203 @@ +[/ + Copyright 2011, 2013 John Maddock. + Copyright 2013 Paul A. Bristow. + Copyright 2013 Christopher Kormanyos. + + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + +[library Boost.Multiprecision + [quickbook 1.7] + [copyright 2002-2013 John Maddock and Christopher Kormanyos] + [purpose Multiprecision Number library] + [license + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + [@http://www.boost.org/LICENSE_1_0.txt]) + ] + [authors [Maddock, John], [Kormanyos, Christopher]] + [/last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] +] + +[import html4_symbols.qbk] + +[import ../example/gmp_snips.cpp] +[import ../example/mpfr_snips.cpp] +[import ../example/mpfi_snips.cpp] +[import ../example/float128_snips.cpp] +[import ../example/cpp_dec_float_snips.cpp] +[import ../example/cpp_bin_float_snips.cpp] +[import ../example/tommath_snips.cpp] +[import ../example/cpp_int_snips.cpp] +[import ../example/random_snips.cpp] +[import ../example/safe_prime.cpp] +[import ../example/mixed_integer_arithmetic.cpp] +[import ../example/logged_adaptor.cpp] +[import ../example/numeric_limits_snips.cpp] + +[template mpfr[] [@http://www.mpfr.org MPFR]] +[template mpfi[] [@http://perso.ens-lyon.fr/nathalie.revol/software.html MPFI]] +[template gmp[] [@http://gmplib.org GMP]] +[template mpf_class[] [@http://gmplib.org/manual/C_002b_002b-Interface-Floats.html#C_002b_002b-Interface-Floats mpf_class]] +[template mpfr_class[] [@http://math.berkeley.edu/~wilken/code/gmpfrxx/ mpfr_class]] +[template mpreal[] [@http://www.holoborodko.com/pavel/mpfr/ mpreal]] +[template mpir[] [@http://mpir.org/ MPIR]] +[template tommath[] [@http://libtom.org/?page=features&newsitems=5&whatfile=ltm libtommath]] +[template quadmath[] [@http://gcc.gnu.org/onlinedocs/libquadmath/ libquadmath]] + +[template super[x]'''<superscript>'''[x]'''</superscript>'''] +[template sub[x]'''<subscript>'''[x]'''</subscript>'''] + +[template equation[name] '''<inlinemediaobject> +<imageobject role="html"> +<imagedata fileref="../'''[name]'''.png"></imagedata> +</imageobject> +<imageobject role="print"> +<imagedata fileref="../'''[name]'''.svg"></imagedata> +</imageobject> +</inlinemediaobject>'''] + +[def __cpp_int [link boost_multiprecision.tut.ints.cpp_int cpp_int]] +[def __gmp_int [link boost_multiprecision.tut.ints.gmp_int gmp_int]] +[def __tom_int [link boost_multiprecision.tut.ints.tom_int tom_int]] +[def __gmp_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]] +[def __mpf_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]] +[def __mpfr_float_backend [link boost_multiprecision.tut.floats.mpfr_float mpfr_float]] +[def __cpp_bin_float [link boost_multiprecision.tut.floats.cpp_bin_float cpp_bin_float]] +[def __cpp_dec_float [link boost_multiprecision.tut.floats.cpp_dec_float cpp_dec_float]] +[def __gmp_rational [link boost_multiprecision.tut.rational.gmp_rational gmp_rational]] +[def __cpp_rational [link boost_multiprecision.tut.rational.cpp_rational cpp_rational]] +[def __tommath_rational [link boost_multiprecision.tut.rational.tommath_rational tommath_rational]] +[def __number [link boost_multiprecision.ref.number number]] +[def __float128 [link boost_multiprecision.tut.floats.float128 float128]] +[def __debug_adaptor [link boost_multiprecision.tut.misc.debug_adaptor debug_adaptor]] +[def __logged_adaptor [link boost_multiprecision.tut.misc.logged_adaptor logged_adaptor]] +[def __rational_adaptor [link boost_multiprecision.tut.rational.rational_adaptor rational_adaptor]] + +[section:intro Introduction] + +The Multiprecision Library provides [link boost_multiprecision.tut.ints integer], +[link boost_multiprecision.tut.rational rational] +and [link boost_multiprecision.tut.floats floating-point] types in C++ that have more +range and precision than C++'s ordinary built-in types. +The big number types in Multiprecision can be used with a wide +selection of basic mathematical operations, elementary transcendental +functions as well as the functions in Boost.Math. +The Multiprecision types can also interoperate with the +built-in types in C++ using clearly defined conversion rules. +This allows Boost.Multiprecision to be used for all +kinds of mathematical calculations involving integer, +rational and floating-point types requiring extended +range and precision. + +Multiprecision consists of a generic interface to the +mathematics of large numbers as well as a selection of +big number back ends, with support for integer, rational and +floating-point types. Boost.Multiprecision provides a selection +of back ends provided off-the-rack in including +interfaces to GMP, MPFR, MPIR, TomMath as well as +its own collection of Boost-licensed, header-only back ends for +integers, rationals and floats. In addition, user-defined back ends +can be created and used with the interface of Multiprecision, +provided the class implementation adheres to the necessary +[link boost_multiprecision.ref.backendconc concepts]. + +Depending upon the number type, precision may be arbitrarily large +(limited only by available memory), fixed at compile time +(for example 50 or 100 decimal digits), or a variable controlled at run-time +by member functions. The types are expression-template-enabled for +better performance than naive user-defined types. + +The Multiprecision library comes in two distinct parts: + +* An expression-template-enabled front-end `number` +that handles all the operator overloading, expression evaluation optimization, and code reduction. +* A selection of back-ends that implement the actual arithmetic operations, and need conform only to the +reduced interface requirements of the front-end. + +Separation of front-end and back-end allows use of highly refined, but restricted license libraries +where possible, but provides Boost license alternatives for users who must have a portable +unconstrained license. Which is to say some back-ends rely on 3rd party libraries, but a header-only Boost license version is always +available (if somewhat slower). + +Should you just wish to cut to the chase and use a fully Boost-licensed number type, then skip to +__cpp_int for multiprecision integers, __cpp_dec_float for multiprecision floating point types +and __cpp_rational for rational types. + +The library is often used via one of the predefined typedefs: for example if you wanted an +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] +integer type using [gmp] as the underlying implementation then you could use: + + #include <boost/multiprecision/gmp.hpp> // Defines the wrappers around the GMP library's types + + boost::multiprecision::mpz_int myint; // Arbitrary precision integer type. + +Alternatively, you can compose your own multiprecision type, by combining `number` with one of the +predefined back-end types. For example, suppose you wanted a 300 decimal digit floating-point type +based on the [mpfr] library. In this case, there's no predefined typedef with that level of precision, +so instead we compose our own: + + #include <boost/multiprecision/mpfr.hpp> // Defines the Backend type that wraps MPFR + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + typedef mp::number<mp::mpfr_float_backend<300> > my_float; + + my_float a, b, c; // These variables have 300 decimal digits precision + +We can repeat the above example, but with the expression templates disabled (for faster compile times, but slower runtimes) +by passing a second template argument to `number`: + + #include <boost/multiprecision/mpfr.hpp> // Defines the Backend type that wraps MPFR + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + typedef mp::number<mp::mpfr_float_backend<300>, et_off> my_float; + + my_float a, b, c; // These variables have 300 decimal digits precision + +We can also mix arithmetic operations between different types, provided there is an unambiguous implicit conversion from one +type to the other: + + #include <boost/multiprecision/cpp_int.hpp> + + namespace mp = boost::multiprecision; // Reduce the typing a bit later... + + mp::int128_t a(3), b(4); + mp::int512_t c(50), d; + + d = c * a; // OK, result of mixed arithmetic is an int512_t + +Conversions are also allowed: + + d = a; // OK, widening conversion. + d = a * b; // OK, can convert from an expression template too. + +However conversions that are inherently lossy are either declared explicit or else forbidden altogether: + + d = 3.14; // Error implicit conversion from float not allowed. + d = static_cast<mp::int512_t>(3.14); // OK explicit construction is allowed + +Mixed arithmetic will fail if the conversion is either ambiguous or explicit: + + number<cpp_int_backend<>, et_off> a(2); + number<cpp_int_backend<>, et_on> b(3); + + b = a * b; // Error, implicit conversion could go either way. + b = a * 3.14; // Error, no operator overload if the conversion would be explicit. + +[h4 Move Semantics] + +On compilers that support rvalue-references, class `number` is move-enabled if the underlying backend is. + +In addition the non-expression template operator overloads (see below) are move aware and have overloads +that look something like: + + template <class B> + number<B, et_off> operator + (number<B, et_off>&& a, const number<B, et_off>& b) + { + return std::move(a += b); + } + +These operator overloads ensure that many expressions can be evaluated without actually generating any temporaries. +However, there are still many simple expressions such as: + + a = b * c; + +Which don't noticeably benefit from move support. Therefore, optimal performance comes from having both +move-support, and expression templates enabled. + +Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted +operations on them are destruction or the assignment of a new value. Any other operation should be considered +a programming error and all of our backends will trigger an assertion if any other operation is attempted. This behavior +allows for optimal performance on move-construction (i.e. no allocation required, we just take ownership of the existing +object's internal state), while maintaining usability in the standard library containers. + +[h4 Expression Templates] + +Class `number` is expression-template-enabled: that means that rather than having a multiplication +operator that looks like this: + + template <class Backend> + number<Backend> operator * (const number<Backend>& a, const number<Backend>& b) + { + number<Backend> result(a); + result *= b; + return result; + } + +Instead the operator looks more like this: + + template <class Backend> + ``['unmentionable-type]`` operator * (const number<Backend>& a, const number<Backend>& b); + +Where the "unmentionable" return type is an implementation detail that, rather than containing the result +of the multiplication, contains instructions on how to compute the result. In effect it's just a pair +of references to the arguments of the function, plus some compile-time information that stores what the operation +is. + +The great advantage of this method is the ['elimination of temporaries]: for example the "naive" implementation +of `operator*` above, requires one temporary for computing the result, and at least another one to return it. It's true +that sometimes this overhead can be reduced by using move-semantics, but it can't be eliminated completely. For example, +lets suppose we're evaluating a polynomial via Horner's method, something like this: + + T a[7] = { /* some values */ }; + //.... + y = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; + +If type `T` is a `number`, then this expression is evaluated ['without creating a single temporary value]. In contrast, +if we were using the [mpfr_class] C++ wrapper for [mpfr] - then this expression would result in no less than 11 +temporaries (this is true even though [mpfr_class] does use expression templates to reduce the number of temporaries somewhat). Had +we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries +are created for this simple expression (note - we actually measure the number of memory allocations performed rather than +the number of temporaries directly, note also that the [mpf_class] wrapper that will be supplied with GMP-5.1 reduces the number of +temporaries to pretty much zero). Note that if we compile with expression templates disabled and rvalue-reference support +on, then actually still have no wasted memory allocations as even though temporaries are created, their contents are moved +rather than copied. +[footnote The actual number generated will depend on the compiler, how well it optimises the code, and whether it supports +rvalue references. The number of 11 temporaries was generated with Visual C++ 10] + +[important +Expression templates can radically reorder the operations in an expression, for example: + + a = (b * c) * a; + +Will get transformed into: + + a *= c; + a *= b; + +If this is likely to be an issue for a particular application, then they should be disabled. +] + +This library also extends expression template support to standard library functions like `abs` or `sin` with `number` +arguments. This means that an expression such as: + + y = abs(x); + +can be evaluated without a single temporary being calculated. Even expressions like: + + y = sin(x); + +get this treatment, so that variable 'y' is used as "working storage" within the implementation of `sin`, +thus reducing the number of temporaries used by one. Of course, should you write: + + x = sin(x); + +Then we clearly can't use `x` as working storage during the calculation, so then a temporary variable +is created in this case. + +Given the comments above, you might be forgiven for thinking that expression-templates are some kind of universal-panacea: +sadly though, all tricks like this have their downsides. For one thing, expression template libraries +like this one, tend to be slower to compile than their simpler cousins, they're also harder to debug +(should you actually want to step through our code!), and rely on compiler optimizations being turned +on to give really good performance. Also, since the return type from expressions involving `number`s +is an "unmentionable implementation detail", you have to be careful to cast the result of an expression +to the actual number type when passing an expression to a template function. For example, given: + + template <class T> + void my_proc(const T&); + +Then calling: + + my_proc(a+b); + +Will very likely result in obscure error messages inside the body of `my_proc` - since we've passed it +an expression template type, and not a number type. Instead we probably need: + + my_proc(my_number_type(a+b)); + +Having said that, these situations don't occur that often - or indeed not at all for non-template functions. +In addition, all the functions in the Boost.Math library will automatically convert expression-template arguments +to the underlying number type without you having to do anything, so: + + mpfr_float_100 a(20), delta(0.125); + boost::math::gamma_p(a, a + delta); + +Will work just fine, with the `a + delta` expression template argument getting converted to an `mpfr_float_100` +internally by the Boost.Math library. + +One other potential pitfall that's only possible in C++11: you should never store an expression template using: + + auto my_expression = a + b - c; + +unless you're absolutely sure that the lifetimes of `a`, `b` and `c` will outlive that of `my_expression`. + +And finally... the performance improvements from an expression template library like this are often not as +dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with +[mpfr_class] and [mpreal], with all three using the underlying [mpfr] library at 50 decimal digits precision then +we see the following typical results for polynomial execution: + +[table Evaluation of Order 6 Polynomial. +[[Library] [Relative Time] [Relative number of memory allocations]] +[[number] [1.0 (0.00957s)] [1.0 (2996 total)]] +[[[mpfr_class]] [1.1 (0.0102s)] [4.3 (12976 total)]] +[[[mpreal]] [1.6 (0.0151s)] [9.3 (27947 total)]] +] + +As you can see, the execution time increases a lot more slowly than the number of memory allocations. There are +a number of reasons for this: + +* The cost of extended-precision multiplication and division is so great, that the times taken for these tend to +swamp everything else. +* The cost of an in-place multiplication (using `operator*=`) tends to be more than an out-of-place +`operator*` (typically `operator *=` has to create a temporary workspace to carry out the multiplication, where +as `operator*` can use the target variable as workspace). Since the expression templates carry out their +magic by converting out-of-place operators to in-place ones, we necessarily take this hit. Even so the +transformation is more efficient than creating the extra temporary variable, just not by as much as +one would hope. + +Finally, note that `number` takes a second template argument, which, when set to `et_off` disables all +the expression template machinery. The result is much faster to compile, but slower at runtime. + +We'll conclude this section by providing some more performance comparisons between these three libraries, +again, all are using [mpfr] to carry out the underlying arithmetic, and all are operating at the same precision +(50 decimal digits): + +[table Evaluation of Boost.Math's Bessel function test data +[[Library] [Relative Time] [Relative Number of Memory Allocations]] +[[mpfr_float_50] [1.0 (5.78s)] [1.0 (1611963)]] +[[number<mpfr_float_backend<50>, et_off>[br](but with rvalue reference support)] + [1.1 (6.29s)] [2.64 (4260868)]] +[[[mpfr_class]] [1.1 (6.28s)] [2.45 (3948316)]] +[[[mpreal]] [1.65 (9.54s)] [8.21 (13226029)]] +] + +[table Evaluation of Boost.Math's Non-Central T distribution test data +[[Library][Relative Time][Relative Number of Memory Allocations]] +[[number] [1.0 (263s)][1.0 (127710873)]] +[[number<mpfr_float_backend<50>, et_off>[br](but with rvalue reference support)] + [1.0 (260s)][1.2 (156797871)]] +[[[mpfr_class]] [1.1 (287s)][2.1 (268336640)]] +[[[mpreal]] [1.5 (389s)][3.6 (466960653)]] +] + +The above results were generated on Win32 compiling with Visual C++ 2010, all optimizations on (/Ox), +with MPFR 3.0 and MPIR 2.3.0. + +[endsect] + +[section:tut Tutorial] + +In order to use this library you need to make two choices: + +* What kind of number do I want ([link boost_multiprecision.tut.ints integer], +[link boost_multiprecision.tut.floats floating point] or [link boost_multiprecision.tut.rational rational]). +* Which back-end do I want to perform the actual arithmetic (Boost-supplied, GMP, MPFR, Tommath etc)? + +[section:ints Integer Types] + +The following back-ends provide integer arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`cpp_int`][boost/multiprecision/cpp_int.hpp][2][None] + [Very versatile, Boost licensed, all C++ integer type which support both [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] and fixed precision integer types.][Slower than [gmp], though typically not as slow as [tommath]]] +[[`gmp_int`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] +[[`tom_int`][boost/multiprecision/tommath.hpp][2][[tommath]][Public domain back-end with no licence restrictions.][Slower than [gmp].]] +] + +[section:cpp_int cpp_int] + +`#include <boost/multiprecision/cpp_int.hpp>` + + namespace boost{ namespace multiprecision{ + + typedef unspecified-type limb_type; + + enum cpp_integer_type { signed_magnitude, unsigned_magnitude }; + enum cpp_int_check_type { checked, unchecked }; + + template <unsigned MinBits = 0, + unsigned MaxBits = 0, + cpp_integer_type SignType = signed_magnitude, + cpp_int_check_type Checked = unchecked, + class Allocator = std::allocator<limb_type> > + class cpp_int_backend; + // + // Expression templates default to et_off if there is no allocator: + // + template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked> + struct expression_template_default<cpp_int_backend<MinBits, MaxBits, SignType, Checked, void> > + { static const expression_template_option value = et_off; }; + + typedef number<cpp_int_backend<> > cpp_int; // arbitrary precision integer + typedef rational_adaptor<cpp_int_backend<> > cpp_rational_backend; + typedef number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number + + // Fixed precision unsigned types: + typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> > uint128_t; + typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> > uint256_t; + typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> > uint512_t; + typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t; + + // Fixed precision signed types: + typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> > int128_t; + typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> > int256_t; + typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> > int512_t; + typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> > int1024_t; + + // Over again, but with checking enabled this time: + typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_int; + typedef rational_adaptor<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_rational_backend; + typedef number<cpp_rational_backend> checked_cpp_rational; + + // Checked fixed precision unsigned types: + typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> > checked_uint128_t; + typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> > checked_uint256_t; + typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> > checked_uint512_t; + typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> > checked_uint1024_t; + + // Fixed precision signed types: + typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> > checked_int128_t; + typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> > checked_int256_t; + typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> > checked_int512_t; + typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> > checked_int1024_t; + + }} // namespaces + +The `cpp_int_backend` type is normally used via one of the convenience typedefs given above. + +This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] +integer types, and both signed and unsigned types. There are five template arguments: + +[variablelist +[[MinBits][Determines the number of Bits to store directly within the object before resorting to dynamic memory + allocation. When zero, this field is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value may improve performance as larger integer + values will be stored internally before memory allocation is required.]] +[[MaxBits][Determines the maximum number of bits to be stored in the type: resulting in a fixed precision type. + When this value is the same as MinBits, then the Allocator parameter is ignored, as no dynamic + memory allocation will ever be performed: in this situation the Allocator parameter should be set to + type `void`. Note that this parameter should not be used simply to prevent large memory + allocations, not only is that role better performed by the allocator, but fixed precision + integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]] +[[SignType][Determines whether the resulting type is signed or not. Note that for +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types + this parameter must be `signed_magnitude`. For fixed precision + types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]] +[[Checked][This parameter has two values: `checked` or `unchecked`. See below.]] +[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if MaxBits == MinBits.]] +] + +When the template parameter Checked is set to `checked` then the result is a ['checked-integer], checked +and unchecked integers have the following properties: + +[table +[[Condition][Checked-Integer][Unchecked-Integer]] +[[Numeric overflow in fixed precision arithmetic][Throws a `std::overflow_error`.][Performs arithmetic modulo 2[super MaxBits]]] +[[Constructing an integer from a value that can not be represented in the target type][Throws a `std::range_error`.] +[Converts the value modulo 2[super MaxBits], signed to unsigned conversions extract the last MaxBits bits of the +2's complement representation of the input value.]] +[[Unsigned subtraction yielding a negative value.][Throws a `std::range_error`.][Yields the value that would +result from treating the unsigned type as a 2's complement signed type.]] +[[Attempting a bitwise operation on a negative value.][Throws a `std::range_error`][Yields the value, but not the bit pattern, +that would result from performing the operation on a 2's complement integer type.]] +] + +Things you should know when using this type: + +* Default constructed `cpp_int_backend`s have the value zero. +* Division by zero results in a `std::overflow_error` being thrown. +* Construction from a string that contains invalid non-numeric characters results in a `std::runtime_error` being thrown. +* Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, +care should be taken to avoid numeric overflow when using this type +unless you actually want modulo-arithmetic behavior. +* The type uses a sign-magnitude representation internally, so type `int128_t` has 128-bits of precision plus an extra sign bit. +In this respect the behaviour of these types differs from built-in 2's complement types. In might be tempting to use a +127-bit type instead, and indeed this does work, but behaviour is still slightly different from a 2's complement built-in type +as the min and max values are identical (apart from the sign), where as they differ by one for a true 2's complement type. +That said it should be noted that there's no requirement for built-in types to be 2's complement either - it's simply that this +is the most common format by far. +* Attempting to print negative values as either an Octal or Hexadecimal string results in a `std::runtime_error` being thrown, +this is a direct consequence of the sign-magnitude representation. +* The fixed precision types `[checked_][u]intXXX_t` have expression template support turned off - it seems to make little +difference to the performance of these types either way - so we may as well have the faster compile times by turning +the feature off. +* Unsigned types support subtraction - the result is "as if" a 2's complement operation had been performed as long as they are not + ['checked-integers] (see above). + In other words they behave pretty much as a built in integer type would in this situation. So for example if we were using + `uint128_t` then `uint128_t(1)-4` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` + of type `uint128_t`. However, had this operation been performed on `checked_uint128_t` then a `std::range_error` would have + been thrown. +* Unary negation of unsigned types results in a compiler error (static assertion). +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* When used at fixed precision, the size of this type is always one machine word larger than you would expect for an N-bit integer: +the extra word stores both the sign, and how many machine words in the integer are actually in use. +The latter is an optimisation for larger fixed precision integers, so that a 1024-bit integer has almost the same performance +characteristics as a 128-bit integer, rather than being 4 times slower for addition and 16 times slower for multiplication + (assuming the values involved would always fit in 128 bits). +Typically this means you can use +an integer type wide enough for the "worst case scenario" with only minor performance degradation even if most of the time +the arithmetic could in fact be done with a narrower type. +* When used at fixed precision and MaxBits is smaller than the number of bits in the largest native integer type, then +internally `cpp_int_backend` switches to a "trivial" implementation where it is just a thin wrapper around a single +integer. Note that it will still be slightly slower than a bare native integer, as it emulates a +signed-magnitude representation rather than simply using the platforms native sign representation: this ensures +there is no step change in behavior as a cpp_int grows in size. +* Fixed precision `cpp_int`'s have some support for `constexpr` values and user-defined literals, see +[link boost_multiprecision.tut.lits here] for the full description. For example `0xfffff_cppi1024` +specifies a 1024-bit integer with the value 0xffff. This can be used to generate compile time constants that are +too large to fit into any built in number type. + +[h5 Example:] + +[cpp_int_eg] + +[endsect] + +[section:gmp_int gmp_int] + +`#include <boost/multiprecision/gmp.hpp>` + + namespace boost{ namespace multiprecision{ + + class gmp_int; + + typedef number<gmp_int > mpz_int; + + }} // namespaces + +The `gmp_int` back-end is used via the typedef `boost::multiprecision::mpz_int`. It acts as a thin wrapper around the [gmp] `mpz_t` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, type `mpz_int` is copy constructible and assignable from: + +* The [gmp] native types: `mpf_t`, `mpz_t`, `mpq_t`. +* Instances of `number<T>` that are wrappers around those types: `number<gmp_float<N> >`, `number<gmp_rational>`. + +It's also possible to access the underlying `mpz_t` via the `data()` member function of `gmp_int`. + +Things you should know when using this type: + +* No changes are made to the GMP library's global settings - so you can safely mix this type with +existing code that uses [gmp]. +* Default constructed `gmp_int`s have the value zero (this is GMP's default behavior). +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +as a result performing formatted output on this type when the argument is negative and either of the flags +`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid integer. +* Division by zero results in a `std::overflow_error` being thrown. +* Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] +is recommended on Win32. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. + +[h5 Example:] + +[mpz_eg] + +[endsect] + +[section:tom_int tom_int] + +`#include <boost/multiprecision/tommath.hpp>` + + namespace boost{ namespace multiprecision{ + + class tommath_int; + + typedef number<tommath_int > tom_int; + + }} // namespaces + +The `tommath_int` back-end is used via the typedef `boost::multiprecision::tom_int`. It acts as a thin wrapper around the [tommath] `tom_int` +to provide an integer type that is a drop-in replacement for the native C++ integer types, but with unlimited precision. + +Things you should know when using this type: + +* Default constructed objects have the value zero (this is [tommath]'s default behavior). +* Although `tom_int` is mostly a drop in replacement for the builtin integer types, it should be noted that it is a +rather strange beast as it's a signed type that is not a 2's complement type. As a result the bitwise operations +`| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative. Similarly the complement +operator`~` is deliberately not implemented for this type. +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +as a result performing formatted output on this type when the argument is negative and either of the flags +`std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid integer. +* Division by zero results in a `std::overflow_error` being thrown. + +[h5 Example:] + +[tommath_eg] + +[endsect] + +[section:egs Examples] + +[import ../example/integer_examples.cpp] + +[section:factorials Factorials] +[FAC1] +[endsect] + +[section:bitops Bit Operations] +[BITOPS] +[endsect] + +[endsect] + +[endsect] + +[section:floats Floating Point Numbers] + +The following back-ends provide floating point arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`cpp_bin_float<N>`][boost/multiprecision/cpp_bin_float.hpp][2][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] +[[`cpp_dec_float<N>`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] +[[`mpf_float<N>`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] +[[`mpfr_float<N>`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licensed [gmp] and [mpfr] libraries.]] +[[`float128`][boost/multiprecision/float128.hpp][2][Either [quadmath] or the Intel C++ Math library.][Very fast and efficient back-end for 128-bit floating point values (113-bit mantissa, equivalent to FORTRAN's QUAD real)][Depends on the compiler being either recent GCC or Intel C++ versions.]] +] + +[section:cpp_bin_float cpp_bin_float] + +`#include <boost/multiprecision/cpp_bin_float.hpp>` + + namespace boost{ namespace multiprecision{ + + enum digit_base_type + { + digit_base_2 = 2, + digit_base_10 = 10 + }; + + template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0> + class cpp_bin_float; + + typedef number<cpp_bin_float<50> > cpp_bin_float_50; + typedef number<cpp_bin_float<100> > cpp_bin_float_100; + + typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single; + typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double; + typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended; + typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad; + + }} // namespaces + +The `cpp_bin_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) +floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `cpp_bin_float` can be used at fixed precision by specifying a non-zero `Digits` template parameter. +The typedefs `cpp_bin_float_50` and `cpp_bin_float_100` provide arithmetic types at 50 and 100 decimal digits precision +respectively. + +Optionally, you can specify whether the precision is specified in decimal digits or binary bits - for example +to declare a `cpp_bin_float` with exactly the same precision as `double` one would use +`number<cpp_bin_float<53, digit_base_2> >`. The typedefs `cpp_bin_float_single`, `cpp_bin_float_double`, +`cpp_bin_float_quad` and `cpp_bin_float_double_extended` provide +software analogues of the IEEE single, double and quad float data types, plus the Intel-extended-double type respectively. +Note that while these types are functionally equivalent to the native IEEE types, but they do not have the same size +or bit-layout as true IEEE compatible types. + +Normally `cpp_bin_float` allocates no memory: all of the space required for its digits are allocated +directly within the class. As a result care should be taken not to use the class with too high a digit count +as stack space requirements can grow out of control. If that represents a problem then providing an allocator +as a template parameter causes `cpp_bin_float` to dynamically allocate the memory it needs: this +significantly reduces the size of `cpp_bin_float` and increases the viable upper limit on the number of digits +at the expense of performance. However, please bear in mind that arithmetic operations rapidly become ['very] expensive +as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. +Note that since the actual type of the objects allocated +is completely opaque, the suggestion would be to use an allocator with `void` `value_type`, for example: +`number<cpp_bin_float<1000, digit_base_10, std::allocator<void> > >`. + +The final template parameters determine the type and range of the exponent: parameter `Exponent` can be +any signed integer type, but note that `MinExponent` and `MaxExponent` can not go right up to the limits +of the `Exponent` type as there has to be a little extra headroom for internal calculations. You will +get a compile time error if this is the case. In addition if MinExponent or MaxExponent are zero, then +the library will choose suitable values that are as large as possible given the constraints of the type +and need for extra headroom for internal calculations. + +There is full standard library and `numeric_limits` support available for this type. + +Things you should know when using this type: + +* Default constructed `cpp_bin_float`s have a value of zero. +* The radix of this type is 2, even when the precision is specified as decimal digits. +* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, +and a NaN is generated for any mathematically undefined operation. +* There is a `std::numeric_limits` specialisation for this type. +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +for example you can convert from `number<cpp_bin_float<50> >` to `number<cpp_bin_float<SomeOtherValue> >`. +Narrowing conversions round to nearest and are `explicit`. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* All arithmetic operations are correctly rounded to nearest. String conversions and the `sqrt` function +are also correctly rounded, but transcendental functions (sin, cos, pow, exp etc) are not. + +[h5 cpp_bin_float example:] + +[cpp_bin_float_eg] + +[endsect] + +[section:cpp_dec_float cpp_dec_float] + +`#include <boost/multiprecision/cpp_dec_float.hpp>` + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void> + class cpp_dec_float; + + typedef number<cpp_dec_float<50> > cpp_dec_float_50; + typedef number<cpp_dec_float<100> > cpp_dec_float_100; + + }} // namespaces + +The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) +floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. +The typedefs `cpp_dec_float_50` and `cpp_dec_float_100` provide arithmetic types at 50 and 100 decimal digits precision +respectively. Optionally, you can specify an integer type to use for the exponent, this defaults to a 32-bit integer type +which is more than large enough for the vast majority of use cases, but larger types such as `long long` can also be specified +if you need a truly huge exponent range. In any case the ExponentType must be a built in signed integer type at least 2 bytes +and 16-bits wide. + +Normally `cpp_dec_float` allocates no memory: all of the space required for its digits are allocated +directly within the class. As a result care should be taken not to use the class with too high a digit count +as stack space requirements can grow out of control. If that represents a problem then providing an allocator +as the final template parameter causes `cpp_dec_float` to dynamically allocate the memory it needs: this +significantly reduces the size of `cpp_dec_float` and increases the viable upper limit on the number of digits +at the expense of performance. However, please bear in mind that arithmetic operations rapidly become ['very] expensive +as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. + +There is full standard library and `numeric_limits` support available for this type. + +Things you should know when using this type: + +* Default constructed `cpp_dec_float`s have a value of zero. +* The radix of this type is 10. As a result it can behave subtly differently from base-2 types. +* The type has a number of internal guard digits over and above those specified in the template argument. +Normally these should not be visible to the user. +* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, +and a NaN is generated for any mathematically undefined operation. +* There is a `std::numeric_limits` specialisation for this type. +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +for example you can convert from `number<cpp_dec_float<50> >` to `number<cpp_dec_float<SomeOtherValue> >`. +Narrowing conversions are truncating and `explicit`. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* The actual precision of a `cpp_dec_float` is always slightly higher than the number of digits specified in +the template parameter, actually how much higher is an implementation detail but is always at least 8 decimal +digits. +* Operations involving `cpp_dec_float` are always truncating. However, note that since their are guard digits +in effect, in practice this has no real impact on accuracy for most use cases. + +[h5 cpp_dec_float example:] + +[cpp_dec_float_eg] + +[endsect] + +[section:gmp_float gmp_float] + +`#include <boost/multiprecision/gmp.hpp>` + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10> + class gmp_float; + + typedef number<gmp_float<50> > mpf_float_50; + typedef number<gmp_float<100> > mpf_float_100; + typedef number<gmp_float<500> > mpf_float_500; + typedef number<gmp_float<1000> > mpf_float_1000; + typedef number<gmp_float<0> > mpf_float; + + }} // namespaces + +The `gmp_float` back-end is used in conjunction with `number` : it acts as a thin wrapper around the [gmp] `mpf_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `gmp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpf_float_50, mpf_float_100, +mpf_float_500, mpf_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpf_float provides a variable precision type whose precision can be controlled via the +`number`s member functions. + +[note This type only provides standard library and `numeric_limits` support when the precision is fixed at compile time.] + +As well as the usual conversions from arithmetic and string types, instances of `number<mpf_float<N> >` are +copy constructible and assignable from: + +* The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`. +* The `number` wrappers around those types: `number<mpf_float<M> >`, `number<gmp_int>`, `number<gmp_rational>`. + +It's also possible to access the underlying `mpf_t` via the `data()` member function of `gmp_float`. + +Things you should know when using this type: + +* Default constructed `gmp_float`s have the value zero (this is the [gmp] library's default behavior). +* No changes are made to the [gmp] library's global settings, so this type can be safely mixed with +existing [gmp] code. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* It is not possible to round-trip objects of this type to and from a string and get back +exactly the same value. This appears to be a limitation of [gmp]. +* Since the underlying [gmp] types have no notion of infinities or NaN's, care should be taken +to avoid numeric overflow or division by zero. That latter will result in a std::overflow_error being thrown, +while generating excessively large exponents may result in instability of the underlying [gmp] +library (in testing, converting a number with an excessively large or small exponent +to a string caused [gmp] to segfault). +* This type can equally be used with [mpir] as the underlying implementation - indeed that is +the recommended option on Win32. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in a `std::overflow_error` being thrown. + +[h5 [gmp] example:] + +[mpf_eg] + +[endsect] + +[section:mpfr_float mpfr_float] + +`#include <boost/multiprecision/mpfr.hpp>` + + namespace boost{ namespace multiprecision{ + + enum mpfr_allocation_type + { + allocate_stack, + allocate_dynamic + }; + + template <unsigned Digits10, mpfr_allocation_type AllocateType = allocate_dynamic> + class mpfr_float_backend; + + typedef number<mpfr_float_backend<50> > mpfr_float_50; + typedef number<mpfr_float_backend<100> > mpfr_float_100; + typedef number<mpfr_float_backend<500> > mpfr_float_500; + typedef number<mpfr_float_backend<1000> > mpfr_float_1000; + typedef number<mpfr_float_backend<0> > mpfr_float; + + typedef number<mpfr_float_backend<50, allocate_stack> > static_mpfr_float_50; + typedef number<mpfr_float_backend<100, allocate_stack> > static_mpfr_float_100; + + }} // namespaces + +The `mpfr_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfr] `mpfr_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100, +mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the +`number`s member functions. + +In addition the second template parameter lets you choose between dynamic allocation (the default, +and uses MPFR's normal allocation routines), +or stack allocation (where all the memory required for the underlying data types is stored +within `mpfr_float_backend`). The latter option can result in significantly faster code, at the +expense of growing the size of `mpfr_float_backend`. It can only be used at fixed precision, and +should only be used for lower digit counts. Note that we can not guarantee that using `allocate_stack` +won't cause any calls to mpfr's allocation routines, as mpfr may call these inside it's own code. +The following table gives an idea of the performance tradeoff's at 50 decimal digits +precision[footnote Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0]: + +[table +[[Type][Bessel function evaluation, relative times]] +[[`number<mpfr_float_backend<50, allocate_static>, et_on>`][1.0 (5.5s)]] +[[`number<mpfr_float_backend<50, allocate_static>, et_off>`][1.05 (5.8s)]] +[[`number<mpfr_float_backend<50, allocate_dynamic>, et_on>`][1.05 (5.8s)]] +[[`number<mpfr_float_backend<50, allocate_dynamic>, et_off>`][1.16 (6.4s)]] +] + +[note This type only provides `numeric_limits` support when the precision is fixed at compile time.] + +As well as the usual conversions from arithmetic and string types, instances of `number<mpfr_float_backend<N> >` are +copy constructible and assignable from: + +* The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`. +* The [mpfr] native type `mpfr_t`. +* The `number` wrappers around those types: `number<mpfr_float_backend<M> >`, `number<mpf_float<M> >`, `number<gmp_int>`, `number<gmp_rational>`. + +It's also possible to access the underlying `mpfr_t` via the data() member function of `mpfr_float_backend`. + +Things you should know when using this type: + +* A default constructed `mpfr_float_backend` is set to a NaN (this is the default [mpfr] behavior). +* All operations use round to nearest. +* No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing +[mpfr] or [gmp] code. +* The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in an infinity. + +[h5 [mpfr] example:] + +[mpfr_eg] + +[endsect] + +[section:float128 float128] + +`#include <boost/multiprecision/float128.hpp>` + + namespace boost{ namespace multiprecision{ + + class float128_backend; + + typedef number<float128_backend, et_off> float128; + + }} // namespaces + +The `float128` number type is a very thin wrapper around GCC's `__float128` or Intel's `_Quad` data types +and provides an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +a 113 bit mantissa, and compatible with FORTRAN's 128-bit QUAD real. + +All the usual standard library and `numeric_limits` support are available, performance should be equivalent +to the underlying native types: for example the LINPACK benchmarks for GCC's `__float128` and +`boost::multiprecision::float128` both achieved 5.6 MFLOPS[footnote On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800.]. + +As well as the usual conversions from arithmetic and string types, instances of `float128` are +copy constructible and assignable from GCC's `__float128` and Intel's `_Quad` data types. + +It's also possible to access the underlying `__float128` or `_Quad` type via the `data()` member +function of `float128_backend`. + +Things you should know when using this type: + +* Default constructed `float128`s have the value zero. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* It is not possible to round-trip objects of this type to and from a string and get back +exactly the same value when compiled with Intel's C++ compiler and using `_Quad` as the underlying type: this is a current limitation of +our code. Round tripping when using `__float128` as the underlying type is possible (both for GCC and Intel). +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in an infinity being produced. +* Type `float128` can be used as a literal type (constexpr support). +* When using the Intel compiler, the underlying type defaults to `__float128` if it's available and `_Quad` if not. You can override +the default by defining either `BOOST_MP_USE_FLOAT128` or `BOOST_MP_USE_QUAD`. +* When the underlying type is Intel's `_Quad` type, the code must be compiled with the compiler option `-Qoption,cpp,--extended_float_type`. + +[h5 float128 example:] + +[float128_eg] + +[endsect] + +[section:fp_eg Examples] + +[import ../example/floating_point_examples.cpp] + +[section:aos Area of Circle] + +[AOS1] +[AOS2] +[AOS3] + +[endsect] + +[section:jel Defining a Special Function.] + +[JEL] + +[endsect] + +[section:nd Calculating a Derivative] + +[ND1] +[ND2] +[ND3] + +[endsect] + +[section:gi Calculating an Integral] + +[GI1] +[GI2] + +[endsect] + +[section:poly_eg Polynomial Evaluation] + +[POLY] + +[endsect] + +[endsect] + +[endsect] + +[section:interval Interval Number Types] + +There is one currently only one interval number type supported - [mpfi]. + +[section:mpfi mpfi_float] + +`#include <boost/multiprecision/mpfi.hpp>` + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10> + class mpfi_float_backend; + + typedef number<mpfi_float_backend<50> > mpfi_float_50; + typedef number<mpfi_float_backend<100> > mpfifloat_100; + typedef number<mpfi_float_backend<500> > mpfifloat_500; + typedef number<mpfi_float_backend<1000> > mpfi_float_1000; + typedef number<mpfi_float_backend<0> > mpfi_float; + + }} // namespaces + +The `mpfi_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfi] `mpfi_t` +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision and implementing interval arithmetic. + +Type `mpfi_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or +at variable precision by setting the template argument to zero. The typedefs mpfi_float_50, mpfi_float_100, +mpfi_float_500, mpfi_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision +respectively. The typedef mpfi_float provides a variable precision type whose precision can be controlled via the +`number`s member functions. + +[note This type only provides `numeric_limits` support when the precision is fixed at compile time.] + +As well as the usual conversions from arithmetic and string types, instances of `number<mpfi_float_backend<N> >` are +copy constructible and assignable from: + +* The [mpfi] native type `mpfi_t`. +* The `number` wrappers around [mpfi] or [mpfr]: `number<mpfi_float_backend<M> >` and `number<mpfr_float<M> >`. +* There is a two argument constructor taking two `number<mpfr_float<M> >` arguments specifying the interval. + +It's also possible to access the underlying `mpfi_t` via the data() member function of `mpfi_float_backend`. + +Things you should know when using this type: + +* A default constructed `mpfi_float_backend` is set to a NaN (this is the default [mpfi] behavior). +* No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing +[mpfr] or [gmp] code. +* The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. +* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* Division by zero results in an infinity. + +There are some additional non member functions for working on intervals: + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfr_float_backend<Digits10>, ExpressionTemplates> lower(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val); + +Returns the lower end of the interval. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfr_float_backend<Digits10>, ExpressionTemplates> upper(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val); + +Returns the upper end of the interval. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfr_float_backend<Digits10>, ExpressionTemplates> median(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val); + +Returns the mid point of the interval. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfr_float_backend<Digits10>, ExpressionTemplates> width(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val); + +Returns the absolute width of the interval. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfi_float_backend<Digits10>, ExpressionTemplates> intersect( + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b); + +Returns the interval which is the intersection of the ['a] and ['b]. Returns an +unspecified empty interval if there is no such intersection. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + number<mpfi_float_backend<Digits10>, ExpressionTemplates> hull( + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b); + +Returns the interval which is the union of ['a] and ['b]. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool overlap(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b); + +Returns `true` only if the intervals ['a] and ['b] overlap. + + template <unsigned Digits10, expression_template_option ExpressionTemplates1, expression_template_option ExpressionTemplates2> + bool in(const number<mpfr_float_backend<Digits10>, ExpressionTemplates1>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates2>& b); + +Returns `true` only if point ['a] is contained within the interval ['b]. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool zero_in(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a); + +Returns `true` only if the interval ['a] contains the value zero. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b); + +Returns `true` only if ['a] is a subset of ['b]. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool proper_subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, + const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b); + +Returns `true` only if ['a] is a proper subset of ['b]. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool empty(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a); + +Returns `true` only if ['a] is an empty interval, equivalent to `upper(a) < lower(a)`. + + template <unsigned Digits10, expression_template_option ExpressionTemplates> + bool singleton(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a); + +Returns `true` if `lower(a) == upper(a)`. + +[h5 [mpfi] example:] + +[mpfi_eg] + +[endsect] + +[endsect] + +[section:rational Rational Number Types] + +The following back-ends provide rational number arithmetic: + +[table +[[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`cpp_rational`][boost/multiprecision/cpp_int.hpp][2][None][An all C++ Boost-licensed implementation.][Slower than [gmp].]] +[[`gmp_rational`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] +[[`tommath_rational`][boost/multiprecision/tommath.hpp][2][[tommath]][All C/C++ implementation that's Boost Software Licence compatible.][Slower than [gmp].]] +[[`rational_adaptor`][boost/multiprecision/rational_adaptor.hpp][N/A][none][All C++ adaptor that allows any integer back-end type to be used as a rational type.][Requires an underlying integer back-end type.]] +[[`boost::rational`][boost/rational.hpp][N/A][None][A C++ rational number type that can used with any `number` integer type.][The expression templates used by `number` end up being "hidden" inside `boost::rational`: performance may well suffer as a result.]] +] + +[section:cpp_rational cpp_rational] + +`#include <boost/multiprecision/cpp_int.hpp>` + + namespace boost{ namespace multiprecision{ + + typedef rational_adaptor<cpp_int_backend<> > cpp_rational_backend; + + typedef number<cpp_rational_backend> cpp_rational; + + }} // namespaces + +The `cpp_rational_backend` type is used via the typedef `boost::multiprecision::cpp_rational`. It provides +a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, instances of `cpp_rational` are copy constructible +and assignable from type `cpp_int`. + +There is also a two argument constructor that accepts a numerator and denominator: both of type `cpp_int`. + +There are also non-member functions: + + cpp_int numerator(const cpp_rational&); + cpp_int denominator(const cpp_rational&); + +which return the numerator and denominator of the number. + +Things you should know when using this type: + +* Default constructed `cpp_rational`s have the value zero. +* Division by zero results in a `std::overflow_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. + +[h5 Example:] + +[cpp_rational_eg] + +[endsect] + +[section:gmp_rational gmp_rational] + +`#include <boost/multiprecision/gmp.hpp>` + + namespace boost{ namespace multiprecision{ + + class gmp_rational; + + typedef number<gmp_rational > mpq_rational; + + }} // namespaces + +The `gmp_rational` back-end is used via the typedef `boost::multiprecision::mpq_rational`. It acts as a thin wrapper around the [gmp] `mpq_t` +to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +As well as the usual conversions from arithmetic and string types, instances of `number<gmp_rational>` are copy constructible +and assignable from: + +* The [gmp] native types: `mpz_t`, `mpq_t`. +* `number<gmp_int>`. + +There is also a two-argument constructor that accepts a numerator and denominator (both of type `number<gmp_int>`). + +There are also non-member functions: + + mpz_int numerator(const mpq_rational&); + mpz_int denominator(const mpq_rational&); + +which return the numerator and denominator of the number. + +It's also possible to access the underlying `mpq_t` via the `data()` member function of `mpq_rational`. + +Things you should know when using this type: + +* Default constructed `mpq_rational`s have the value zero (this is the [gmp] default behavior). +* Division by zero results in a `std::overflow_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. +* No changes are made to the [gmp] library's global settings, so this type can coexist with existing +[gmp] code. +* The code can equally be used with [mpir] as the underlying library - indeed that is the preferred option on Win32. + +[h5 Example:] + +[mpq_eg] + +[endsect] + +[section:tommath_rational tommath_rational] + +`#include <boost/multiprecision/tommath.hpp>` + + namespace boost{ namespace multiprecision{ + + typedef rational_adpater<tommath_int> tommath_rational; + typedef number<tommath_rational > tom_rational; + + }} // namespaces + +The `tommath_rational` back-end is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around +`boost::rational<tom_int>` +to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. + +The advantage of using this type rather than `boost::rational<tom_int>` directly, is that it is expression-template enabled, +greatly reducing the number of temporaries created in complex expressions. + +There are also non-member functions: + + tom_int numerator(const tom_rational&); + tom_int denominator(const tom_rational&); + +which return the numerator and denominator of the number. + +Things you should know when using this type: + +* Default constructed `tom_rational`s have the value zero (this the inherited Boost.Rational behavior). +* Division by zero results in a `std::overflow_error` being thrown. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be +interpreted as a valid rational number. +* No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code. +* Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational +needs some improvement in this area. + +[h5 Example:] + +[mp_rat_eg] + +[endsect] + +[section:br Use With Boost.Rational] + +All of the integer types in this library can be used as template arguments to `boost::rational<IntType>`. + +Note that using the library in this way largely negates the effect of the expression templates in `number`. + +[endsect] + +[section:rational_adaptor rational_adaptor] + + namespace boost{ namespace multiprecision{ + + template <class IntBackend> + class rational_adpater; + + }} + +The class template `rational_adaptor` is a back-end for `number` which converts any existing integer back-end +into a rational-number back-end. + +So for example, given an integer back-end type `MyIntegerBackend`, the use would be something like: + + typedef number<MyIntegerBackend> MyInt; + typedef number<rational_adaptor<MyIntegerBackend> > MyRational; + + MyRational r = 2; + r /= 3; + MyInt i = numerator(r); + assert(i == 2); + +[endsect] + +[endsect] + +[section:misc Miscellaneous Number Types.] + +Backend types listed in this section are predominantly designed to aid debugging. + +[section:logged_adaptor logged_adaptor] + +`#include <boost/multiprecision/logged_adaptor.hpp>` + + namespace boost{ namespace multiprecision{ + + template <class Backend> + void log_postfix_event(const Backend& result, const char* event_description); + template <class Backend, class T> + void log_postfix_event(const Backend& result1, const T& result2, const char* event_description); + + template <class Backend> + void log_prefix_event(const Backend& arg1, const char* event_description); + template <class Backend, class T> + void log_prefix_event(const Backend& arg1, const T& arg2, const char* event_description); + template <class Backend, class T, class U> + void log_prefix_event(const Backend& arg1, const T& arg2, const U& arg3, const char* event_description); + template <class Backend, class T, class U, class V> + void log_prefix_event(const Backend& arg1, const T& arg2, const U& arg3, const V& arg4, const char* event_description); + + template <Backend> + class logged_adaptor; + + }} // namespaces + +The `logged_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around +some other backend to class `number` and logs all the events that take place on that object. Before any number operation takes +place, it calls `log_prefix_event` with the arguments to the operation (up to 4), plus a string describing the operation. +Then after the operation it calls `log_postfix_event` with the result of the operation, plus a string describing the operation. +Optionally, `log_postfix_event` takes a second result argument: this occurs when the result of the operation is not a `number`, +for example when `fpclassify` is called, `log_postfix_event` will be called with `result1` being the argument to the function, and +`result2` being the integer result of `fpclassify`. + +The default versions of `log_prefix_event` and `log_postfix_event` do nothing, it is therefore up to the user to overload these +for the particular backend being observed. + +This type provides `numeric_limits` support whenever the template argument Backend does so. + +This type is particularly useful when combined with an interval number type - in this case we can use `log_postfix_event` +to monitor the error accumulated after each operation. We could either set some kind of trap whenever the accumulated error +exceeds some threshold, or simply print out diagnostic information. Using this technique we can quickly locate the cause of +numerical instability in a particular routine. The following example demonstrates this technique in a trivial algorithm +that deliberately introduces cancellation error: + +[logged_adaptor] + +When we examine program output we can clearly see that the diameter of the interval increases after each subtraction: + +[logged_adaptor_output] + +[endsect] + +[section:debug_adaptor debug_adaptor] + +`#include <boost/multiprecision/debug_adaptor.hpp>` + + namespace boost{ namespace multiprecision{ + + template <Backend> + class debug_adaptor; + + }} // namespaces + +The `debug_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around +some other backend to class `number` and intercepts all operations on that object storing the result as a string within itself. + +This type provides `numeric_limits` support whenever the template argument Backend does so. + +This type is particularly useful when your debugger provides a good view of `std::string`: when this is the case +multiprecision values can easily be inspected in the debugger by looking at the `debug_value` member of `debug_adaptor`. +The down side of this approach is that runtimes are much slower when using this type. Set against that it can make +debugging very much easier, certainly much easier than sprinkling code with `printf` statements. + +When used in conjunction with the Visual C++ debugger visualisers, the value of a multiprecision type that uses this +backend is displayed in the debugger just a builtin value would be, here we're inspecting a value of type +`number<debug_adaptor<cpp_dec_float<50> > >`: + +[$../debugger1.png] + +Otherwise you will need to expand out the view and look at the "debug_value" member: + +[$../debugger2.png] + +It works for all the backend types equally too, here it is inspecting a `number<debug_adaptor<gmp_rational> >`: + +[$../debugger3.png] + + +[endsect] + +[section:visualizers Visual C++ Debugger Visualizers] + +Let's face it debugger multiprecision numbers is hard - simply because we can't easily inspect the value of the numbers. +Visual C++ provides a partial solution in the shape of "visualizers" which provide improved views of complex data structures, +these visualizers need to be added to the `[Visualizer]` section of `autoexp.dat` located in the `Common7/Packages/Debugger` +directory of your Visual Studio installation. The actual visualizer code is in the sandbox +[@https://svn.boost.org/svn/boost/sandbox/boost_docs/subprojects/DebuggerVisualizers/multiprecision.vis.txt here] - just cut and paste the code +into your `autoexp.dat` file. + +[note These visualizers have only been tested with VC10, also given the ability of buggy visualizers to crash your Visual C++ +debugger, make sure you back up `autoexp.dat` file before using these!!] + +The first visualizer provides improved views of `debug_adaptor`: + +[$../debugger1.png] + +The next visualizer provides improved views of cpp_int: small numbers are displayed as actual values, while larger numbers are +displayed as an array of hexadecimal parts, with the most significant part first. + +Here's what it looks like for small values: + +[$../debugger4.png] + +And for larger values: + +[$../debugger5.png] + +There is also a `~raw` child member that +lets you see the actual members of the class: + +[$../debugger6.png] + +The visualizer for `cpp_dec_float` shows the first few digits of the value in the preview field, and the full array of digits +when you expand the view. As before the `~raw` child gives you access to the actual data members: + +[$../debugger7.png] + +[endsect] + +[endsect] + +[section:conversions Constructing and Interconverting Between Number Types] + +All of the number types that are based on `number` have certain conversion rules in common. +In particular: + +* Any number type can be constructed (or assigned) from any builtin arithmetic type, as long + as the conversion isn't lossy (for example float to int conversion): + + cpp_dec_float_50 df(0.5); // OK construction from double + cpp_int i(450); // OK constructs from signed int + cpp_int j = 3.14; // Error, lossy conversion. + +* A number can be explicitly constructed from an arithmetic type, even when the conversion is lossy: + + cpp_int i(3.14); // OK explicit conversion + i = static_cast<cpp_int>(3.14) // OK explicit conversion + i.assign(3.14); // OK, explicit assign and avoid a temporary from the cast above + i = 3.14; // Error, no implicit assignment operator for lossy conversion. + cpp_int j = 3.14; // Error, no implicit constructor for lossy conversion. + +* A `number` can be converted to any built in type, via the `convert_to` member function: + + mpz_int z(2); + int i = z.template convert_to<int>(); // sets i to 2 + +* Conversions to rational numbers from floating point ones are always allowed, and are exact and implicit +as long as the rational number uses an unbounded integer type. Please be aware that constructing a rational +number from an extended precision floating point type with a large exponent range can effectively run the system +out of memory, as in the extreme case ['2[super max_exponent] / CHAR_BITS] bytes of storage may be required. This +does not represent a problem for built in floating point types however, as the exponent range for these is rather +limited. + +* Conversions to floating point numbers from rational ones are rounded to nearest (less than 0.5ulp error) +as long as the floating point number is binary, and the integer type used by the rational number is unbounded. + +Additional conversions may be supported by particular backends. + +* A `number` can be converted to any built in type, via an explicit conversion operator: +this functionality is only available on compilers supporting C++11's explicit conversion syntax. + + mpz_int z(2); + int i = z; // Error, implicit conversion not allowed. + int j = static_cast<int>(z); // OK explicit conversion. + +* Any number type can be ['explicitly] constructed (or assigned) from a `const char*` or a `std::string`: + + // pi to 50 places from a string: + cpp_dec_float_50 df("3.14159265358979323846264338327950288419716939937510"); + // Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly: + cpp_int i("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000"); + // Invalid input always results in a std::runtime_error being thrown: + i = static_cast<cpp_int>("3.14"); + // implicit conversions from strings are not allowed: + i = "23"; // Error, no assignment operator for implicit conversion from string + // assign member function, avoids having to create a temporary via a static_cast: + i.assign("23"); // OK + +* Any number type will interoperate with the builtin types in arithmetic expressions as long as the conversions +are not lossy: + + // pi to 50 places from a string: + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; + // Multiply by 2 - using an integer literal here is usually more efficient + // than constructing a temporary: + df *= 2; + + // You can't mix integer types with floats though: + cpp_int i = 2; + i *= 3.14; // Error, no *= operator will be found. + +* Any number type can be streamed to and from the C++ iostreams: + + + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; + // Now print at full precision: + std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10) + << df << std::endl + cpp_int i = 1; + i <<= 256; + // Now print in hex format with prefix: + std::cout << std::hex << std::showbase << i << std::endl; + +* Interconversions between number types of the same family are allowed and are implicit conversions if no +loss of precision is involved, and explicit if it is: + + int128_t i128 = 0; + int266_t i256 = i128; // OK implicit widening conversion + i128_t = i256; // Error, no assignment operator found, narrowing conversion is explicit + i128_t = static_cast<int128_t>(i256); // OK, explicit narrowing conversion + + mpz_int z = 0; + mpf_float f = z; // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit + + mpf_float_50 f50 = 2; + f = f50; // OK, conversion from fixed to variable precision, f will have 50 digits precision. + f50 = f; // Error, conversion from variable to fixed precision is potentially lossy, explicit cast required. + +* Some interconversions between number types are completely generic, and are always available, albeit the conversions are always ['explicit]: + + cpp_int cppi(2); + // We can always convert between numbers of the same category - + // int to int, rational to rational, or float to float, so this is OK + // as long as we use an explicit conversion: + mpz_int z(cppi); + // We can always promote from int to rational, int to float, or rational to float: + cpp_rational cppr(cppi); // OK, int to rational + cpp_dec_float_50 df(cppi); // OK, int to float + df = static_cast<cpp_dec_float_50>(cppr); // OK, explicit rational to float conversion + // However narrowing and/or implicit conversions always fail: + cppi = df; // Compiler error, conversion not allowed + +* Other interconversions may be allowed as special cases, whenever the backend allows it: + + mpf_t m; // Native GMP type. + mpf_init_set_ui(m, 0); // set to a value; + mpf_float i(m); // copies the value of the native type. + +More information on what additional types a backend supports conversions from are given in the tutorial for each backend. +The converting constructor will be implicit if the backend's converting constructor is also implicit, and explicit if the +backends converting constructor is also explicit. + +[endsect] + +[section:random Generating Random Numbers] + +Random numbers are generated in conjunction with Boost.Random. However, since Boost.Random is unaware +of [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] numbers, it's necessary to include the header: + + #include <boost/multiprecision/random.hpp> + +In order to act as a bridge between the two libraries. + +Integers with /N/ random bits are generated using `independent_bits_engine`: + +[random_eg1] + +Alternatively we can generate integers in a given range using `uniform_int_distribution`, this will +invoke the underlying engine multiple times to build up the required number of bits in the result: + +[random_eg2] + +Floating point values in \[0,1) are generated using `uniform_01`, the trick here is to ensure +that the underlying generator produces as many random bits as there are digits in the floating +point type. As above `independent_bits_engine` can be used for this purpose, note that we also have to +convert decimal digits (in the floating point type) to bits (in the random number generator): + +[random_eg3] + +Finally, we can modify the above example to produce numbers distributed according to some distribution: + +[random_eg4] + +[endsect] + +[section:primetest Primality Testing] + +The library implements a Miller-Rabin test for primality: + + #include <boost/multiprecision/miller_rabin.hpp> + + template <class Backend, expression_template_option ExpressionTemplates, class Engine> + bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials, Engine& gen); + + template <class Backend, expression_template_option ExpressionTemplates, class Engine> + bool miller_rabin_test(const number<Backend, ExpressionTemplates>& n, unsigned trials); + +These functions perform a Miller-Rabin test for primality, if the result is `false` then /n/ is definitely composite, +while if the result is true then n is probably prime. The probability to declare a composite n as probable prime is +at most 0.25[super trials]. Note that this does not allow a statement about the probability of n being actually +prime (for that, the prior probability would have to be known). The algorithm used performs some +trial divisions to exclude small prime factors, does one Fermat test to exclude many more composites, and then +uses the Miller-Rabin algorithm straight out of +Knuth Vol 2, which recommends 25 trials for a pretty strong likelihood that /n/ is prime. + +The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the `mt19937` +generator is used. Note that when producing random primes then you should probably use a different random number generator +to produce candidate prime numbers for testing, than is used internally by `miller_rabin_test` for determining +whether the value is prime. It also helps of course to seed the generators with some source of randomness. + +The following example searches for a prime `p` for which `(p-1)/2` is also probably prime: + +[safe_prime] + +[endsect] + +[section:lits Literal Types and `constexpr` Support] + +[note The features described in this section make heavy use of C++11 language features, currently +(as of May 2013) only +GCC-4.7 and later, and Clang 3.3 and later have the support required to make these features work.] + +There is limited support for `constexpr` and user-defined literals in the library, currently the +`number` front end supports `constexpr` +on default construction and all forwarding constructors, but not on any of the non-member operators. So if +some type `B` is a literal type, then `number<B>` is also a literal type, and you will be able to +compile-time-construct such a type from any literal that `B` is compile-time-constructible from. +However, you will not be able to perform compile-time arithmetic on such types. + +Currently the only backend type provided by the library that is also a literal type are instantiations +of `cpp_int_backend` where the Allocator parameter is type `void`, and the Checked parameter is +`boost::multiprecision::unchecked`. + +For example: + + using namespace boost::multiprecision; + + constexpr int128_t i = 0; // OK, fixed precision int128_t has no allocator. + constexpr uint1024_t j = 0xFFFFFFFF00000000uLL; // OK, fixed precision uint1024_t has no allocator. + + constexpr checked_uint128_t k = -1; // Error, checked type is not a literal type as we need runtime error checking. + constexpr cpp_int l = 2; // Error, type is not a literal as it performs memory management. + +There is also limited support for user defined-literals - these are limited to unchecked, fixed precision `cpp_int`'s +which are specified in hexadecimal notation. The suffixes supported are: + +[table +[[Suffix][Meaning]] +[[_cppi][Specifies a value of type: `number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >`, where N is chosen +to contain just enough digits to hold the number specified.]] +[[_cppui][Specifies a value of type: `number<cpp_int_backend<N,N,unsigned_magnitude,unchecked,void> >`, where N is chosen +to contain just enough digits to hold the number specified.]] +[[_cppi['N]][Specifies a value of type `number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >`.]] +[[_cppui['N]][Specifies a value of type `number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >`.]] +] + +In each case, use of these suffixes with hexadecimal values produces a `constexpr` result. + +Examples: + + // + // Any use of user defined literals requires that we import the literal-operators + // into current scope first: + using namespace boost::multiprecision::literals; + // + // To keep things simple in the example, we'll make our types used visible to this scope as well: + using namespace boost::multiprecision; + // + // The value zero as a number<cpp_int_backend<4,4,signed_magnitude,unchecked,void> >: + constexpr auto a = 0x0_cppi; + // The type of each constant has 4 bits per hexadecimal digit, + // so this is of type uint256_t (ie number<cpp_int_backend<256,256,unsigned_magnitude,unchecked,void> >): + constexpr auto b = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui; + // + // Smaller values can be assigned to larger values: + int256_t c = 0x1234_cppi; // OK + // + // However, this does not currently work in constexpr contexts: + constexpr int256_t d = 0x1_cppi; // Compiler error + // + // Constants can be padded out with leading zeros to generate wider types: + constexpr uint256_t e = 0x0000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFF_cppui; // OK + // + // However, specific width types are best produced with specific-width suffixes, + // ones supported by default are `_cpp[u]i128`, `_cpp[u]i256`, `_cpp[u]i512`, `_cpp[u]i1024`. + // + constexpr int128_t f = 0x1234_cppi128; // OK, always produces an int128_t as the result. + constexpr uint1024_t g = 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccc_cppui1024; + // + // If other specific width types are required, then there is a macro for generating the operators + // for these. The macro can be used at namespace scope only: + // + BOOST_MP_DEFINE_SIZED_CPP_INT_LITERAL(2048); + // + // Now we can create 2048-bit literals as well: + constexpr auto h = 0xff_cppi2048; // h is of type number<cpp_int_backend<2048,2048,signed_magnitude,unchecked,void> > + // + // Finally negative values are handled via the unary minus operator: + // + constexpr int1024_t i = -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui1024; + // + // Which means this also works: + constexpr int1024_t j = -g; // OK: unary minus operator is constexpr. + +[endsect] + +[section:rounding Rounding Rules for Conversions] + +As a general rule, all conversions between unrelated types are performed using basic arithmetic operations, therefore +conversions are either exact, or follow the same rounding rules as arithmetic for the type in question. + +The following table summarises the situation for conversions from native types: + +[table +[[Backend][Rounding Rules]] +[[__cpp_int][Conversions from integer types are exact if the target has sufficient precision, otherwise they + truncate to the first 2^MaxBits bits (modulo arithmetic). Conversions from floating point types + are truncating to the nearest integer.]] +[[__gmp_int][Conversions are performed by the GMP library except for conversion from `long double` which is truncating.]] +[[__tom_int][Conversions from floating point types are truncating, all others are performed by libtommath and are exact.]] +[[__gmp_float][Conversions are performed by the GMP library except for conversion from `long double` which should be exact + provided the target type has as much precision as a `long double`.]] +[[__mpfr_float_backend][All conversions are performed by the underlying MPFR library.]] +[[__cpp_dec_float][All conversions are performed using basic arithmetic operations and are truncating.]] +[[__gmp_rational][See __gmp_int]] +[[__cpp_rational][See __cpp_int]] +[[__tommath_rational][See __tom_int]] +] + +[endsect] + +[section:mixed Mixed Precision Arithmetic] + +Mixed precision arithmetic is fully supported by the library. + +There are two different forms: + +* Where the operands are of different precision. +* Where the operands are of the same precision, but yield a higher precision result. + +[h4 Mixing Operands of Differing Precision] + +If the arguments to a binary operator are of different precision, then the operation is allowed +as long as there is an unambiguous implicit conversion from one argument type to the other. +In all cases the arithmetic is performed "as if" the lower precision type is promoted to the +higher precision type before applying the operator. However, particular backends may optimise +this and avoid actually creating a temporary if they are able to do so. + +For example: + + mpfr_float_50 a(2), b; + mpfr_float_100 c(3), d; + static_mpfr_float_50 e(5), f; + mpz_int i(20); + + d = a * c; // OK, result of operand is an mpfr_float_100. + b = a * c; // Error, can't convert the result to an mpfr_float_50 as it will lose digits. + f = a * e; // Error, operator is ambiguous, result could be of either type. + f = e * i; // OK, unambiguous conversion from mpz_int to static_mpfr_float_50 + +[h4 Operands of the Same Precision] + +Sometimes you want to apply an operator to two arguments of the same precision in +such a way as to obtain a result of higher precision. The most common situation +occurs with fixed precision integers, where you want to multiply two N-bit numbers +to obtain a 2N-bit result. This is supported in this library by the following +free functions: + + template <class ResultType, class Source1 class Source2> + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + + template <class ResultType, class Source1 class Source2> + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + + template <class ResultType, class Source1 class Source2> + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + +These functions apply the named operator to the arguments ['a] and ['b] and store the +result in ['result], returning ['result]. In all cases they behave "as if" +arguments ['a] and ['b] were first promoted to type `ResultType` before applying the +operator, though particular backends may well avoid that step by way of an optimization. + +The type `ResultType` must be an instance of class `number`, and the types `Source1` and `Source2` +may be either instances of class `number` or native integer types. The latter is an optimization +that allows arithmetic to be performed on native integer types producing an extended precision result. + +For example: + +[mixed_eg] + +Produces the output: + +[mixed_output] + +[h4 Backends With Optimized Mixed Precision Arithmetic] + +The following backends have at least some direct support for mixed precision arithmetic, +and therefore avoid creating unnecessary temporaries when using the interfaces above. +Therefore when using these types it's more efficient to use mixed precision arithmetic, +than it is to explicitly cast the operands to the result type: + +__mpfr_float_backend, __mpf_float, __cpp_int. + +[endsect] + +[section:gen_int Generic Integer Operations] + +All of the [link boost_multiprecision.ref.number.integer_functions non-member integer operations] are overloaded for the +built in integer types in +`<boost/multiprecision/integer.hpp>`. +Where these operations require a temporary increase in precision (such as for powm), then +if no built in type is available, a __cpp_int of appropriate precision will be used. + +Some of these functions are trivial, others use compiler intrinsics (where available) to ensure optimal +evaluation. + +The overloaded functions are: + + template <class Integer, class I2> + Integer& multiply(Integer& result, const I2& a, const I2& b); + +Multiplies two `I2` values, to produce a wider `Integer` result. + +Returns `result = a * b` without overflow or loss of precision in the multiplication. + + template <class Integer, class I2> + Integer& add(Integer& result, const I2& a, const I2& b); + +Adds two `I2` values, to produce a wider `Integer` result. + +Returns `result = a + b` without overflow or loss of precision in the addition. + + template <class Integer, class I2> + Integer& subtract(Integer& result, const I2& a, const I2& b); + +Subtracts two `I2` values, to produce a wider `Integer` result. + +Returns `result = a - b` without overflow or loss of precision in the subtraction. + + template <class Integer> + Integer powm(const Integer& b, const Integer& p, const Integer& m); + +Returns b[super p] % m. + + template <class Integer> + void divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r); + +Sets `q = x / y` and `r = x % y`. + + template <class Integer1, class Integer2> + Integer2 integer_modulus(const Integer1& x, Integer2 val); + +Returns x % val; + + template <class Integer> + unsigned lsb(const Integer& x); + +Returns the (zero-based) index of the least significant bit of `x`. + +Throws a `std::domain_error` if `x <= 0`. + + template <class Integer> + unsigned msb(const Integer& x); + +Returns the (zero-based) index of the most significant bit of `x`. + +Throws a `std::domain_error` if `x <= 0`. + + template <class Integer> + bool bit_test(const Integer& val, unsigned index); + +Returns `true` if bit `index` is set in `val`. + + template <class Integer> + Integer& bit_set(Integer& val, unsigned index); + +Sets the `index` bit in `val`. + + template <class Integer> + Integer& bit_unset(Integer& val, unsigned index); + +Unsets the `index` bit in `val`. + + template <class Integer> + Integer& bit_flip(Integer& val, unsigned index); + +Flips the `index` bit in `val`. + + template <class Integer> + Integer sqrt(const Integer& x); + template <class Integer> + Integer sqrt(const Integer& x, Integer& r); + +Returns the integer square root `s` of x and sets `r` to the remainder ['x - s[super 2]]. + + template <class Engine> + bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials); + +The regular Miller-Rabin functions in `<boost/multiprecision/miller_rabin.hpp>` are defined in terms of the above +generic operations, and so function equally well for built in and multiprecision types. + +[endsect] + +[section:serial Boost.Serialization Support] + +Support for serialization comes in two forms: + +* Classes __number, __debug_adaptor, __logged_adaptor and __rational_adaptor have "pass through" serialization +support which requires the underlying backend to be serializable. +* Backends __cpp_int, __cpp_bin_float, __cpp_dec_float and __float128 have full support for Boost.Serialization. + +[endsect] + +[section:limits Numeric Limits] + +Boost.Multiprecision tries hard to implement `std::numeric_limits` for all types +as far as possible and meaningful because experience with Boost.Math +has shown that this aids portability. + +The [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3690.pdf C++ standard library] +defines `std::numeric_limits` in section 18.3.2. + +This in turn refers to the C standard +[@http://www.open-std.org/jtc1/sc22/wg11/docs/n507.pdf SC22/WG11 N507 DRAFT INTERNATIONAL ISO/IEC STANDARD + WD 10967-1] +Information technology Language independent arithmetic Part 1: Integer and Floating point arithmetic. + +That C Standard in turn refers to + +[@http://754r.ucbtest.org/standards/754.pdf IEEE754 IEEE Standard for Binary +Floating-Point Arithmetic] + +There is a useful summary at +[@http://www.cplusplus.com/reference/limits/numeric_limits/ C++ reference]. + +The chosen backend often determines how completely `std::numeric_limits` is available. + +Compiler options, processor type, and definition of macros or assembler instructions to control denormal numbers will alter +the values in the tables given below. + +[warning GMP's `mpf_t` does not have a concept of overflow: +operations that lead to overflow eventually run of out of resources +and terminate with stack overflow (often after several seconds).] + +[section:constants std::numeric_limits<> constants] + + +[h4 is_specialized] + +`true` for all arithmetic types (integer, floating and fixed-point) +for which `std::numeric_limits<T>::numeric_limits` is specialized. + +A typical test is + + if (std::numeric_limits<T>::is_specialized == false) + { + std::cout << "type " << typeid(T).name() << " is not specialized for std::numeric_limits!" << std::endl; + // ... + } + +Typically `numeric_limits<T>::is_specialized` is `true` for all `T` where the compile-time constant +members of `numeric_limits` are indeed known at compile time, and don't vary at runtime. For example +floating point types with runtime-variable precision such as `mpfr_float` have no `numeric_limits` +specialization as it would be impossible to define all the members at compile time. In contrast +the precision of a type such as `mpfr_float_50` is known at compile time, and so it ['does] have a +`numeric_limits` specialization. + +Note that not all the `std::numeric_limits` member constants and functions are meaningful for all user-defined types (UDT), +such as the decimal and binary multiprecision types provided here. More information on this is given in the sections below. + +[h4 infinity] + +For floating-point types, [infin] is defined wherever possible, +but clearly infinity is meaningless for __arbitrary_precision arithmetic backends, +and there is one floating point type (GMP's `mpf_t`, see __mpf_float) which has no notion +of infinity or NaN at all. + +A typical test whether infinity is implemented is + + if(std::numeric_limits<T>::has_infinity) + { + std::cout << std::numeric_limits<T>::infinity() << std::endl; + } + +and using tests like this is strongly recommended to improve portability. + +If the backend is switched to a type that does not support infinity then, +without checks like this, there will be trouble. + +[h4 is_signed] + +`std::numeric_limits<T>::is_signed == true` if the type `T` is signed. + +For built-in binary types, the sign is held in a single bit, +but for other types (cpp_dec_float and cpp_bin_float) +it may be a separate storage element, usually `bool`. + +[h4 is_exact] + +`std::numeric_limits<T>::is_exact == true` if type T uses exact representations. + +This is defined as `true` for all integer types and `false` for floating-point types. + +[@http://stackoverflow.com/questions/14203654/stdnumeric-limitsis-exact-what-is-a-usable-definition A usable definition] +has been discussed. + +ISO/IEC 10967-1, Language independent arithmetic, noted by the C++ Standard defines + + A floating point type F shall be a finite subset of [real]. + +The important practical distinction is that all integers (up to `max()`) can be stored exactly. + +[@http://en.wikipedia.org/wiki/Rational_number Rational] +types using two integer types are also exact. + +Floating-point types [*cannot store all real values] +(those in the set of [real]) [*exactly]. +For example, 0.5 can be stored exactly in a binary floating-point, but 0.1 cannot. +What is stored is the nearest representable real value, that is, rounded to nearest. + +Fixed-point types (usually decimal) are also defined as exact, in that they only +store a [*fixed precision], so half cents or pennies (or less) cannot be stored. +The results of computations are rounded up or down, +just like the result of integer division stored as an integer result. + +There are number of proposals to +[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html +add Decimal Floating Point Support to C++]. + +[@http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2849.pdf Decimal TR]. + +And also +[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html +C++ Binary Fixed-Point Arithmetic]. + +[h4 is_bounded] + +`std::numeric_limits<T>::is_bounded == true` if the set of values represented by the type `T` is finite. + +This is `true` for all built-in integer, fixed and floating-point types, +and most multi-precision types. + +It is only `false` for a few __arbitrary_precision types like `cpp_int`. + +Rational and fixed-exponent representations are exact but not integer. + +[h4 is_modulo] + +`std::numeric_limits<T>::is_modulo` is defined as `true` if adding two positive values of type T +can yield a result less than either value. + +`is_modulo == true` means that the type does not overflow, but, for example, +'wraps around' to zero, when adding one to the `max()` value. + +For most built-in integer types, `std::numeric_limits<>::is_modulo` is `true`. + +`bool` is the only exception. + +The modulo behaviour is sometimes useful, +but also can be unexpected, and sometimes undesired, behaviour. + +Overflow of signed integers can be especially unexpected, +possibly causing change of sign. + +Boost.Multiprecision integer type `cpp_int` is not modulo +because as an __arbitrary_precision types, +it expands to hold any value that the machine resources permit. + +However fixed precision __cpp_int's may be modulo if they are unchecked +(i.e. they behave just like built in integers), but not if they are checked +(overflow causes an exception to be raised). + +Built-in and multi-precision floating-point types are normally not modulo. + +Where possible, overflow is to `std::numeric_limits<>::infinity()`, +provided `std::numeric_limits<>::has_infinity == true`. + +[h4 radix] + +Constant `std::numeric_limits<T>::radix` returns either 2 (for built-in and binary types) +or 10 (for decimal types). + +[h4 digits] + +The number of `radix` digits that be represented without change: + +* for integer types, the number of [*non-sign bits] in the significand. +* for floating types, the number of [*radix digits] in the significand. + +The values include any implicit bit, so for example, for the ubiquious +`double` using 64 bits +([@http://en.wikipedia.org/wiki/Double_precision_floating-point_format IEEE binary64 ]), +`digits` == 53, even though there are only 52 actual bits of the significand stored in the representation. +The value of `digits` reflects the fact that there is one implicit bit which is always set to 1. + +The Boost.Multiprecision binary types do not use an implicit bit, so the +`digits` member reflects exactly how many bits of precision were requested: + + typedef number<cpp_bin_float<53, digit_base_2> > float64; + typedef number<cpp_bin_float<113, digit_base_2> > float128; + std::numeric_limits<float64>::digits == 53. + std::numeric_limits<float128>::digits == 113. + +For the most common case of `radix == 2`, +`std::numeric_limits<T>::digits` is the number of bits in the representation, +not counting any sign bit. + +For a decimal integer type, when `radix == 10`, it is the number of decimal digits. + +[h4 digits10] + +Constant `std::numeric_limits<T>::digits10` returns the number of +decimal digits that can be represented without change or loss. + +For example, `numeric_limits<unsigned char>::digits10` is 2. + +This somewhat inscrutable definition means that an `unsigned char` +can hold decimal values `0..99` +without loss of precision or accuracy, usually from truncation. + +Had the definition been 3 then that would imply it could hold 0..999, +but as we all know, an 8-bit `unsigned char` can only hold 0..255, +and an attempt to store 256 or more will involve loss or change. + +For bounded integers, it is thus [*one less] than number of decimal digits +you need to display the biggest integer `std::numeric_limits<T>::max()`. +This value can be used to predict the layout width required for + +[digits10_1] + +For example, `unsigned short` is often stored in 16 bits, +so the maximum value is 0xFFFF or 65535. + +[digits10_2] + + +For bounded floating-point types, +if we create a `double` with a value with `digits10` (usually 15) decimal digits, +`1e15` or `1000000000000000` : + +[digits10_3] + +and we can increment this value to `1000000000000001` +as expected and show the difference too. + +But if we try to repeat this with more than `digits10` digits, + +[digits10_4] + +then we find that when we add one it has no effect, +and display show that there is loss of precision. See +[@http://en.wikipedia.org/wiki/Loss_of_significance Loss of significance or cancellation error]. + +So `digits10` is the number of decimal digits [*guaranteed] to be correct. + +For example, 'round-tripping' for `double`: + +* If a decimal string with at most `digits10`( == 15) significant decimal digits +is converted to `double` and then converted back to the +same number of significant decimal digits, +then the final string will match the original 15 decimal digit string. +* If a `double` floating-point number is converted to a decimal string +with at least 17 decimal digits +and then converted back to `double`, +then the result will be binary identical to the original `double` value. + +For most purposes, you will much more likely want +`std::numeric_limits<>::max_digits10`, +the number of decimal digits that ensure that a change of one least significant bit (ULP) +produces a different decimal digits string. + +For nearly all floating-point types, `max_digits10` is `digits10+2`, +but you should use `max_digits10` where possible. + +If `max_digits10` is not available, you should using the +[@http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF Kahan formula for floating-point type T] + + max_digits10 = std::numeric_limits<T>::digits * 3010U/10000U; + +The factor is log[sub 10](2) = 0.3010 +but must be evaluated at compile time using only integers. + +(See also +[@http://www.loria.fr/~zimmerma/mca/mca-cup-0.5.9.pdf Richard P. Brent and Paul Zimmerman, Modern Computer Arithmetic] +Equation 3.8 on page 116.). + +The extra two (or 3) least significant digits are 'noisy' and may be junk, +but if you want to 'round-trip' - printing a value out and reading it back in - +you must use `os.precision(std::numeric_limits<T>::max_digits10)`. +For at least one popular compiler, you must also use `std::scientific` format. + +[h4 max_digits10] + +`std::numeric_limits<T>::max_digits10` was added for floating-point +because `digits10` decimal digits are insufficient to show +a least significant bit (ULP) change giving puzzling displays like + + 0.666666666666667 != 0.666666666666667 + +from failure to 'round-trip', for example: + +[max_digits10_2] + +If you wish to ensure that a change of one least significant bit (ULP) +produces a different decimal digits string, +then `max_digits10` is the precision to use. + +For example: + +[max_digits10_3] + +will display [pi] to the maximum possible precision using a `double`. + +[max_digits10_4] + +For integer types, `max_digits10` is implementation-dependant, +but is usually `digits10 + 2`. +This is the output field width required for the maximum value of the type T +`std::numeric_limits<T>::max()` including a sign and a space. + +So this will produce neat columns. + + std::cout << std::setw(std::numeric_limits<int>::max_digits10) ... + +[note For Microsoft Visual Studio 2010, +`std::numeric_limits<float>::max_digits10` is wrongly defined as 8. It should be 9.] + +[note For Microsoft Visual Studio, and default float format, a small range of values +approximately 0.0001 to 0.004, with exponent values of 3f2 to 3f6, +are wrongly input by one least significant bit, +probably every third value of significand. + +A workaround is using scientific or exponential format `<< std::scientific`.] + +[note BOOST_NO_CXX11_NUMERIC_LIMITS is a suitable feature-test macro to determine if +`std::numeric_limits<float>::max_digits10` is implemented on any platform. +If `max_digits10` is not available, you should using the +[@http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF Kahan formula for floating-point type T]. +See above.] + +[max_digits10_1] [/ example for using max_digits10] + +[h4 round_style] + +The rounding style determines how the result of floating-point operations +is treated when the result cannot be [*exactly represented] in the significand. +Various rounding modes may be provided: + +* round to nearest up or down (default for floating-point types). +* round up (toward positive infinity). +* round down (toward negative infinity). +* round toward zero (integer types). +* no rounding (if decimal radix). +* rounding mode is not determinable. + +For integer types, `std::numeric_limits<T>::round_style` is always towards zero, so + + std::numeric_limits<T>::round_style == std::round_to_zero; + +A decimal type, `cpp_dec_float` rounds in no particular direction, +which is to say it doesn't round at all. +And since there are several guard digits, +it's not really the same as truncation (round toward zero) either. + +For floating-point types, it is normal to round to nearest. + + std::numeric_limits<T>::round_style == std::round_to_nearest; + +See function `std::numeric_limits<T>::round_error` for the maximum error (in ULP) +that rounding can cause. + +[h4 has_denorm_loss] + +`true` if a loss of precision is detected as a +[@http://en.wikipedia.org/wiki/Denormalization denormalization] loss, +rather than an inexact result. + +Always `false` for integer types. + +`false` for all types which do not have `has_denorm` == `std::denorm_present`. + +[h4 denorm_style] + +[@http://en.wikipedia.org/wiki/Denormal_number Denormalized values] are +representations with a variable number of exponent bits that can permit +gradual underflow, so that, if type T is `double`. + + std::numeric_limits<T>::denorm_min() < std::numeric_limits<T>::min() + +A type may have any of the following `enum float_denorm_style` values: + +* `std::denorm_absent`, if it does not allow denormalized values. +(Always used for all integer and exact types). +* `std::denorm_present`, if the floating-point type allows denormalized values. +*`std::denorm_indeterminate`, if indeterminate at compile time. + +[h4 Tinyness before rounding] + +`bool std::numeric_limits<T>::tinyness_before` + +`true` if a type can determine that a value is too small +to be represent as a normalized value before rounding it. + +Generally true for `is_iec559` floating-point built-in types, +but false for integer types. + +Standard-compliant IEEE 754 floating-point implementations may detect the floating-point underflow at three predefined moments: + +# After computation of a result with absolute value smaller than +`std::numeric_limits<T>::min()`, +such implementation detects ['tinyness before rounding] (e.g. UltraSparc). + +# After rounding of the result to `std::numeric_limits<T>::digits` bits, +if the result is tiny, such implementation detects ['tinyness after rounding] +(e.g. SuperSparc). + +# If the conversion of the rounded tiny result to subnormal form +resulted in the loss of precision, such implementation detects ['denorm loss]. + +[endsect] [/section:constants std::numeric_limits<> Constants] + +[section:functions std::numeric_limits<> functions] + +[h4 max function] + +Function `std::numeric_limits<T>::max()` returns the largest finite value +that can be represented by the type T. If there is no such value (and +`numeric_limits<T>::bounded` is `false`) then returns `T()`. + +For built-in types there is usually a corresponding MACRO value TYPE_MAX, +where TYPE is CHAR, INT, FLOAT etc. + +Other types, including those provided by a typedef, +for example `INT64_T_MAX` for `int64_t`, may provide a macro definition. + +To cater for situations where no `numeric_limits` specialization is available +(for example because the precision of the type varies at runtime), +packaged versions of this (and other functions) are provided using + + #include <boost/math/tools/precision.hpp> + + T = boost::math::tools::max_value<T>(); + +Of course, these simply use `std::numeric_limits<T>::max()` if available, +but otherwise 'do something sensible'. + +[h4 lowest function] + +Since C++11: `std::numeric_limits<T>::lowest()` is + +* For integral types, the same as function `min()`. +* For floating-point types, generally the negative of `max()` +(but implementation-dependent). + +[digits10_5] + +[h4 min function] + +Function `std::numeric_limits<T>::min()` returns the minimum finite value +that can be represented by the type T. + +For built-in types there is usually a corresponding MACRO value TYPE_MIN, +where TYPE is CHAR, INT, FLOAT etc. + +Other types, including those provided by a typedef, +for example `INT64_T_MIN` for `int64_t`, may provide a macro definition. + +For floating-point types, +it is more fully defined as the ['minimum positive normalized value]. + +See `std::numeric_limits<T>::denorm_min()` for the smallest denormalized value, provided + + std::numeric_limits<T>::has_denorm == std::denorm_present + + +To cater for situations where no `numeric_limits` specialization is available +(for example because the precision of the type varies at runtime), +packaged versions of this (and other functions) are provided using + + #include <boost/math/tools/precision.hpp> + + T = boost::math::tools::min_value<T>(); + +Of course, these simply use `std::numeric_limits<T>::min()` if available. + +[h4 denorm_min function] + +Function `std::numeric_limits<T>::denorm_min()` +returns the smallest +[@http://en.wikipedia.org/wiki/Denormal_number denormalized value], +provided + + std::numeric_limits<T>::has_denorm == std::denorm_present + +[denorm_min_1] + +The exponent is effectively reduced from -308 to -324 +(though it remains encoded as zero and leading zeros appear in the significand, +thereby losing precision until the significand reaches zero). + +[h4 round_error] + +Function `std::numeric_limits<T>::round_error()` returns the maximum error +(in units of [@http://en.wikipedia.org/wiki/Unit_in_the_last_place ULP]) +that can be caused by any basic arithmetic operation. + + round_style == std::round_indeterminate; + +The rounding style is indeterminable at compile time. + +For floating-point types, when rounding is to nearest, +only half a bit is lost by rounding, and `round_error == 0.5`. +In contrast when rounding is towards zero, or plus/minus infinity, +we can loose up to one bit from rounding, and `round_error == 1`. + +For integer types, rounding always to zero, so at worst almost one bit can be rounded, +so `round_error == 1`. + +`round_error()` can be used with `std::numeric_limits<T>::epsilon()` to estimate +the maximum potential error caused by rounding. For typical floating-point types, +`round_error() = 1/2`, so half epsilon is the maximum potential error. + +[round_error_1] + +There are, of course, many occasions when much bigger loss of precision occurs, +for example, caused by +[@http://en.wikipedia.org/wiki/Loss_of_significance Loss of significance or cancellation error] +or very many iterations. + +[h4 epsilon] + +Function `std::numeric_limits<T>::epsilon()` is meaningful only for non-integral types. + +It returns the difference between `1.0` and the next value representable +by the floating-point type T. +So it is a one least-significant-bit change in this floating-point value. + +For `double` (`float_64t`) it is `2.2204460492503131e-016` +showing all possibly significant 17 decimal digits. + +[epsilon_1] + +We can explicitly increment by one bit using the function `boost::math::float_next()` +and the result is the same as adding `epsilon`. + +[epsilon_2] + +Adding any smaller value, like half `epsilon`, will have no effect on this value. + +[epsilon_3] + +So this cancellation error leaves the values equal, despite adding half `epsilon`. + +To achieve greater portability over platform and floating-point type, +Boost.Math and Boost.Multiprecion provide a package of functions that +'do something sensible' if the standard `numeric_limits` is not available. +To use these `#include <boost/math/tools/precision.hpp>`. + +[epsilon_4] + +[h5 Tolerance for Floating-point Comparisons] + +`epsilon` is very useful to compute a tolerance when comparing floating-point values, +a much more difficult task than is commonly imagined. + +For more information you probably want (but still need) see +[@http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html What Every Computer Scientist Should Know About Floating-Point Arithmetic] + +The naive test comparing the absolute difference between two values and a tolerance +does not give useful results if the values are too large or too small. + +So Boost.Test uses an algorithm first devised by Knuth +for reliably checking if floating-point values are close enough. + +See Donald. E. Knuth. The art of computer programming (vol II). +Copyright 1998 Addison-Wesley Longman, Inc., 0-201-89684-2. +Addison-Wesley Professional; 3rd edition. + +See also: + +[@http://adtmag.com/articles/2000/03/15/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx Alberto Squassia, Comparing floats] + +[@http://adtmag.com/articles/2000/03/16/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx Alberto Squassia, Comparing floats code] + +[@boost:/libs/test/doc/html/utf/testing-tools/floating_point_comparison.html floating-point comparison]. + +[tolerance_1] + +used thus: + + BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance); + +(There is also a version using tolerance as a percentage rather than a fraction). + +[tolerance_2] + +[h4 Infinity - positive and negative] + +For floating-point types only, for which +`std::numeric_limits<T>::has_infinity == true`, +function `std::numeric_limits<T>::infinity()` +provides an implementation-defined representation for [infin]. + +The 'representation' is a particular bit pattern reserved for infinity. +For IEEE754 system (for which `std::numeric_limits<T>::is_iec559 == true`) +[@http://en.wikipedia.org/wiki/IEEE_754-1985#Positive_and_negative_infinity positive and negative infinity] +are assigned bit patterns for all defined floating-point types. + +Confusingly, the string resulting from outputting this representation, is also +implementation-defined. And the string that can be input to generate the representation is also implementation-defined. + +For example, the output is `1.#INF` on Microsoft systems, but `inf` on most *nix platforms. + +This implementation-defined-ness has hampered use of infinity (and NaNs) +but Boost.Math and Boost.Multiprecision work hard to provide a sensible representation +for [*all] floating-point types, not just the built-in types, +which with the use of suitable facets to define the input and output strings, makes it possible +to use these useful features portably and including Boost.Serialization. + +[h4 Not-A-Number NaN] + +[h5 Quiet_NaN] + +For floating-point types only, for which +`std::numeric_limits<T>::has_quiet_NaN == true`, +function `std::numeric_limits<T>::quiet_NaN()` +provides an implementation-defined representation for NaN. + +[@http://en.wikipedia.org/wiki/NaN NaNs] are values to indicate that the +result of an assignment or computation is meaningless. +A typical example is `0/0` but there are many others. + +NaNs may also be used, to represent missing values: for example, +these could, by convention, be ignored in calculations of statistics like means. + +Many of the problems with a representation for +[@http://en.wikipedia.org/wiki/NaN Not-A-Number] has hampered portable use, +similar to those with infinity. + +[nan_1] + +But using Boost.Math and suitable facets can permit portable use +of both NaNs and positive and negative infinity. + +[facet_1] + +[h5 Signaling NaN] + +For floating-point types only, for which +`std::numeric_limits<T>::has_signaling_NaN == true`, +function `std::numeric_limits<T>::signaling_NaN()` +provides an implementation-defined representation for NaN that causes a hardware trap. +It should be noted however, that at least one implementation of this function causes a hardware +trap to be triggered simply by calling `std::numeric_limits<T>::signaling_NaN()`, and not only +by using the value returned. + +[endsect] [/section:functions std::numeric_limits<> functions] + +[/ Tables of values for numeric_limits for various built-in and cpp_bin_float types] +[include numeric_limits_32_tables.qbk] +[/include numeric_limits_64_tables.qbk] + +[section:how_to_tell How to Determine the Kind of a Number From `std::numeric_limits`] + +Based on the information above, one can see that different kinds of numbers can be +differentiated based on the information stored in `std::numeric_limits`. This is +in addition to the traits class [link boost_multiprecision.ref.number.traits_class_support +number_category] provided by this library. + +[h4 Integer Types] + +For an integer type T, all of the following conditions hold: + + std::numeric_limits<T>::is_specialized == true + std::numeric_limits<T>::is_integer == true + std::numeric_limits<T>::is_exact == true + std::numeric_limits<T>::min_exponent == 0 + std::numeric_limits<T>::max_exponent == 0 + std::numeric_limits<T>::min_exponent10 == 0 + std::numeric_limits<T>::max_exponent10 == 0 + +In addition the type is /signed/ if: + + std::numeric_limits<T>::is_signed == true + +If the type is arbitrary precision then: + + std::numeric_limits<T>::is_bounded == false + +Otherwise the type is bounded, and returns a non zero value +from: + + std::numeric_limits<T>::max() + +and has: + + std::numeric_limits<T>::is_modulo == true + +if the type implements modulo arithmetic on overflow. + +[h4 Rational Types] + +Rational types are just like integers except that: + + std::numeric_limits<T>::is_integer == false + +[h4 Fixed Precision Types] + +There appears to be no way to tell these apart from rational types, unless they set: + + std::numeric_limits<T>::is_exact == false + +This is because these types are in essence a rational type with a fixed denominator. + +[h4 Floating Point Types] + +For a floating point type T, all of the following conditions hold: + + std::numeric_limits<T>::is_specialized == true + std::numeric_limits<T>::is_integer == false + std::numeric_limits<T>::is_exact == false + std::numeric_limits<T>::min_exponent != 0 + std::numeric_limits<T>::max_exponent != 0 + std::numeric_limits<T>::min_exponent10 != 0 + std::numeric_limits<T>::max_exponent10 != 0 + +In addition the type is /signed/ if: + + std::numeric_limits<T>::is_signed == true + +And the type may be decimal or binary depending on the value of: + + std::numeric_limits<T>::radix + +In general, there are no arbitrary precision floating point types, and so: + + std::numeric_limits<T>::is_bounded == false + +[h4 Exact Floating Point Types] + +Exact floating point types are a [@http://en.wikipedia.org/wiki/Field_%28mathematics%29 field] +composed of an arbitrary precision integer scaled by an exponent. Such types +have no division operator and are the same as floating point types except: + + std::numeric_limits<T>::is_exact == true + +[h4 Complex Numbers] + +For historical reasons, complex numbers do not specialize `std::numeric_limits`, instead you must +inspect `std::numeric_limits<T::value_type>`. + +[endsect] + +[endsect] [/section:limits Numeric Limits] + + +[section:input_output Input Output] + + +[h4 Loopback testing] + +['Loopback] or ['round-tripping] refers to writing out a value as a decimal digit string using `std::iostream`, +usually to a `std::stringstream`, and then reading the string back in to another value, +and confirming that the two values are identical. A trivial example using `float` is: + + float write; // Value to round-trip. + std::stringstream ss; // Read and write std::stringstream. + ss.precision(std::numeric_limits<T>::max_digits10); // Ensure all potentially significant bits are output. + ss.flags(std::ios_base::fmtflags(std::ios_base::scientific)); // Use scientific format. + ss << write; // Output to string. + float read; // Expected. + ss >> read; // Read decimal digits string from stringstream. + BOOST_CHECK_EQUAL(write, read); // Should be the same. + +and this can be run in a loop for all possible values of a 32-bit float. +For other floating-point types `T`, including built-in `double`, +it takes far too long to test all values, +so a reasonable test strategy is to use a large number of random values. + + T write; + std::stringstream ss; + ss.precision(std::numeric_limits<T>::max_digits10); // Ensure all potentially significant bits are output. + ss.flags(f); // Changed from default iostream format flags if desired. + ss << write; // Output to stringstream. + + T read; + ss >> read; // Get read using operator>> from stringstream. + BOOST_CHECK_EQUAL(read, write); + + read = static_cast<T>(ss.str()); // Get read by converting from decimal digits string representation of write. + BOOST_CHECK_EQUAL(read, write); + + read = static_cast<T>(write.str(0, f)); // Get read using format specified when written. + BOOST_CHECK_EQUAL(read, write); + + +The test at +[@../../test/test_cpp_bin_float_io.cpp test_cpp_bin_float_io.cpp] +allows any floating-point type to be ['round_tripped] using a wide range of fairly random values. +It also includes tests compared a collection of +[@../../test/string_data.ipp stringdata] test cases in a file. + +[h4 Comparing with output using Built-in types] + +One can make some comparisons with the output of + + <number<cpp_bin_float<53, digit_count_2> > + +which has the same number of significant bits (53) as 64-bit double precision floating-point. + +However, although most outputs are identical, there are differences on some platforms +caused by the implementation-dependent behaviours allowed by the C99 specification +[@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf C99 ISO/IEC 9899:TC2], +incorporated by C++. + +[:['"For e, E, f, F, g, and G conversions, if the number of significant decimal digits +is at most DECIMAL_DIG, then the result should be correctly rounded. +If the number of significant decimal digits is more than DECIMAL_DIG +but the source value is exactly representable with DECIMAL_DIG digits, +then the result should be an exact representation with trailing zeros. +Otherwise, the source value is bounded by two adjacent decimal strings L < U, +both having DECIMAL_DIG significant digits; +the value of the resultant decimal string D should satisfy L<= D <= U, +with the extra stipulation that the error should have a correct sign +for the current rounding direction."]] + +So not only is correct rounding for the full number of digits not required, +but even if the *optional* recommended practice is followed, +then the value of these last few digits is unspecified +as long as the value is within certain bounds. + +[note Do not expect the output from different platforms +to be [*identical], but `cpp_dec_float`, `cpp_bin_float` (and other backends) outputs should be +correctly rounded to the number of digits requested by the set precision and format.] + + +[h4 Macro BOOST_MP_MIN_EXPONENT_DIGITS] + +[@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf C99 Standard] +for [/e and E] format specifiers, 7.19.6 Formatted input/output functions requires: + +\"The exponent always contains at least two digits, +and only as many more digits as necessary to represent the exponent.\" + +So to conform to the C99 standard (incorporated by C++) + + #define BOOST_MP_MIN_EXPONENT_DIGITS 2 + +Confusingly, Microsoft (and MinGW) do not conform to this standard and provide +[*at least three digits], for example `1e+001`. +So if you want the output to match that from +built-in floating-point types on compilers that use Microsofts runtime then use: + + #define BOOST_MP_MIN_EXPONENT_DIGITS 3 + +Also useful to get the minimum exponent field width is + + #define BOOST_MP_MIN_EXPONENT_DIGITS 1 + +producing a compact output like `2e+4`, +useful when conserving space is important. + +Larger values are also supported, for example, value 4 for `2e+0004` +which may be useful to ensure that columns line up. + +[endsect] [/section:input_output Input Output] + + +[endsect] + +[section:ref Reference] + +[section:number number] + +[h4 Synopsis] + + namespace boost{ namespace multiprecision{ + + enum expression_template_option { et_on = 1, et_off = 0 }; + + template <class Backend> struct expression_template_default + { static const expression_template_option value = et_on; }; + + template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value> + class number + { + number(); + number(see-below); + number& operator=(see-below); + number& assign(see-below); + + // Member operators + number& operator+=(const ``['see-below]``&); + number& operator-=(const ``['see-below]``&); + number& operator*=(const ``['see-below]``&); + number& operator/=(const ``['see-below]``&); + number& operator++(); + number& operator--(); + number operator++(int); + number operator--(int); + + number& operator%=(const ``['see-below]``&); + number& operator&=(const ``['see-below]``&); + number& operator|=(const ``['see-below]``&); + number& operator^=(const ``['see-below]``&); + number& operator<<=(const ``['integer-type]``&); + number& operator>>=(const ``['integer-type]``&); + + // Use in Boolean context: + operator ``['convertible-to-bool-type]``()const; + // swap: + void swap(number& other); + // Sign: + bool is_zero()const; + int sign()const; + // string conversion: + std::string str()const; + // Generic conversion mechanism + template <class T> + T convert_to()const; + template <class T> + explicit operator T ()const; + // precision control: + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + // Comparison: + int compare(const number<Backend>& o)const; + template <class V> + typename enable_if<is_convertible<V, number<Backend, ExpressionTemplates> >, int>::type + compare(const V& o)const; + // Access to the underlying implementation: + Backend& backend(); + const Backend& backend()const; + }; + + // Non member operators: + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator/(const ``['see-below]``&, const ``['see-below]``&); + // Integer only operations: + ``['unmentionable-expression-template-type]`` operator%(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator&(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator|(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator^(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator<<(const ``['see-below]``&, const ``['integer-type]``&); + ``['unmentionable-expression-template-type]`` operator>>(const ``['see-below]``&, const ``['integer-type]``&); + // Comparison operators: + bool operator==(const ``['see-below]``&, const ``['see-below]``&); + bool operator!=(const ``['see-below]``&, const ``['see-below]``&); + bool operator< (const ``['see-below]``&, const ``['see-below]``&); + bool operator> (const ``['see-below]``&, const ``['see-below]``&); + bool operator<=(const ``['see-below]``&, const ``['see-below]``&); + bool operator>=(const ``['see-below]``&, const ``['see-below]``&); + + // Swap: + template <class Backend, expression_template_option ExpressionTemplates> + void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b); + + // iostream support: + template <class Backend, expression_template_option ExpressionTemplates> + std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r); + std::ostream& operator << (std::ostream& os, const ``['unmentionable-expression-template-type]``& r); + template <class Backend, expression_template_option ExpressionTemplates> + std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r); + + // Arithmetic with a higher precision result: + template <class ResultType, class Source1 class Source2> + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + template <class ResultType, class Source1 class Source2> + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + template <class ResultType, class Source1 class Source2> + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + + // Non-member function standard library support: + ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['number-or-expression-template-type]``&); + + ``['unmentionable-expression-template-type]`` ldexp (const ``['number-or-expression-template-type]``&, ``['integer-type]``); + ``['unmentionable-expression-template-type]`` frexp (const ``['number-or-expression-template-type]``&, ``['integer-type]``*); + ``['unmentionable-expression-template-type]`` pow (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` scalbn(const ``['number-or-expression-template-type]``&, ``['integer-type]``); + ``['unmentionable-expression-template-type]`` logb (const ``['number-or-expression-template-type]``&); + ``['integer-type]`` ilogb (const ``['number-or-expression-template-type]``&); + + // Traits support: + template <class T> + struct component_type; + template <class T> + struct number_category; + template <class T> + struct is_number; + template <class T> + struct is_number_expression; + + // Integer specific functions: + ``['unmentionable-expression-template-type]`` gcd(const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lcm(const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``&, unsigned); + ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); + ``['unmentionable-expression-template-type]`` sqrt(const ``['number-or-expression-template-type]``&); + template <class Backend, expression_template_option ExpressionTemplates> + number<Backend, EXpressionTemplates> sqrt(const ``['number-or-expression-template-type]``&, number<Backend, EXpressionTemplates>&); + template <class Backend, expression_template_option ExpressionTemplates> + void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, + number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r); + template <class Integer> + Integer integer_modulus(const ``['number-or-expression-template-type]``& x, Integer val); + unsigned lsb(const ``['number-or-expression-template-type]``& x); + unsigned msb(const ``['number-or-expression-template-type]``& x); + template <class Backend, class ExpressionTemplates> + bool bit_test(const number<Backend, ExpressionTemplates>& val, unsigned index); + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_set(number<Backend, ExpressionTemplates>& val, unsigned index); + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_unset(number<Backend, ExpressionTemplates>& val, unsigned index); + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_flip(number<Backend, ExpressionTemplates>& val, unsigned index); + template <class Engine> + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials); + + // Rational number support: + typename component_type<``['number-or-expression-template-type]``>::type numerator (const ``['number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type denominator(const ``['number-or-expression-template-type]``&); + + }} // namespaces + + namespace boost{ namespace math{ + + // Boost.Math interoperability functions: + int fpclassify (const ``['number-or-expression-template-type]``&, int); + bool isfinite (const ``['number-or-expression-template-type]``&, int); + bool isnan (const ``['number-or-expression-template-type]``&, int); + bool isinf (const ``['number-or-expression-template-type]``&, int); + bool isnormal (const ``['number-or-expression-template-type]``&, int); + + }} // namespaces + + // numeric_limits support: + namespace std{ + + template <class Backend, expression_template_option ExpressionTemplates> + struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> > + { + /* Usual members here */ + }; + + } + +[h4 Description] + + enum expression_template_option { et_on = 1, et_off = 0 }; + +This enumerated type is used to specify whether expression templates are turned on (et_on) or turned off (et_off). + + template <class Backend> struct expression_template_default + { static const expression_template_option value = et_on; }; + +This traits class specifies the default expression template option to be used with a particular Backend type. +It defaults to `et_on`. + + template <class Backend, expression_template_option ExpressionTemplates = expression_template_default<Backend>::value> + class number; + +Class `number` has two template arguments: + +[variablelist +[[Backend][The actual arithmetic back-end that does all the work.]] +[[ExpressionTemplates][A Boolean value: when `et_on`, then expression templates are enabled, otherwise when set to `et_off` they are disabled. + The default for this parameter is computed via the traits class `expression_template_default` whose member `value` defaults to `et_on` unless + the traits class is specialized for a particular backend.]] +] + + number(); + number(see-below); + number& operator=(see-below); + number& assign(see-below); + +Type `number` is default constructible, and both copy constructible and assignable from: + +* Itself. +* An expression template which is the result of one of the arithmetic operators. +* Any builtin arithmetic type, as long as the result would not be lossy (for example float to integer conversion). +* Any type that the Backend is implicitly constructible or assignable from. +* An rvalue reference to another `number`. Move-semantics are used for construction if the backend also +supports rvalue reference construction. In the case of assignment, move semantics are always supported +when the argument is an rvalue reference irrespective of the backend. +* Any type in the same family, as long as no loss of precision is involved. For example from `int128_t` to `int256_t`, +or `cpp_dec_float_50` to `cpp_dec_float_100`. + +Type `number` is explicitly constructible from: + +* Any type mentioned above. +* A `std::string` or any type which is convertible to `const char*`. +* Any arithmetic type (including those that would result in lossy conversions). +* Any type in the same family, including those that result in loss of precision. +* Any type that the Backend is explicitly constructible from. +* Any pair of types for which a generic interconversion exists: that is from integer to integer, integer +to rational, integer to float, rational to rational, rational to float, or float to float. + +The assign member function is available for any type for which an explicit converting constructor exists. +It is intended to be used where a temporary generated from an explicit assignment would be expensive, for example: + + mpfr_float_50 f50; + mpfr_float_100 f100; + + f50 = static_cast<mpfr_float_50>(f100); // explicit cast create a temporary + f50.assign(f100); // explicit call to assign create no temporary + +In addition, if the type has multiple components (for example rational or complex number types), then there is a +two argument constructor: + + number(arg1, arg2); + +Where the two args must either be arithmetic types, or types that are convertible to the two components of `this`. + + number& operator+=(const ``['see-below]``&); + number& operator-=(const ``['see-below]``&); + number& operator*=(const ``['see-below]``&); + number& operator/=(const ``['see-below]``&); + number& operator++(); + number& operator--(); + number operator++(int); + number operator--(int); + // Integer only operations: + number& operator%=(const ``['see-below]``&); + number& operator&=(const ``['see-below]``&); + number& operator|=(const ``['see-below]``&); + number& operator^=(const ``['see-below]``&); + number& operator<<=(const ``['integer-type]``&); + number& operator>>=(const ``['integer-type]``&); + +These operators all take their usual arithmetic meanings. + +The arguments to these operators is either: + +* Another `number<Backend, ExpressionTemplates>`. +* An expression template derived from `number<Backend>`. +* Any type implicitly convertible to `number<Backend, ExpressionTemplates>`, including some other instance of class `number`. + +For the left and right shift operations, the argument must be a builtin +integer type with a positive value (negative values result in a `std::runtime_error` being thrown). + + operator ``['convertible-to-bool-type]``()const; + +Returns an ['unmentionable-type] that is usable in Boolean contexts (this allows `number` to be used in any +Boolean context - if statements, conditional statements, or as an argument to a logical operator - without +type `number` being convertible to type `bool`. + +This operator also enables the use of `number` with any of the following operators: +`!`, `||`, `&&` and `?:`. + + void swap(number& other); + +Swaps `*this` with `other`. + + bool is_zero()const; + +Returns `true` is `*this` is zero, otherwise `false`. + + int sign()const; + +Returns a value less than zero if `*this` is negative, a value greater than zero if `*this` is positive, and zero +if `*this` is zero. + + std::string str(unsigned precision, bool scientific = true)const; + +Returns the number formatted as a string, with at least /precision/ digits, and in scientific format +if /scientific/ is true. + + template <class T> + T convert_to()const; + + template <class T> + explicit operator T ()const; + +Provides a generic conversion mechanism to convert `*this` to type `T`. Type `T` may be any arithmetic type. +Optionally other types may also be supported by specific `Backend` types. + + + static unsigned default_precision(); + static void default_precision(unsigned digits10); + unsigned precision()const; + void precision(unsigned digits10); + +These functions are only available if the Backend template parameter supports runtime changes to precision. They get and set +the default precision and the precision of `*this` respectively. + + int compare(const number<Backend, ExpressionTemplates>& o)const; + template <class V> + typename enable_if<is_convertible<V, number<Backend, ExpressionTemplates> >, int>::type + compare(const V& other)const; + +Returns: + +* A value less that 0 for `*this < other` +* A value greater that 0 for `*this > other` +* Zero for `*this == other` + + Backend& backend(); + const Backend& backend()const; + +Returns the underlying back-end instance used by `*this`. + +[h4 Non-member operators] + + // Non member operators: + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator+(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator-(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator*(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator/(const ``['see-below]``&, const ``['see-below]``&); + // Integer only operations: + ``['unmentionable-expression-template-type]`` operator%(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator&(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator|(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator^(const ``['see-below]``&, const ``['see-below]``&); + ``['unmentionable-expression-template-type]`` operator<<(const ``['see-below]``&, const ``['integer-type]``&); + ``['unmentionable-expression-template-type]`` operator>>(const ``['see-below]``&, const ``['integer-type]``&); + // Comparison operators: + bool operator==(const ``['see-below]``&, const ``['see-below]``&); + bool operator!=(const ``['see-below]``&, const ``['see-below]``&); + bool operator< (const ``['see-below]``&, const ``['see-below]``&); + bool operator> (const ``['see-below]``&, const ``['see-below]``&); + bool operator<=(const ``['see-below]``&, const ``['see-below]``&); + bool operator>=(const ``['see-below]``&, const ``['see-below]``&); + +These operators all take their usual arithmetic meanings. + +The arguments to these functions must contain at least one of the following: + +* A `number`. +* An expression template type derived from `number`. +* Any type for which `number` has an implicit constructor - for example a builtin arithmetic type. + +The return type of these operators is either: + +* An ['unmentionable-type] expression template type when `ExpressionTemplates` is `true`. +* Type `number<Backend, et_off>` when `ExpressionTemplates` is `false`. +* Type `bool` if the operator is a comparison operator. + +Finally note that the second argument to the left and right shift operations must be a builtin integer type, +and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). + +[h4 swap] + + template <class Backend, ExpressionTemplates> + void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b); + +Swaps `a` and `b`. + +[h4 Iostream Support] + + template <class Backend, expression_template_option ExpressionTemplates> + std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r); + template <class Unspecified...> + std::ostream& operator << (std::ostream& os, const unmentionable-expression-template& r); + template <class Backend, expression_template_option ExpressionTemplates> + inline std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r) + +These operators provided formatted input-output operations on `number` types, and expression templates derived from them. + +It's down to the back-end type to actually implement string conversion. However, the back-ends provided with +this library support all of the iostream formatting flags, field width and precision settings. + +[h4 Arithmetic with a higher precision result] + + template <class ResultType, class Source1 class Source2> + ResultType& add(ResultType& result, const Source1& a, const Source2& b); + + template <class ResultType, class Source1 class Source2> + ResultType& subtract(ResultType& result, const Source1& a, const Source2& b); + + template <class ResultType, class Source1 class Source2> + ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); + +These functions apply the named operator to the arguments ['a] and ['b] and store the +result in ['result], returning ['result]. In all cases they behave "as if" +arguments ['a] and ['b] were first promoted to type `ResultType` before applying the +operator, though particular backends may well avoid that step by way of an optimization. + +The type `ResultType` must be an instance of class `number`, and the types `Source1` and `Source2` +may be either instances of class `number` or native integer types. The latter is an optimization +that allows arithmetic to be performed on native integer types producing an extended precision result. + +[h4 Non-member standard library function support] + + ``['unmentionable-expression-template-type]`` abs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fabs (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sqrt (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` floor (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ceil (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` trunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` itrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` ltrunc (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lltrunc(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` round (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` iround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` lround (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` llround(const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` exp (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` log10 (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` acos (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` asin (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` cosh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` sinh (const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` tanh (const ``['number-or-expression-template-type]``&); + + ``['unmentionable-expression-template-type]`` ldexp (const ``['number-or-expression-template-type]``&, ``['integer-type]``); + ``['unmentionable-expression-template-type]`` frexp (const ``['number-or-expression-template-type]``&, ``['integer-type]``*); + ``['unmentionable-expression-template-type]`` pow (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` fmod (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` atan2 (const ``['number-or-expression-template-type]``&, const ``['number-or-expression-template-type]``&); + ``['unmentionable-expression-template-type]`` scalbn(const ``['number-or-expression-template-type]``&, ``['integer-type]``); + ``['unmentionable-expression-template-type]`` logb (const ``['number-or-expression-template-type]``&); + ``['integer-type]`` ilogb (const ``['number-or-expression-template-type]``&); + +These functions all behave exactly as their standard library C++11 counterparts do: their argument is either an instance of `number` or +an expression template derived from it; If the argument is of type `number<Backend, et_off>` then that is also the return type, +otherwise the return type is an expression template. + +The integer type arguments to `ldexp`, `frexp`, `scalbn` and `ilogb` may be either type `int`, or the actual +type of the exponent of the number type. + +These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that +don't have native support for these functions. Please note however, that this default support requires the precision of the type +to be a compile time constant - this means for example that the [gmp] MPF Backend will not work with these functions when that type is +used at variable precision. + +Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types (if any other types +such as fixed precision or complex types are added to the library later, then these functions may be extended to support those number types). + +The precision of these functions is generally determined by the backend implementation. For example the precision +of these functions when used with __mpfr_float_backend is determined entirely by [mpfr]. When these functions use our own +implementations, the accuracy of the transcendental functions is generally a few epsilon. Note however, that the trigonometrical +functions incur the usual accuracy loss when reducing arguments by large multiples of [pi]. Also note that both __mpf_float +and __cpp_dec_float have a number of guard digits beyond their stated precision, so the error rates listed for these +are in some sense artificially low. + +The following table shows the error rates we observe for these functions with various backend types, functions not listed +here are exact (tested on Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): + +[table +[[Function][mpfr_float_50][mpf_float_50][cpp_dec_float_50]] +[[sqrt][1eps][0eps][0eps]] +[[exp][1eps][0eps][0eps]] +[[log][1eps][0eps][0eps]] +[[log10][1eps][0eps][0eps]] +[[cos][700eps][0eps][0eps]] +[[sin][1eps][0eps][0eps]] +[[tan][0eps][0eps][0eps]] +[[acos][0eps][0eps][0eps]] +[[asin][0eps][0eps][0eps]] +[[atan][1eps][0eps][0eps]] +[[cosh][1045eps[footnote It's likely that the inherent error in the input values to our test cases are to blame here.]][0eps][0eps]] +[[sinh][2eps][0eps][0eps]] +[[tanh][1eps][0eps][0eps]] +[[pow][0eps][4eps][3eps]] +[[atan2][1eps][0eps][0eps]] +] +[h4 Traits Class Support] + + template <class T> + struct component_type; + +If this is a type with multiple components (for example rational or complex types), then this trait has a single member +`type` that is the type of those components. + + template <class T> + struct number_category; + +A traits class that inherits from `mpl::int_<N>` where `N` is one of the enumerated values `number_kind_integer`, `number_kind_floating_point`, +`number_kind_rational`, `number_kind_fixed_point`, or `number_kind_unknown`. This traits class is specialized for any type that has +`std::numeric_limits` support as well as for classes in this library: which means it can be used for generic code that must work +with built in arithmetic types as well as multiprecision ones. + + template <class T> + struct is_number; + +A traits class that inherits from `mpl::true_` if T is an instance of `number<>`, otherwise from `mpl::false_`. + + template <class T> + struct is_number_expression; + +A traits class that inherits from `mpl::true_` if T is an expression template type derived from `number<>`, otherwise from `mpl::false_`. + + + +[h4 Integer functions] + +In addition to functioning with types from this library, these functions are also overloaded for built in integer +types if you include `<boost/multiprecision/integer.hpp>`. Further, when used with fixed precision types (whether +built in integers or multiprecision ones), the functions will promote to a wider type internally when the algorithm +requires it. Versions overloaded for built in integer types return that integer type rather than an expression +template. + + ``['unmentionable-expression-template-type]`` gcd(const ``['number-or-expression-template-type]``& a, const ``['number-or-expression-template-type]``& b); + +Returns the largest integer `x` that divides both `a` and `b`. + + ``['unmentionable-expression-template-type]`` lcm(const ``['number-or-expression-template-type]``& a, const ``['number-or-expression-template-type]``& b); + +Returns the smallest integer `x` that is divisible by both `a` and `b`. + + ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``& b, unsigned p); + +Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so +large as to take "effectively forever" to compute, or else simply run the host machine out of memory. This is the one function in +this category that is not overloaded for built in integer types, further, it's probably not a good idea to use it with +fixed precision `cpp_int`'s either. + + ``['unmentionable-expression-template-type]`` powm(const ``['number-or-expression-template-type]``& b, const ``['number-or-expression-template-type]``& p, const ``['number-or-expression-template-type]``& m); + +Returns ['b[super p] mod m] as an expression template. Fixed precision types are promoted internally to ensure accuracy. + + ``['unmentionable-expression-template-type]`` sqrt(const ``['number-or-expression-template-type]``& a); + +Returns the largest integer `x` such that `x * x < a`. + + template <class Backend, expression_template_option ExpressionTemplates> + number<Backend, EXpressionTemplates> sqrt(const ``['number-or-expression-template-type]``& a, number<Backend, EXpressionTemplates>& r); + +Returns the largest integer `x` such that `x * x < a`, and sets the remainder `r` such that `r = a - x * x`. + + template <class Backend, expression_template_option ExpressionTemplates> + void divide_qr(const ``['number-or-expression-template-type]``& x, const ``['number-or-expression-template-type]``& y, + number<Backend, ExpressionTemplates>& q, number<Backend, ExpressionTemplates>& r); + +Divides x by y and returns both the quotient and remainder. After the call `q = x / y` and `r = x % y`. + + template <class Integer> + Integer integer_modulus(const ``['number-or-expression-template-type]``& x, Integer val); + +Returns the absolute value of `x % val`. + + unsigned lsb(const ``['number-or-expression-template-type]``& x); + +Returns the (zero-based) index of the least significant bit that is set to 1. + +Throws a `std::range_error` if the argument is <= 0. + + unsigned msb(const ``['number-or-expression-template-type]``& x); + +Returns the (zero-based) index of the most significant bit. + +Throws a `std::range_error` if the argument is <= 0. + + template <class Backend, class ExpressionTemplates> + bool bit_test(const number<Backend, ExpressionTemplates>& val, unsigned index); + +Returns `true` if the bit at /index/ in /val/ is set. + + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_set(number<Backend, ExpressionTemplates>& val, unsigned index); + +Sets the bit at /index/ in /val/, and returns /val/. + + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_unset(number<Backend, ExpressionTemplates>& val, unsigned index); + +Unsets the bit at /index/ in /val/, and returns /val/. + + template <class Backend, class ExpressionTemplates> + number<Backend, ExpressionTemplates>& bit_flip(number<Backend, ExpressionTemplates>& val, unsigned index); + +Flips the bit at /index/ in /val/, and returns /val/. + + template <class Engine> + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials, Engine& gen); + bool miller_rabin_test(const ``['number-or-expression-template-type]``& n, unsigned trials); + +Tests to see if the number /n/ is probably prime - the test excludes the vast majority of composite numbers +by excluding small prime factors and performing a single Fermat test. Then performs /trials/ Miller-Rabin +tests. Returns `false` if /n/ is definitely composite, or `true` if /n/ is probably prime with the +probability of it being composite less than 0.25^trials. Fixed precision types are promoted internally +to ensure accuracy. + +[h4 Rational Number Functions] + + typename component_type<``['number-or-expression-template-type]``>::type numerator (const ``['number-or-expression-template-type]``&); + typename component_type<``['number-or-expression-template-type]``>::type denominator(const ``['number-or-expression-template-type]``&); + +These functions return the numerator and denominator of a rational number respectively. + +[h4 Boost.Math Interoperability Support] + + namespace boost{ namespace math{ + + int fpclassify (const ``['number-or-expression-template-type]``&, int); + bool isfinite (const ``['number-or-expression-template-type]``&, int); + bool isnan (const ``['number-or-expression-template-type]``&, int); + bool isinf (const ``['number-or-expression-template-type]``&, int); + bool isnormal (const ``['number-or-expression-template-type]``&, int); + + }} // namespaces + +These floating-point classification functions behave exactly as their Boost.Math equivalents. + +Other Boost.Math functions and templates may also be +specialized or overloaded to ensure interoperability. + +[h4 std::numeric_limits support] + + namespace std{ + + template <class Backend, ExpressionTemplates> + struct numeric_limits<boost::multiprecision<Backend, ExpressionTemplates> > + { + /* Usual members here */ + }; + + } + +Class template `std::numeric_limits` is specialized for all instantiations of `number` whose precision is known at compile time, plus those +types whose precision is unlimited (though it is much less useful in those cases). It is not specialized for types +whose precision can vary at compile time (such as `mpf_float`). + +[endsect] + +[section:cpp_int_ref cpp_int] + + namespace boost{ namespace multiprecision{ + + typedef unspecified-type limb_type; + + enum cpp_integer_type { signed_magnitude, unsigned_magnitude }; + enum cpp_int_check_type { checked, unchecked }; + + template <unsigned MinDigits = 0, + unsigned MaxDits = 0, + cpp_integer_type SignType = signed_magnitude, + cpp_int_check_type Checked = unchecked, + class Allocator = std::allocator<limb_type> > + class cpp_int_backend; + // + // Expression templates default to et_off if there is no allocator: + // + template <unsigned MinDigits, unsigned MaxDigits, cpp_integer_type SignType, cpp_int_check_type Checked> + struct expression_template_default<cpp_int_backend<MinDigits, MaxDigits, SignType, Checked, void> > + { static const expression_template_option value = et_off; }; + + typedef number<cpp_int_backend<> > cpp_int; // arbitrary precision integer + typedef rational_adaptor<cpp_int_backend<> > cpp_rational_backend; + typedef number<cpp_rational_backend> cpp_rational; // arbitrary precision rational number + + // Fixed precision unsigned types: + typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> > uint128_t; + typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> > uint256_t; + typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> > uint512_t; + typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t; + + // Fixed precision signed types: + typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> > int128_t; + typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> > int256_t; + typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> > int512_t; + typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> > int1024_t; + + // Over again, but with checking enabled this time: + typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_int; + typedef rational_adaptor<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_rational_backend; + typedef number<cpp_rational_backend> checked_cpp_rational; + + // Checked fixed precision unsigned types: + typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> > checked_uint128_t; + typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> > checked_uint256_t; + typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> > checked_uint512_t; + typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> > checked_uint1024_t; + + // Fixed precision signed types: + typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> > checked_int128_t; + typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> > checked_int256_t; + typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> > checked_int512_t; + typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> > checked_int1024_t; + + }} // namespaces + +Class template `cpp_int_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The template arguments are: + +[variablelist +[[MinBits][Determines the number of Bits to store directly within the object before resorting to dynamic memory + allocation. When zero, this field is determined automatically based on how many bits can be stored + in union with the dynamic storage header: setting a larger value may improve performance as larger integer + values will be stored internally before memory allocation is required.]] +[[MaxBits][Determines the maximum number of bits to be stored in the type: resulting in a fixed precision type. + When this value is the same as MinBits, then the Allocator parameter is ignored, as no dynamic + memory allocation will ever be performed: in this situation the Allocator parameter should be set to + type `void`. Note that this parameter should not be used simply to prevent large memory + allocations, not only is that role better performed by the allocator, but fixed precision + integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]] +[[SignType][Determines whether the resulting type is signed or not. Note that for +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types + this parameter must be `signed_magnitude`. For fixed precision + types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]] +[[Checked][This parameter has two values: `checked` or `unchecked`. See the [link boost_multiprecision.tut.ints.cpp_int tutorial] for more information.]] +[[Allocator][The allocator to use for dynamic memory allocation, or type `void` if MaxBits == MinBits.]] +] + +The type of `number_category<cpp_int<Args...> >::type` is `mpl::int_<number_kind_integer>`. + +More information on this type can be found in the [link boost_multiprecision.tut.ints.cpp_int tutorial]. + +[endsect] + +[section:gmp_int_ref gmp_int] + + namespace boost{ namespace multiprecision{ + + class gmp_int; + + typedef number<gmp_int > mpz_int; + + }} // namespaces + +Class template `gmp_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The type of `number_category<cpp_int<Args...> >::type` is `mpl::int_<number_kind_integer>`. + +More information on this type can be found in the [link boost_multiprecision.tut.ints.gmp_int tutorial]. + +[endsect] + +[section:tom_int_ref tom_int] + + namespace boost{ namespace multiprecision{ + + class tommath_int; + + typedef number<tommath_int > tom_int; + + }} // namespaces + +Class template `tommath_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The type of `number_category<cpp_int<Args...> >::type` is `mpl::int_<number_kind_integer>`. + +More information on this type can be found in the [link boost_multiprecision.tut.ints.tom_int tutorial]. + +[endsect] + +[section:mpf_ref gmp_float] + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10> + class gmp_float; + + typedef number<gmp_float<50> > mpf_float_50; + typedef number<gmp_float<100> > mpf_float_100; + typedef number<gmp_float<500> > mpf_float_500; + typedef number<gmp_float<1000> > mpf_float_1000; + typedef number<gmp_float<0> > mpf_float; + + }} // namespaces + +Class template `gmp_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type +should support. When this parameter is zero, then the precision can be set at runtime via `number::default_precision` +and `number::precision`. Note that this type does not in any way change the GMP library's global state (for example +it does not change the default precision of the mpf_t data type), therefore you can safely mix this type with existing +code that uses GMP, and also mix `gmp_float`s of differing precision. + +The type of `number_category<cpp_int<Args...> >::type` is `mpl::int_<number_kind_floating_point>`. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.gmp_float tutorial]. + +[endsect] + +[section:mpfr_ref mpfr_float_backend] + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10> + class mpfr_float_backend; + + typedef number<mpfr_float_backend<50> > mpfr_float_50; + typedef number<mpfr_float_backend<100> > mpfr_float_100; + typedef number<mpfr_float_backend<500> > mpfr_float_500; + typedef number<mpfr_float_backend<1000> > mpfr_float_1000; + typedef number<mpfr_float_backend<0> > mpfr_float; + + }} // namespaces + +Class template `mpfr_float_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type +should support. When this parameter is zero, then the precision can be set at runtime via `number::default_precision` +and `number::precision`. Note that this type does not in any way change the GMP or MPFR library's global state (for example +it does not change the default precision of the mpfr_t data type), therefore you can safely mix this type with existing +code that uses GMP or MPFR, and also mix `mpfr_float_backend`s of differing precision. + +The type of `number_category<cpp_int<Args...> >::type` is `mpl::int_<number_kind_floating_point>`. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.mpfr_float tutorial]. + +[endsect] + +[section:cpp_bin_float_ref cpp_bin_float] + + namespace boost{ namespace multiprecision{ + + enum digit_base_type + { + digit_base_2 = 2, + digit_base_10 = 10 + }; + + template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0> + class cpp_bin_float; + + typedef number<cpp_bin_float<50> > cpp_bin_float_50; + typedef number<cpp_bin_float<100> > cpp_bin_float_100; + + typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single; + typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double; + typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended; + typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad; + + }} // namespaces + +Class template `cpp_bin_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes six template parameters: + +[variablelist +[[Digits][The number of digits precision the type +should support. This is normally expressed as base-10 digits, but that can be changed via the second template parameter.]] +[[base][An enumerated value (either `digit_base_10` or `digit_base_2`) that indicates whether `Digits` is base-10 or base-2]] +[[Allocator][The allocator used: defaults to type `void`, meaning all storage is within the class, and no dynamic +allocation is performed, but can be set to a standard library allocator if dynamic allocation makes more sense.]] +[[Exponent][A signed integer type to use as the type of the exponent - defaults to `int`.]] +[[ExponentMin][The smallest (most negative) permitted exponent, defaults to zero, meaning "define as small as possible +given the limitations of the type and our internal requirements".]] +[[ExponentMax][The largest (most positive) permitted exponent, defaults to zero, meaning "define as large as possible +given the limitations of the type and our internal requirements".]] +] + +The type of `number_category<cpp_bin_float<Args...> >::type` is `mpl::int_<number_kind_floating_point>`. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_bin_float tutorial]. + +[h4 Implementation Notes] + +Internally, an N-bit `cpp_bin_float` is represented as an N-bit unsigned integer along with an exponent and a sign. +The integer part is normalized so that it's most significant bit is always 1. The decimal point is assumed to be +directly after the most significant bit of the integer part. The special values zero, infinity and NaN all have +the integer part set to zero, and the exponent to one of 3 special values above the maximum permitted exponent. + +Multiplication is trivial: multiply the two N-bit integer mantissa's to obtain a 2N-bit number, then round and +adjust the sign and exponent. + +Addition and subtraction proceed similarly - if the exponents are such that there is overlap between the two +values, then left shift the larger value to produce a number with between N and 2N bits, then perform integer +addition or subtraction, round, and adjust the exponent. + +Division proceeds as follows: first scale the numerator by some power of 2 so that integer division will +produce either an N-bit or N+1 bit result plus a remainder. If we get an N bit result then the size of +twice the remainder compared to the denominator gives us the rounding direction. Otherwise we have one extra bit +in the result which we can use to determine rounding (in this case ties occur only if the remainder is zero and +the extra bit is a 1). + +Square root uses integer square root in a manner analogous to division. + +Decimal string to binary conversion proceeds as follows: first parse the digits to +produce an integer multiplied by a decimal exponent. Note that we stop parsing digits +once we have parsed as many as can possibly effect the result - this stops the integer +part growing too large when there are a very large number of input digits provided. +At this stage if the decimal exponent is positive then the result is an integer and we +can in principle simply multiply by 10^N to get an exact integer result. In practice +however, that could produce some very large integers. We also need to be able to divide +by 10^N in the event that the exponent is negative. Therefore calculation of the 10^N +values plus the multiplication or division are performed using limited precision +integer arithmetic, plus an exponent, and a track of the accumulated error. At the end of +the calculation we will either be able to round unambiguously, or the error will be such +that we can't tell which way to round. In the latter case we simply up the precision and try +again until we have an unambiguously rounded result. + +Binary to decimal conversion proceeds very similarly to the above, our aim is to calculate +`mantissa * 2^shift * 10^E` where `E` is the decimal exponent and `shift` is calculated +so that the result is an N bit integer assuming we want N digits printed in the result. +As before we use limited precision arithmetic to calculate the result and up the +precision as necessary until the result is unambiguously correctly rounded. In addition +our initial calculation of the decimal exponent may be out by 1, so we have to correct +that and loop as well in the that case. + +[endsect] + +[section:cpp_dec_ref cpp_dec_float] + + namespace boost{ namespace multiprecision{ + + template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void> + class cpp_dec_float; + + typedef number<cpp_dec_float<50> > cpp_dec_float_50; + typedef number<cpp_dec_float<100> > cpp_dec_float_100; + + }} // namespaces + +Class template `cpp_dec_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes three template parameters: + +[variablelist +[[Digits10][The number of decimal digits precision the type +should support. Note that this type does not normally perform any dynamic memory allocation, and as a result the `Digits10` +template argument should not be set too high or the class's size will grow unreasonably large.]] +[[ExponentType][A signed integer type that represents the exponent of the number]] +[[Allocator][The allocator used: defaults to type `void`, meaning all storage is within the class, and no dynamic +allocation is performed, but can be set to a standard library allocator if dynamic allocation makes more sense.]] +] + +The type of `number_category<cpp_dec_float<Args...> >::type` is `mpl::int_<number_kind_floating_point>`. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_dec_float tutorial]. + +[endsect] + +[section:internals Internal Support Code] + +There are some traits classes which authors of new backends should be aware of: + + namespace boost{ namespace multiprecision{ namespace detail{ + + template<typename From, typename To> + struct is_explicitly_convertible; + + }}} + +Inherits from `boost::integral_constant<bool,true>` if type `From` has an explicit conversion from `To`. + +For compilers that support C++11 SFINAE-expressions this trait should "just work". Otherwise it inherits +from `boost::is_convertible<From, To>::type`, and will need to be specialised for Backends that have +constructors marked as `explicit`. + + template <class From, class To> + struct is_lossy_conversion + { + static const bool value = see below; + }; + +Member `value` is true if the conversion from `From` to `To` would result in a loss of precision, and `false` otherwise. + +The default version of this trait simply checks whether the ['kind] of conversion (for example from a floating point to an integer type) +is inherently lossy. Note that if either of the types `From` or `To` are of an unknown number category (because `number_category` is not +specialised for that type) then this trait will be `true`. + + template<typename From, typename To> + struct is_restricted_conversion + { + static const bool value = see below; + }; + +Member `value` is `true` if `From` is only explicitly convertible to `To` and not implicitly convertible, or +if `is_lossy_conversion<From, To>::value` is `true`. Otherwise `false`. + +Note that while this trait is the ultimate arbiter of which constructors are marked as `explicit` in class `number`, +authors of backend types should generally specialise one of the traits above, rather than this one directly. + + template <class T> + is_signed_number; + template <class T> + is_unsigned_number; + +These two traits inherit from either `mpl::true_` or `mpl::false_`, by default types are assumed to be signed unless +`is_unsigned_number` is specialized for that type. + +[endsect] + +[section:backendconc Backend Requirements] + +The requirements on the `Backend` template argument to `number` are split up into +sections: compulsory and optional. + +Compulsory requirements have no default implementation in the library, therefore if the feature +they implement is to be supported at all, then they must be implemented by the backend. + +Optional requirements have default implementations that are called if the backend doesn't provide +it's own. Typically the backend will implement these to improve performance. + +In the following tables, type B is the `Backend` template argument to `number`, `b` and `b2` are +a variables of type B, `cb`, `cb2` and `cb3` are constant variables of type `const B`, +`rb` is a variable of type `B&&`, `a` and `a2` are variables of Arithmetic type, +`s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, +`pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, +`pexp` is a variable of type `B::exp_type*`, `i` is a variable of type `int`, `pi` pointer to a variable of type `int`, +B2 is another type that meets these requirements, b2 is a variable of type B2, `ss` is variable of type `std::streamsize` +and `ff` is a variable of type `std::ios_base::fmtflags`. + +[table Compulsory Requirements on the Backend type. +[[Expression][Return Type][Comments][Throws]] +[[`B::signed_types`][`mpl::list<type-list>`][A list of signed integral types that can be assigned to type B. The types shall be + listed in order of size, smallest first, and shall terminate in the type that is `std::intmax_t`.][[space]]] +[[`B::unsigned_types`][`mpl::list<type-list>`][A list of unsigned integral types that can be assigned to type B. The types shall be + listed in order of size, smallest first, and shall terminate in the type that is `std::uintmax_t`.][[space]]] +[[`B::float_types`][`mpl::list<type-list>`][A list of floating-point types that can be assigned to type B.The types shall be + listed in order of size, smallest first, and shall terminate in type `long double`.][[space]]] +[[`B::exponent_type`][A signed integral type.][The type of the exponent of type B. This type is required only for floating point types.][[space]]] +[[`B()`][ ][Default constructor.][[space]]] +[[`B(cb)`][ ][Copy Constructor.][[space]]] +[[`b = b`][`B&`][Assignment operator.][[space]]] +[[`b = a`][`B&`][Assignment from an Arithmetic type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`b = s`][`B&`][Assignment from a string.][Throws a `std::runtime_error` if the string could not be interpreted as a valid number.]] +[[`b.swap(b)`][`void`][Swaps the contents of its arguments.][`noexcept`]] +[[`cb.str(ss, ff)`][`std::string`][Returns the string representation of `b` with `ss` digits and formatted according to the flags set in `ff`. + If `ss` is zero, then returns as many digits as are required to reconstruct the original value.][[space]]] +[[`b.negate()`][`void`][Negates `b`.][[space]]] +[[`cb.compare(cb2)`][`int`][Compares `cb` and `cb2`, returns a value less than zero if `cb < cb2`, a value greater than zero if `cb > cb2` and zero + if `cb == cb2`.][`noexcept`]] +[[`cb.compare(a)`][`int`][Compares `cb` and `a`, returns a value less than zero if `cb < a`, a value greater than zero if `cb > a` and zero + if `cb == a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`eval_add(b, cb)`][`void`][Adds `cb` to `b`.][[space]]] +[[`eval_subtract(b, cb)`][`void`][Subtracts `cb` from `b`.][[space]]] +[[`eval_multiply(b, cb)`][`void`][Multiplies `b` by `cb`.][[space]]] +[[`eval_divide(b, cb)`][`void`][Divides `b` by `cb`.] + [`std::overflow_error` if cb has the value zero, and `std::numeric_limits<number<B> >::has_infinity == false`]] +[[`eval_modulus(b, cb)`][`void`][Computes `b %= cb`, only required when `B` is an integer type.] + [`std::overflow_error` if cb has the value zero.]] +[[`eval_bitwise_and(b, cb)`][`void`][Computes `b &= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_bitwise_or(b, cb)`][`void`][Computes `b |= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_bitwise_xor(b, cb)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type.][[space]]] +[[`eval_complement(b, cb)`][`void`][Computes the ones-complement of `cb` and stores the result in `b`, only required when `B` is an integer type.][[space]]] +[[`eval_left_shift(b, ui)`][`void`][Computes `b <<= ui`, only required when `B` is an integer type.][[space]]] +[[`eval_right_shift(b, ui)`][`void`][Computes `b >>= ui`, only required when `B` is an integer type.][[space]]] +[[`eval_convert_to(pa, cb)`][`void`][Converts `cb` to the type of `*pa` and store the result in `*pa`. Type `B` shall support + conversion to at least types `std::intmax_t`, `std::uintmax_t` and `long long`. + Conversion to other arithmetic types can then be synthesised using other operations. + Conversions to other types are entirely optional.][[space]]] +[[`eval_frexp(b, cb, pexp)`][`void`][Stores values in `b` and `*pexp` such that the value of `cb` is b * 2[super *pexp], only required when `B` is a floating-point type.][[space]]] +[[`eval_ldexp(b, cb, exp)`][`void`][Stores a value in `b` that is cb * 2[super exp], only required when `B` is a floating-point type.][[space]]] +[[`eval_frexp(b, cb, pi)`][`void`][Stores values in `b` and `*pi` such that the value of `cb` is b * 2[super *pi], only required when `B` is a floating-point type.] + [`std::runtime_error` if the exponent of cb is too large to be stored in an `int`.]] +[[`eval_ldexp(b, cb, i)`][`void`][Stores a value in `b` that is cb * 2[super i], only required when `B` is a floating-point type.][[space]]] +[[`eval_floor(b, cb)`][`void`][Stores the floor of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] +[[`eval_ceil(b, cb)`][`void`][Stores the ceiling of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] +[[`eval_sqrt(b, cb)`][`void`][Stores the square root of `cb` in `b`, only required when `B` is a floating-point type.][[space]]] +[[`boost::multiprecision::number_category<B>::type`][`mpl::int_<N>`][`N` is one of the values `number_kind_integer`, `number_kind_floating_point`, `number_kind_rational` or `number_kind_fixed_point`. + Defaults to `number_kind_floating_point`.][[space]]] +] + +[table Optional Requirements on the Backend Type +[[Expression][Returns][Comments][Throws]] + +[[['Construct and assign:]]] +[[`B(rb)`][`B`][Move constructor. Afterwards variable `rb` shall be in sane state, albeit with unspecified value. + Only destruction and assignment to the moved-from variable `rb` need be supported after the operation.][`noexcept`]] +[[`b = rb`][`B&`][Move-assign. Afterwards variable `rb` shall be in sane state, albeit with unspecified value. + Only destruction and assignment to the moved-from variable `rb` need be supported after the operation.][`noexcept`]] +[[`B(a)`][`B`][Direct construction from an arithmetic type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, this operation is simulated using default-construction followed by assignment.][[space]]] +[[`B(b2)`][`B`][Copy constructor from a different back-end type. When not provided, a generic interconversion routine is used. + This constructor may be `explicit` if the corresponding frontend constructor should also be `explicit`.][[space]]] +[[`b = b2`][`b&`][Assignment operator from a different back-end type. When not provided, a generic interconversion routine is used.][[space]]] +[[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. + Only applies to rational and complex number types. + When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] +[[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. + Only applies to rational and complex number types. + When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] + +[[['Comparisons:]]] +[[`eval_eq(cb, cb2)`][`bool`][Returns `true` if `cb` and `cb2` are equal in value. + When not provided, the default implementation returns `cb.compare(cb2) == 0`.][`noexcept`]] +[[`eval_eq(cb, a)`][`bool`][Returns `true` if `cb` and `a` are equal in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, return the equivalent of `eval_eq(cb, B(a))`.][[space]]] +[[`eval_eq(a, cb)`][`bool`][Returns `true` if `cb` and `a` are equal in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version returns `eval_eq(cb, a)`.][[space]]] +[[`eval_lt(cb, cb2)`][`bool`][Returns `true` if `cb` is less than `cb2` in value. + When not provided, the default implementation returns `cb.compare(cb2) < 0`.][`noexcept`]] +[[`eval_lt(cb, a)`][`bool`][Returns `true` if `cb` is less than `a` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_lt(cb, B(a))`.][[space]]] +[[`eval_lt(a, cb)`][`bool`][Returns `true` if `a` is less than `cb` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_gt(cb, a)`.][[space]]] +[[`eval_gt(cb, cb2)`][`bool`][Returns `true` if `cb` is greater than `cb2` in value. + When not provided, the default implementation returns `cb.compare(cb2) > 0`.][`noexcept`]] +[[`eval_gt(cb, a)`][`bool`][Returns `true` if `cb` is greater than `a` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_gt(cb, B(a))`.][[space]]] +[[`eval_gt(a, cb)`][`bool`][Returns `true` if `a` is greater than `cb` in value. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default implementation returns `eval_lt(cb, a)`.][[space]]] +[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`. The default version of this function + returns `cb.compare(ui_type(0)) == 0`, where `ui_type` is `ui_type` is + `typename mpl::front<typename B::unsigned_types>::type`.][[space]]] +[[`eval_get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero. + The default version of this function + returns `cb.compare(ui_type(0))`, where `ui_type` is `ui_type` is + `typename mpl::front<typename B::unsigned_types>::type`.][[space]]] + +[[['Basic arithmetic:]]] +[[`eval_add(b, a)`][`void`][Adds `a` to `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_add(b, B(a))`][[space]]] +[[`eval_add(b, cb, cb2)`][`void`][Add `cb` to `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_add(b, cb2)`.][[space]]] +[[`eval_add(b, cb, a)`][`void`][Add `cb` to `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_add(b, cb, B(a))`.][[space]]] +[[`eval_add(b, a, cb)`][`void`][Add `a` to `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_add(b, cb, a)`.][[space]]] +[[`eval_subtract(b, a)`][`void`][Subtracts `a` from `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_subtract(b, B(a))`][[space]]] +[[`eval_subtract(b, cb, cb2)`][`void`][Subtracts `cb2` from `cb` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_subtract(b, cb2)`.][[space]]] +[[`eval_subtract(b, cb, a)`][`void`][Subtracts `a` from `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_subtract(b, cb, B(a))`.][[space]]] +[[`eval_subtract(b, a, cb)`][`void`][Subtracts `cb` from `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_subtract(b, cb, a); b.negate();`.][[space]]] +[[`eval_multiply(b, a)`][`void`][Multiplies `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_multiply(b, B(a))`][[space]]] +[[`eval_multiply(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_multiply(b, cb2)`.][[space]]] +[[`eval_multiply(b, cb, a)`][`void`][Multiplies `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_multiply(b, cb, B(a))`.][[space]]] +[[`eval_multiply(b, a, cb)`][`void`][Multiplies `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_multiply(b, cb, a)`.][[space]]] +[[`eval_multiply_add(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and adds the result to `b`. + When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, cb2)` followed by + `eval_add(b, t)`.][[space]]] +[[`eval_multiply_add(b, cb, a)`][`void`][Multiplies `a` by `cb` and adds the result to `b`. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, a)` followed by + `eval_add(b, t)`.][[space]]] +[[`eval_multiply_add(b, a, cb)`][`void`][Multiplies `a` by `cb` and adds the result to `b`. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided does the equivalent of `eval_multiply_add(b, cb, a)`.][[space]]] +[[`eval_multiply_subtract(b, cb, cb2)`][`void`][Multiplies `cb` by `cb2` and subtracts the result from `b`. + When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, cb2)` followed by + `eval_subtract(b, t)`.][[space]]] +[[`eval_multiply_subtract(b, cb, a)`][`void`][Multiplies `a` by `cb` and subtracts the result from `b`. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided does the equivalent of creating a temporary `B t` and `eval_multiply(t, cb, a)` followed by + `eval_subtract(b, t)`.][[space]]] +[[`eval_multiply_subtract(b, a, cb)`][`void`][Multiplies `a` by `cb` and subtracts the result from `b`. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided does the equivalent of `eval_multiply_subtract(b, cb, a)`.][[space]]] +[[`eval_multiply_add(b, cb, cb2, cb3)`][`void`][Multiplies `cb` by `cb2` and adds the result to `cb3` storing the result in `b`. + When not provided does the equivalent of `eval_multiply(b, cb, cb2)` followed by + `eval_add(b, cb3)`. + For brevity, only a version showing all arguments of type `B` is shown here, but you can replace up to any 2 of + `cb`, `cb2` and `cb3` with any type listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`eval_multiply_subtract(b, cb, cb2, cb3)`][`void`][Multiplies `cb` by `cb2` and subtracts from the result `cb3` storing the result in `b`. + When not provided does the equivalent of `eval_multiply(b, cb, cb2)` followed by + `eval_subtract(b, cb3)`. + For brevity, only a version showing all arguments of type `B` is shown here, but you can replace up to any 2 of + `cb`, `cb2` and `cb3` with any type listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`.][[space]]] +[[`eval_divide(b, a)`][`void`][Divides `b` by `a`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_divide(b, B(a))`] + [`std::overflow_error` if `a` has the value zero, and `std::numeric_limits<number<B> >::has_infinity == false`]] +[[`eval_divide(b, cb, cb2)`][`void`][Divides `cb` by `cb2` and stores the result in `b`. + When not provided, does the equivalent of `b = cb; eval_divide(b, cb2)`.] + [`std::overflow_error` if `cb2` has the value zero, and `std::numeric_limits<number<B> >::has_infinity == false`]] +[[`eval_divide(b, cb, a)`][`void`][Divides `cb` by `a` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_divide(b, cb, B(a))`.] + [`std::overflow_error` if `a` has the value zero, and `std::numeric_limits<number<B> >::has_infinity == false`]] +[[`eval_divide(b, a, cb)`][`void`][Divides `a` by `cb` and stores the result in `b`. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_divide(b, B(a), cb)`.] + [`std::overflow_error` if cb has the value zero, and `std::numeric_limits<number<B> >::has_infinity == false`]] +[[`eval_increment(b)`][void][Increments the value of `b` by one. + When not provided, does the equivalent of `eval_add(b, static_cast<ui_type>(1u))`. + Where `ui_type` is `typename mpl::front<typename B::unsigned_types>::type`.][[space]]] +[[`eval_decrement(b)`][void][Decrements the value of `b` by one. + When not provided, does the equivalent of `eval_subtract(b, static_cast<ui_type>(1u))`. + Where `ui_type` is `typename mpl::front<typename B::unsigned_types>::type`.][[space]]] + +[[['Integer specific operations:]]] +[[`eval_modulus(b, a)`][`void`][Computes `b %= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_modulus(b, B(a))`] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_modulus(b, cb, cb2)`][`void`][Computes `cb % cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_modulus(b, cb2)`.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_modulus(b, cb, a)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_modulus(b, cb, B(a))`.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_modulus(b, a, cb)`][`void`][Computes `cb % a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_modulus(b, B(a), cb)`.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_bitwise_and(b, a)`][`void`][Computes `b &= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_and(b, B(a))`][[space]]] +[[`eval_bitwise_and(b, cb, cb2)`][`void`][Computes `cb & cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_and(b, cb2)`.][[space]]] +[[`eval_bitwise_and(b, cb, a)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_and(b, cb, B(a))`.][[space]]] +[[`eval_bitwise_and(b, a, cb)`][`void`][Computes `cb & a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_and(b, cb, a)`.][[space]]] +[[`eval_bitwise_or(b, a)`][`void`][Computes `b |= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_or(b, B(a))`][[space]]] +[[`eval_bitwise_or(b, cb, cb2)`][`void`][Computes `cb | cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_or(b, cb2)`.][[space]]] +[[`eval_bitwise_or(b, cb, a)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_or(b, cb, B(a))`.][[space]]] +[[`eval_bitwise_or(b, a, cb)`][`void`][Computes `cb | a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_or(b, cb, a)`.][[space]]] +[[`eval_bitwise_xor(b, a)`][`void`][Computes `b ^= cb`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, the default version calls `eval_bitwise_xor(b, B(a))`][[space]]] +[[`eval_bitwise_xor(b, cb, cb2)`][`void`][Computes `cb ^ cb2` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_bitwise_xor(b, cb2)`.][[space]]] +[[`eval_bitwise_xor(b, cb, a)`][`void`][Computes `cb ^ a` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_xor(b, cb, B(a))`.][[space]]] +[[`eval_bitwise_xor(b, a, cb)`][`void`][Computes `a ^ cb` and stores the result in `b`, only required when `B` is an integer type. The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + When not provided, does the equivalent of `eval_bitwise_xor(b, cb, a)`.][[space]]] +[[`eval_left_shift(b, cb, ui)`][`void`][Computes `cb << ui` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_left_shift(b, a);`.][[space]]] +[[`eval_right_shift(b, cb, ui)`][`void`][Computes `cb >> ui` and stores the result in `b`, only required when `B` is an integer type. + When not provided, does the equivalent of `b = cb; eval_right_shift(b, a);`.][[space]]] +[[`eval_qr(cb, cb2, b, b2)`][`void`][Sets `b` to the result of `cb / cb2` and `b2` to the result of `cb % cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_integer_modulus(cb, ui)`][`unsigned`][Returns the result of `cb % ui`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.] + [`std::overflow_error` if `a` has the value zero.]] +[[`eval_lsb(cb)`][`unsigned`][Returns the index of the least significant bit that is set. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_msb(cb)`][`unsigned`][Returns the index of the most significant bit that is set. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_test(cb, ui)`][`bool`][Returns true if `cb` has bit `ui` set. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_set(b, ui)`][`void`][Sets the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_unset(b, ui)`][`void`][Unsets the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_bit_flip(b, ui)`][`void`][Flips the bit at index `ui` in `b`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_gcd(b, cb, cb2)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_lcm(b, cb, cb2)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_gcd(b, cb, a)`][`void`][Sets `b` to the greatest common divisor of `cb` and `cb2`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_gcd(b, cb, B(a))`.][[space]]] +[[`eval_lcm(b, cb, a)`][`void`][Sets `b` to the least common multiple of `cb` and `cb2`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_lcm(b, cb, B(a))`.][[space]]] +[[`eval_gcd(b, a, cb)`][`void`][Sets `b` to the greatest common divisor of `cb` and `a`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_gcd(b, cb, a)`.][[space]]] +[[`eval_lcm(b, a, cb)`][`void`][Sets `b` to the least common multiple of `cb` and `a`. Only required when `B` is an integer type. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types` or `B::float_types`. + The default version of this function calls `eval_lcm(b, cb, a)`.][[space]]] +[[`eval_powm(b, cb, cb2, cb3)`][`void`][Sets `b` to the result of ['(cb^cb2)%cb3]. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, cb2, a)`][`void`][Sets `b` to the result of ['(cb^cb2)%a]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, a, cb2)`][`void`][Sets `b` to the result of ['(cb^a)%cb2]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_powm(b, cb, a, a2)`][`void`][Sets `b` to the result of ['(cb^a)%a2]. + The type of `a` shall be listed in one of the type lists + `B::signed_types`, `B::unsigned_types`. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_integer_sqrt(b, cb, b2)`][`void`][Sets `b` to the largest integer which when squared is less than `cb`, also + sets `b2` to the remainder, ie to ['cb - b[super 2]]. + The default version of this function is synthesised from other operations above.][[space]]] + +[[['Sign manipulation:]]] +[[`eval_abs(b, cb)`][`void`][Set `b` to the absolute value of `cb`. + The default version of this functions assigns `cb` to `b`, and then calls `b.negate()` if + `eval_get_sign(cb) < 0`.][[space]]] +[[`eval_fabs(b, cb)`][`void`][Set `b` to the absolute value of `cb`. + The default version of this functions assigns `cb` to `b`, and then calls `b.negate()` if + `eval_get_sign(cb) < 0`.][[space]]] + +[[['Floating point functions:]]] +[[`eval_fpclassify(cb)`][`int`][Returns one of the same values returned by `std::fpclassify`. Only required when `B` is an floating-point type. + The default version of this function will only test for zero `cb`.][[space]]] +[[`eval_trunc(b, cb)`][`void`][Performs the equivalent operation to `std::trunc` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_round(b, cb)`][`void`][Performs the equivalent operation to `std::round` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_exp(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_log(b, cb)`][`void`][Performs the equivalent operation to `std::log` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_log10(b, cb)`][`void`][Performs the equivalent operation to `std::log10` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_sin(b, cb)`][`void`][Performs the equivalent operation to `std::sin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_cos(b, cb)`][`void`][Performs the equivalent operation to `std::cos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_tan(b, cb)`][`void`][Performs the equivalent operation to `std::exp` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_asin(b, cb)`][`void`][Performs the equivalent operation to `std::asin` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_acos(b, cb)`][`void`][Performs the equivalent operation to `std::acos` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_atan(b, cb)`][`void`][Performs the equivalent operation to `std::atan` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_sinh(b, cb)`][`void`][Performs the equivalent operation to `std::sinh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_cosh(b, cb)`][`void`][Performs the equivalent operation to `std::cosh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_tanh(b, cb)`][`void`][Performs the equivalent operation to `std::tanh` on argument `cb` and stores the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_fmod(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::fmod` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_pow(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::pow` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_atan2(b, cb, cb2)`][`void`][Performs the equivalent operation to `std::atan` on arguments `cb` and `cb2`, and store the result in `b`. Only required when `B` is an floating-point type. + The default version of this function is synthesised from other operations above.][[space]]] +[[`eval_scalbn(b, cb, e)`][`void`][Scales value `cb` by ['r[super e]], where ['r] is the radix of the type. The default version of this function + is implemented in terms of eval_ldexp, consequently this function must be provided for types with a radix other than 2.]] +[[`eval_ilogb(cb)`][`B::exponent_type`][Returns the exponent ['e] of value `cb` such that ['1 <= cb*r[super -e] < r], where ['r] is the radix of type B. + The default version of this function is implemented in terms of eval_frexp, consequently this function must be provided for types with a radix other than 2.]] +[[`eval_logb(b, cb)`][`B::exponent_type`][Sets `b` to the exponent ['e] of value `cb` such that ['1 <= cb*r[super -b] < r], where ['r] is the radix of type B. + The default version of this function is implemented in terms of `eval_ilogb`.]] +] + +When the tables above place no ['throws] requirements on an operation, then it is up to each type modelling this concept to +decide when or whether throwing an exception is desirable. However, thrown exceptions should always either be the type, or +inherit from the type `std::runtime_error`. For example, a floating point type might choose to throw `std::overflow_error` +whenever the result of an operation would be infinite, and `std::underflow_error` whenever it would round to zero. + +[note +The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - +in point of fact this naming convention shouldn't be necessary, but rather works around some compiler bugs.] + +[endsect] + +[section:headers Header File Structure] + +[table Top level headers +[[Header][Contains]] +[[cpp_int.hpp][The `cpp_int` backend type.]] +[[gmp.hpp][Defines all [gmp] related backends.]] +[[miller_rabin.hpp][Miller Rabin primality testing code.]] +[[number.hpp][Defines the `number` backend, is included by all the backend headers.]] +[[mpfr.hpp][Defines the mpfr_float_backend backend.]] +[[random.hpp][Defines code to interoperate with Boost.Random.]] +[[rational_adaptor.hpp][Defines the `rational_adaptor` backend.]] +[[cpp_dec_float.hpp][Defines the `cpp_dec_float` backend.]] +[[tommath.hpp][Defines the `tommath_int` backend.]] +[[concepts/number_archetypes.hpp][Defines a backend concept archetypes for testing use.]] +] + +[table Implementation Headers +[[Header][Contains]] +[[cpp_int/add.hpp][Add and subtract operators for `cpp_int_backend`.]] +[[cpp_int/bitwise.hpp][Bitwise operators for `cpp_int_backend`.]] +[[cpp_int/checked.hpp][Helper functions for checked arithmetic for `cpp_int_backend`.]] +[[cpp_int/comparison.hpp][Comparison operators for `cpp_int_backend`.]] +[[cpp_int/cpp_int_config.hpp][Basic setup and configuration for `cpp_int_backend`.]] +[[cpp_int/divide.hpp][Division and modulus operators for `cpp_int_backend`.]] +[[cpp_int/limits.hpp][`numeric_limits` support for `cpp_int_backend`.]] +[[cpp_int/misc.hpp][Miscellaneous operators for `cpp_int_backend`.]] +[[cpp_int/multiply.hpp][Multiply operators for `cpp_int_backend`.]] +[[detail/big_lanczos.hpp][Lanczos support for Boost.Math integration.]] +[[detail/default_ops.hpp][Default versions of the optional backend non-member functions.]] +[[detail/generic_interconvert.hpp][Generic interconversion routines.]] +[[detail/number_base.hpp][All the expression template code, metaprogramming, and operator overloads for `number`.]] +[[detail/no_et_ops.hpp][The non-expression template operators.]] +[[detail/functions/constants.hpp][Defines constants used by the floating point functions.]] +[[detail/functions/pow.hpp][Defines default versions of the power and exponential related floating point functions.]] +[[detail/functions/trig.hpp][Defines default versions of the trigonometric related floating point functions.]] +] + +[endsect] + +[endsect] + +[section:perf Performance Comparison] + +[section:overhead The Overhead in the Number Class Wrapper] + +Using a simple [@../../performance/arithmetic_backend.hpp backend class] that wraps any built in arithmetic type +we can measure the overhead involved in wrapping a type inside the `number` frontend, and the effect that turning +on expression templates has. The following table compares the performance between `double` and a `double` wrapped +inside class `number`: + +[table +[[Type][Bessel Function Evaluation][Non-Central T Evaluation]] +[[`double`] [[*1.0 (0.016s)]] [[*1.0] (0.46s)]] +[[`number<arithmetic_backend<double>, et_off>`] [1.2 (0.019s)] [[*1.0](0.46s)]] +[[`number<arithmetic_backend<double>, et_on>`] [1.2 (0.019s)] [1.7 (0.79s)]] +] + +As you can see whether or not there is an overhead, and how large it is depends on the actual situation, +but the overhead is in any cases small. Expression templates generally add a greater overhead the +more complex the expression becomes due to the logic of figuring out how to best unpack and evaluate +the expression, but of course this is also the situation where you save more temporaries. For a +"trivial" backend like this, saving temporaries has no benefit, but for larger types it becomes +a bigger win. + +The following table compares arithmetic using either `long long` or `number<arithmetic_backend<long long> >` +for the [@../../performance/voronoi_performance.cpp voronoi-diagram builder test]: + +[table +[[Type][Relative time]] +[[`long long`][[*1.0](0.0823s)]] +[[`number<arithmetic_backend<long long>, et_off>`][1.05 (0.0875s)]] +] + +This test involves mainly creating a lot of temporaries and performing a small amount of arithmetic on them, +with very little difference in performance between the native and "wrapped" types. + +The test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [tommath]-0.42.0. The tests were run on 32-bit +Windows Vista machine. + +[endsect] + +[section:realworld Floating-Point Real World Tests] + +These tests test the total time taken to execute all of Boost.Math's test cases for these functions. +In each case the best performing library gets a relative score of 1, with the total execution time +given in brackets. The first three libraries listed are the various floating point types provided +by this library, while for comparison, two popular C++ front-ends to [mpfr] ([mpfr_class] and [mpreal]) +are also shown. + +[table Bessel Function Performance +[[Library][50 Decimal Digits][100 Decimal Digits]] +[[mpfr_float] [1.2 (5.78s)] [1.2 (9.56s)]] +[[static_mpfr_float] [1.1 (5.47s)] [1.1 (9.09s)]] +[[mpf_float] [[*1.0] (4.82s)] [[*1.0](8.07s)]] +[[cpp_dec_float] [1.8 (8.54s)] [2.6 (20.66s)]] +[[[mpfr_class]] [1.3 (6.28s)] [1.2(10.06s)]] +[[[mpreal]] [2.0 (9.54s)] [1.7 (14.08s)]] +] + +[table Non-Central T Distribution Performance +[[Library][50 Decimal Digits]] +[[mpfr_float] [1.3 (263.27s)]] +[[static_mpfr_float] [1.2 (232.88s)]] +[[mpf_float] [[*1.0] (195.73s)]] +[[cpp_dec_float] [1.9 (366.38s)]] +[[[mpfr_class]] [1.5 (286.94s)]] +[[[mpreal]] [2.0 (388.70s)]] +] + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[endsect] + +[section:int_real_world Integer Real World Tests] + +The first set of [@../../performance/voronoi_performance.cpp tests] measure the times taken to +execute the multiprecision part of the Voronoi-diagram builder from Boost.Polygon. The tests +mainly create a large number of temporaries "just in case" multiprecision arithmetic is required, +for comparison, also included in the tests is Boost.Polygon's own partial-multiprecision integer +type which was custom written for this specific task: + +[table +[[Integer Type][Relative Performance (Actual time in parenthesis)]] +[[polygon::detail::extended_int][1(0.138831s)]] +[[int256_t][1.19247(0.165551s)]] +[[int512_t][1.23301(0.17118s)]] +[[int1024_t][1.21463(0.168628s)]] +[[checked_int256_t][1.31711(0.182855s)]] +[[checked_int512_t][1.57413(0.218538s)]] +[[checked_int1024_t][1.36992(0.190187s)]] +[[cpp_int][1.63244(0.226632s)]] +[[mpz_int][5.42511(0.753172s)]] +[[tom_int][29.0793(4.03709s)]] +] + +Note how for this use case, any dynamic allocation is a performance killer. + +The next [@../../performance/miller_rabin_performance.cpp tests] measure the time taken to generate 1000 128-bit +random numbers and test for primality using the Miller Rabin test. This is primarily a test of modular-exponentiation +since that is the rate limiting step: + +[table +[[Integer Type][Relative Performance (Actual time in parenthesis)]] +[[cpp_int][5.25827(0.379597s)]] +[[cpp_int (no Expression templates)][5.15675(0.372268s)]] +[[cpp_int (128-bit cache)][5.10882(0.368808s)]] +[[cpp_int (256-bit cache)][5.50623(0.397497s)]] +[[cpp_int (512-bit cache)][4.82257(0.348144s)]] +[[cpp_int (1024-bit cache)][5.00053(0.360991s)]] +[[int1024_t][4.37589(0.315897s)]] +[[checked_int1024_t][4.52396(0.326587s)]] +[[mpz_int][1(0.0721905s)]] +[[mpz_int (no Expression templates)][1.0248(0.0739806s)]] +[[tom_int][2.60673(0.188181s)]] +[[tom_int (no Expression templates)][2.64997(0.191303s)]] +] + +It's interesting to note that expression templates have little effect here - perhaps because the actual expressions involved +are relatively trivial in this case - so the time taken for multiplication and division tends to dominate. Also note +how increasing the internal cache size used by `cpp_int` is quite effective in this case in cutting out memory allocations +altogether - cutting about a third off the total runtime. Finally the much quicker times from GMP and tommath are down to their +much better modular-exponentiation algorithms (GMP's is about 5x faster). That's an issue which needs to be addressed +in a future release for __cpp_int. + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[endsect] + +[section:float_performance Float Algorithm Performance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0575156s)][[*1] (0.0740086s)][[*1] (0.219073s)]] +[[gmp_float][2.45065 (0.14095s)][2.01398 (0.149052s)][1.09608 (0.240122s)]] +[[mpfr_float][2.6001 (0.149546s)][2.12079 (0.156957s)][1.09078 (0.23896s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.46115 (0.0855392s)][2.60353 (0.114398s)][3.62562 (0.264905s)]] +[[gmp_float][[*1] (0.0585424s)][[*1] (0.0439398s)][[*1] (0.0730648s)]] +[[mpfr_float][2.40441 (0.14076s)][3.2877 (0.144461s)][2.40379 (0.175632s)]] +] +[table Operator +(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.118146s)][[*1] (0.144714s)][[*1] (0.315639s)]] +[[gmp_float][4.5555 (0.538213s)][3.83096 (0.554395s)][1.95079 (0.615745s)]] +[[mpfr_float][5.74477 (0.678719s)][4.85295 (0.702291s)][2.70354 (0.853342s)]] +] +[table Operator +=(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.101188s)][[*1] (0.122394s)][[*1] (0.251975s)]] +[[gmp_float][5.199 (0.526079s)][4.39327 (0.537712s)][2.42151 (0.610159s)]] +[[mpfr_float][6.08318 (0.615547s)][5.18525 (0.634645s)][3.1022 (0.781677s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0895163s)][[*1] (0.129248s)][1.5088 (0.374512s)]] +[[gmp_float][1.72566 (0.154474s)][1.22567 (0.158415s)][[*1] (0.248219s)]] +[[mpfr_float][1.83764 (0.164499s)][1.34284 (0.173559s)][1.00226 (0.248781s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.105285s)][[*1] (0.142741s)][[*1] (0.278718s)]] +[[gmp_float][2.34437 (0.246828s)][1.28814 (0.183871s)][1.00731 (0.280754s)]] +[[mpfr_float][2.8032 (0.295136s)][2.09178 (0.298582s)][1.25213 (0.34899s)]] +] +[table Operator -(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.13719s)][[*1] (0.184428s)][[*1] (0.344212s)]] +[[gmp_float][4.0804 (0.559791s)][3.06776 (0.565781s)][2.07736 (0.715053s)]] +[[mpfr_float][5.10114 (0.699828s)][3.88684 (0.716843s)][2.50074 (0.860784s)]] +] +[table Operator -=(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.100984s)][[*1] (0.123148s)][[*1] (0.246181s)]] +[[gmp_float][5.68353 (0.573944s)][4.68636 (0.577116s)][2.6958 (0.663655s)]] +[[mpfr_float][6.19738 (0.625834s)][5.18544 (0.638577s)][3.18738 (0.784673s)]] +] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.03667 (0.284251s)][1.30576 (0.536527s)][1.44686 (4.81057s)]] +[[gmp_float][[*1] (0.274196s)][[*1] (0.410891s)][[*1] (3.32484s)]] +[[mpfr_float][1.24537 (0.341477s)][1.15785 (0.475749s)][1.1796 (3.92199s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][3.97453 (0.240262s)][9.91222 (0.463473s)][50.7926 (4.36527s)]] +[[gmp_float][[*1] (0.0604505s)][[*1] (0.0467577s)][[*1] (0.0859431s)]] +[[mpfr_float][2.56974 (0.155342s)][3.56312 (0.166603s)][3.22964 (0.277565s)]] +] +[table Operator *(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.331877s)][1.01058 (0.586122s)][6.688 (4.7931s)]] +[[gmp_float][1.72433 (0.572266s)][[*1] (0.579987s)][[*1] (0.716672s)]] +[[mpfr_float][2.5553 (0.848047s)][1.74987 (1.0149s)][1.80403 (1.2929s)]] +] +[table Operator *=(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.321397s)][1.00772 (0.574887s)][6.65946 (4.7468s)]] +[[gmp_float][1.77419 (0.570218s)][[*1] (0.570482s)][[*1] (0.712791s)]] +[[mpfr_float][2.62172 (0.842611s)][1.77691 (1.01369s)][1.77511 (1.26528s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.96096 (4.00777s)][4.53244 (7.86435s)][6.11936 (51.5509s)]] +[[gmp_float][[*1] (1.35354s)][[*1] (1.73512s)][[*1] (8.42422s)]] +[[mpfr_float][1.30002 (1.75963s)][1.39045 (2.41261s)][1.66762 (14.0484s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][8.60726 (1.8181s)][15.4122 (3.67479s)][34.5119 (24.729s)]] +[[gmp_float][1.24394 (0.262756s)][[*1] (0.238433s)][[*1] (0.716536s)]] +[[mpfr_float][[*1] (0.211229s)][1.12178 (0.26747s)][1.02237 (0.732562s)]] +] +[table Operator /(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.10976 (1.97569s)][3.73601 (3.9133s)][11.3085 (25.4533s)]] +[[gmp_float][[*1] (0.936452s)][[*1] (1.04746s)][[*1] (2.25081s)]] +[[mpfr_float][1.3423 (1.257s)][1.51575 (1.58768s)][3.31513 (7.46175s)]] +] +[table Operator /=(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.17401 (1.96883s)][3.79591 (3.8965s)][11.2328 (25.2606s)]] +[[gmp_float][[*1] (0.905621s)][[*1] (1.0265s)][[*1] (2.24882s)]] +[[mpfr_float][1.37953 (1.24933s)][1.53073 (1.57129s)][3.30546 (7.43339s)]] +] +[table Operator construct +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.00929804s)][[*1] (0.0268321s)][[*1] (0.0310685s)]] +[[gmp_float][30.8781 (0.287106s)][7.59969 (0.203916s)][6.51873 (0.202527s)]] +[[mpfr_float][23.5296 (0.218779s)][8.11058 (0.217624s)][7.16325 (0.222552s)]] +] +[table Operator construct(unsigned) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0603971s)][[*1] (0.0735485s)][[*1] (0.116464s)]] +[[gmp_float][3.91573 (0.236498s)][2.88171 (0.211945s)][1.81075 (0.210887s)]] +[[mpfr_float][4.90052 (0.295977s)][4.01118 (0.295017s)][2.62005 (0.305141s)]] +] +[table Operator construct(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0610288s)][[*1] (0.0759005s)][[*1] (0.118511s)]] +[[gmp_float][8.26247 (0.504249s)][6.69042 (0.507806s)][4.32819 (0.51294s)]] +[[mpfr_float][10.1593 (0.620013s)][8.45884 (0.64203s)][5.51472 (0.653557s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.95848 (0.0223061s)][3.33461 (0.033471s)][3.0159 (0.132732s)]] +[[gmp_float][[*1] (0.00753971s)][[*1] (0.0100374s)][[*1] (0.0440106s)]] +[[mpfr_float][1.25424 (0.00945658s)][1.24943 (0.012541s)][1.09428 (0.0481601s)]] +] + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[endsect] + +[section:integer_performance Integer Algorithm Performance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.23704 (0.0274266s)][1.09358 (0.0383278s)][1.26645 (0.0558828s)][1.32188 (0.0916899s)]] +[[cpp_int(fixed)][1.62044 (0.0359271s)][1.5277 (0.053543s)][1.73059 (0.076363s)][1.71537 (0.118983s)]] +[[gmp_int][1.87515 (0.0415741s)][1.21699 (0.042653s)][1.15599 (0.0510088s)][[*1] (0.0693631s)]] +[[tommath_int][[*1] (0.0221711s)][[*1] (0.035048s)][[*1] (0.0441255s)][1.04441 (0.0724435s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0155377s)][[*1] (0.0209523s)][[*1] (0.0306377s)][[*1] (0.043125s)]] +[[cpp_int(fixed)][1.31904 (0.0204948s)][1.76211 (0.0369203s)][1.52941 (0.0468577s)][1.60412 (0.0691778s)]] +[[gmp_int][1.96204 (0.0304855s)][2.02569 (0.0424428s)][2.11505 (0.0648002s)][2.65993 (0.114709s)]] +[[tommath_int][14.0654 (0.218543s)][10.8239 (0.226786s)][7.76691 (0.23796s)][6.10039 (0.263079s)]] +] +[table Operator +(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.026624s)][[*1] (0.0291407s)][[*1] (0.0373209s)][[*1] (0.0464919s)]] +[[cpp_int(fixed)][1.31378 (0.034978s)][1.54897 (0.045138s)][1.53649 (0.0573431s)][1.27833 (0.0594319s)]] +[[gmp_int][25.5775 (0.680974s)][24.0117 (0.699717s)][19.5633 (0.730121s)][16.8939 (0.785432s)]] +[[tommath_int][19.4694 (0.518354s)][18.4246 (0.536907s)][14.7715 (0.551288s)][12.3637 (0.574812s)]] +] +[table Operator +=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.18405 (0.0196905s)][1.22304 (0.0206476s)][1.25861 (0.0217397s)][1.29525 (0.0220829s)]] +[[cpp_int(fixed)][[*1] (0.0166298s)][[*1] (0.0168822s)][[*1] (0.0172728s)][[*1] (0.0170492s)]] +[[gmp_int][39.9082 (0.663668s)][39.4584 (0.666147s)][38.5504 (0.665873s)][39.2231 (0.668722s)]] +[[tommath_int][30.6219 (0.509238s)][30.4135 (0.513447s)][30.9077 (0.533863s)][32.3086 (0.550835s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.06986 (0.0296064s)][[*1] (0.0381508s)][1.05932 (0.053186s)][1.1766 (0.0844721s)]] +[[cpp_int(fixed)][1.3304 (0.0368163s)][1.44506 (0.0551303s)][1.4431 (0.0724545s)][1.57255 (0.112898s)]] +[[gmp_int][1.48072 (0.0409761s)][1.19003 (0.0454007s)][1.0794 (0.0541942s)][[*1] (0.0717934s)]] +[[tommath_int][[*1] (0.0276731s)][1.10891 (0.0423057s)][[*1] (0.0502076s)][1.08479 (0.0778811s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0147372s)][[*1] (0.0170001s)][[*1] (0.0232882s)][[*1] (0.0310734s)]] +[[cpp_int(fixed)][1.4267 (0.0210256s)][1.98887 (0.0338109s)][1.83788 (0.0428009s)][1.81269 (0.0563264s)]] +[[gmp_int][2.07504 (0.0305803s)][2.40928 (0.0409579s)][2.58711 (0.0602493s)][3.26438 (0.101435s)]] +[[tommath_int][13.5424 (0.199577s)][12.1793 (0.207048s)][9.28855 (0.216314s)][7.49327 (0.232842s)]] +] +[table Operator -(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0277377s)][[*1] (0.0296807s)][[*1] (0.0372392s)][[*1] (0.0455855s)]] +[[cpp_int(fixed)][1.19867 (0.0332484s)][1.48639 (0.0441169s)][1.43253 (0.0533464s)][1.27697 (0.0582111s)]] +[[gmp_int][24.1794 (0.670683s)][22.9073 (0.679904s)][18.8758 (0.702922s)][16.5837 (0.755975s)]] +[[tommath_int][18.149 (0.503413s)][17.4116 (0.516787s)][14.0411 (0.52288s)][11.8237 (0.538987s)]] +] +[table Operator -=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.26896 (0.0203467s)][1.25722 (0.0206147s)][1.36108 (0.0225485s)][1.18351 (0.0226161s)]] +[[cpp_int(fixed)][[*1] (0.0160342s)][[*1] (0.0163971s)][[*1] (0.0165667s)][[*1] (0.0191094s)]] +[[gmp_int][41.1339 (0.659547s)][40.3982 (0.662411s)][39.925 (0.661425s)][34.636 (0.661874s)]] +[[tommath_int][31.1543 (0.499533s)][31.0303 (0.508806s)][30.7699 (0.509756s)][27.7054 (0.529434s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.11839 (0.0757577s)][1.61061 (0.207951s)][1.4501 (0.696912s)][1.72796 (2.64108s)]] +[[cpp_int(fixed)][1.01115 (0.0684934s)][1.28687 (0.166152s)][[*1] (0.480595s)][[*1] (1.52844s)]] +[[gmp_int][[*1] (0.0677384s)][[*1] (0.129113s)][1.09011 (0.523902s)][1.03374 (1.58s)]] +[[tommath_int][1.6322 (0.110562s)][2.71751 (0.350866s)][2.05222 (0.986288s)][2.0644 (3.15531s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.01611 (0.0229536s)][1.12175 (0.0298152s)][1.16413 (0.0416439s)][1.31747 (0.0666043s)]] +[[cpp_int(fixed)][1.30215 (0.0294152s)][1.669 (0.0443606s)][1.72395 (0.0616701s)][1.88315 (0.095202s)]] +[[gmp_int][[*1] (0.0225897s)][[*1] (0.0265791s)][[*1] (0.0357725s)][[*1] (0.0505547s)]] +[[tommath_int][10.8281 (0.244603s)][10.1516 (0.26982s)][8.76424 (0.313519s)][8.04364 (0.406644s)]] +] +[table Operator *(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0570721s)][[*1] (0.0856141s)][[*1] (0.143279s)][[*1] (0.252785s)]] +[[cpp_int(fixed)][1.10857 (0.0632686s)][1.2951 (0.110878s)][1.20827 (0.173121s)][1.18463 (0.299456s)]] +[[gmp_int][12.0605 (0.68832s)][8.13434 (0.696415s)][5.21762 (0.747577s)][3.11601 (0.787681s)]] +[[tommath_int][10.0524 (0.57371s)][7.33116 (0.627651s)][4.85202 (0.695193s)][3.35808 (0.848871s)]] +] +[table Operator *=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][111.27 (7.43118s)][67.7078 (7.34138s)][43.3851 (7.4075s)][25.3089 (7.55455s)]] +[[cpp_int(fixed)][[*1] (0.0667848s)][[*1] (0.108427s)][[*1] (0.170738s)][[*1] (0.298493s)]] +[[gmp_int][46.3718 (3.09693s)][28.4639 (3.08626s)][18.1719 (3.10264s)][10.5223 (3.14083s)]] +[[tommath_int][276.674 (18.4776s)][169.146 (18.34s)][108.491 (18.5236s)][63.3261 (18.9024s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.68035 (0.595251s)][2.04702 (0.707471s)][1.62314 (0.921536s)][1.43112 (1.38811s)]] +[[cpp_int(fixed)][[*1] (0.222079s)][[*1] (0.34561s)][[*1] (0.567748s)][[*1] (0.969945s)]] +[[gmp_int][3.79283 (0.842308s)][2.73668 (0.945824s)][1.86649 (1.05969s)][1.32141 (1.2817s)]] +[[tommath_int][13.2531 (2.94324s)][11.2054 (3.87271s)][9.83293 (5.58262s)][13.0164 (12.6252s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][4.06026 (0.225473s)][3.45732 (0.340049s)][3.00195 (0.547957s)][2.80587 (0.978029s)]] +[[cpp_int(fixed)][2.43766 (0.135367s)][2.56264 (0.252052s)][2.44011 (0.445402s)][2.38009 (0.829617s)]] +[[gmp_int][[*1] (0.0555316s)][[*1] (0.0983563s)][[*1] (0.182534s)][[*1] (0.348566s)]] +[[tommath_int][35.9988 (1.99907s)][27.1024 (2.66569s)][21.8333 (3.98531s)][25.8066 (8.99528s)]] +] +[table Operator /(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.50505 (0.705756s)][1.39347 (1.58556s)][2.63348 (3.57438s)][4.75451 (8.52733s)]] +[[cpp_int(fixed)][[*1] (0.468925s)][1.12378 (1.27869s)][2.29966 (3.12128s)][4.4844 (8.04288s)]] +[[gmp_int][2.17234 (1.01866s)][[*1] (1.13785s)][[*1] (1.35728s)][[*1] (1.79352s)]] +[[tommath_int][4.74612 (2.22557s)][2.70088 (3.07319s)][3.65634 (4.96268s)][6.79408 (12.1853s)]] +] +[table Operator /=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.76281 (0.0574966s)][1.76471 (0.0604224s)][1.56085 (0.0716403s)][1.31422 (0.124043s)]] +[[cpp_int(fixed)][[*1] (0.0326164s)][[*1] (0.0342393s)][[*1] (0.0458981s)][[*1] (0.0943852s)]] +[[gmp_int][20.2862 (0.661664s)][19.4043 (0.664389s)][14.4881 (0.664976s)][7.14238 (0.674135s)]] +[[tommath_int][32.9555 (1.07489s)][30.1525 (1.0324s)][22.8324 (1.04796s)][11.7456 (1.10861s)]] +] +[table Operator % +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.8501 (0.364131s)][1.46527 (0.476653s)][1.27509 (0.689738s)][1.20064 (1.11769s)]] +[[cpp_int(fixed)][[*1] (0.196817s)][[*1] (0.325301s)][[*1] (0.540932s)][[*1] (0.930916s)]] +[[gmp_int][3.2533 (0.640305s)][2.15441 (0.700832s)][1.47898 (0.800029s)][1.07439 (1.00016s)]] +[[tommath_int][15.3501 (3.02116s)][12.1106 (3.9396s)][11.0689 (5.98752s)][13.5535 (12.6172s)]] +] +[table Operator %(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.82761 (0.104331s)][2.01496 (0.202512s)][2.10004 (0.389523s)][2.17252 (0.768097s)]] +[[cpp_int(fixed)][1.78851 (0.102099s)][1.96844 (0.197838s)][2.02956 (0.376451s)][2.07257 (0.73276s)]] +[[gmp_int][[*1] (0.057086s)][[*1] (0.100505s)][[*1] (0.185483s)][[*1] (0.353552s)]] +[[tommath_int][36.3018 (2.07233s)][26.3075 (2.64402s)][21.9525 (4.07183s)][25.6759 (9.07775s)]] +] +[table Operator construct +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.40211 (0.0026854s)][[*1] (0.00278639s)][[*1] (0.00322813s)][[*1] (0.0027185s)]] +[[cpp_int(fixed)][[*1] (0.00191526s)][1.40721 (0.00392103s)][1.90346 (0.00614463s)][2.14621 (0.00583447s)]] +[[gmp_int][98.705 (0.189046s)][68.9726 (0.192184s)][58.8994 (0.190135s)][70.0525 (0.190438s)]] +[[tommath_int][105.602 (0.202255s)][74.1994 (0.206748s)][63.6455 (0.205456s)][76.8935 (0.209035s)]] +] +[table Operator construct(unsigned) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.73436 (0.00348927s)][[*1] (0.00263476s)][[*1] (0.0027009s)][[*1] (0.00318651s)]] +[[cpp_int(fixed)][[*1] (0.00201185s)][1.36851 (0.0036057s)][2.07362 (0.00560064s)][1.66856 (0.00531688s)]] +[[gmp_int][97.2414 (0.195635s)][76.3759 (0.201232s)][72.7396 (0.196462s)][63.8129 (0.20334s)]] +[[tommath_int][210.112 (0.422713s)][162.652 (0.42855s)][158.33 (0.427634s)][134.626 (0.428987s)]] +] +[table Operator construct(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.34403 (0.00739542s)][1.66376 (0.00713834s)][1.22989 (0.0074969s)][1.23708 (0.00711417s)]] +[[cpp_int(fixed)][[*1] (0.00315501s)][[*1] (0.00429049s)][[*1] (0.00609561s)][[*1] (0.0057508s)]] +[[gmp_int][222.866 (0.703144s)][164.331 (0.705059s)][115.363 (0.70321s)][122.347 (0.703596s)]] +[[tommath_int][218.681 (0.689941s)][163.796 (0.702765s)][114.57 (0.698376s)][122.422 (0.704027s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.16358 (2.74442s)][1.39847 (8.11559s)][1.64677 (22.2518s)][1.95096 (64.4961s)]] +[[cpp_int(fixed)][[*1] (2.35859s)][1.30986 (7.60133s)][1.67681 (22.6577s)][2.0895 (69.0758s)]] +[[gmp_int][1.03392 (2.4386s)][[*1] (5.80319s)][[*1] (13.5124s)][[*1] (33.0586s)]] +[[tommath_int][5.25978 (12.4057s)][4.4619 (25.8932s)][4.15577 (56.1542s)][3.91192 (129.323s)]] +] +[table Operator powm +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.50722 (2.91621s)][3.5561 (13.406s)][4.37066 (73.483s)][4.88831 (473.91s)]] +[[cpp_int(fixed)][1.93385 (2.24931s)][3.18107 (11.9922s)][4.20753 (70.7403s)][4.8158 (466.88s)]] +[[gmp_int][[*1] (1.16313s)][[*1] (3.76986s)][[*1] (16.8128s)][[*1] (96.9476s)]] +[[tommath_int][1.44081 (1.67584s)][1.8794 (7.08507s)][2.19115 (36.8394s)][2.17186 (210.557s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.17175 (0.00160006s)][1.41999 (0.00329476s)][1.40856 (0.00813784s)][1.52964 (0.0229767s)]] +[[cpp_int(fixed)][[*1] (0.00136554s)][[*1] (0.00232027s)][[*1] (0.00577741s)][1.14754 (0.0172372s)]] +[[gmp_int][1.50501 (0.00205515s)][1.52968 (0.00354926s)][1.01989 (0.0058923s)][[*1] (0.015021s)]] +[[tommath_int][12.2161 (0.0166816s)][16.9577 (0.0393463s)][18.7474 (0.108311s)][22.7368 (0.341528s)]] +] +[table Operator | +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0301617s)][[*1] (0.0423404s)][[*1] (0.0522358s)][[*1] (0.0813156s)]] +[[cpp_int(fixed)][1.0638 (0.0320861s)][1.22566 (0.0518951s)][1.28515 (0.0671305s)][1.16118 (0.094422s)]] +[[gmp_int][1.76553 (0.0532514s)][1.51489 (0.0641408s)][1.70708 (0.0891706s)][1.77346 (0.14421s)]] +[[tommath_int][4.37637 (0.131999s)][3.46212 (0.146587s)][2.91875 (0.152463s)][4.19621 (0.341217s)]] +] +[table Operator |(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0289129s)][[*1] (0.0351119s)][[*1] (0.0406779s)][[*1] (0.0525891s)]] +[[cpp_int(fixed)][1.06091 (0.030674s)][1.25979 (0.0442336s)][1.36194 (0.0554009s)][1.37438 (0.0722772s)]] +[[gmp_int][4.92854 (0.142498s)][4.34687 (0.152627s)][3.71442 (0.151095s)][2.981 (0.156768s)]] +[[tommath_int][10.9847 (0.317598s)][9.37065 (0.329021s)][8.53651 (0.347248s)][11.2155 (0.589813s)]] +] +[table Operator ^ +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0305149s)][[*1] (0.04217s)][[*1] (0.0525977s)][[*1] (0.0816632s)]] +[[cpp_int(fixed)][1.01544 (0.0309861s)][1.24872 (0.0526585s)][1.26661 (0.066621s)][1.15965 (0.0947007s)]] +[[gmp_int][1.64675 (0.0502505s)][1.47181 (0.0620663s)][1.66038 (0.0873322s)][1.67895 (0.137108s)]] +[[tommath_int][4.30668 (0.131418s)][3.45859 (0.145849s)][2.91462 (0.153303s)][4.15538 (0.339342s)]] +] +[table Operator ^(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.01566 (0.0296088s)][[*1] (0.0356634s)][[*1] (0.0401898s)][[*1] (0.0514097s)]] +[[cpp_int(fixed)][[*1] (0.0291524s)][1.2393 (0.0441976s)][1.38556 (0.0556856s)][1.38899 (0.0714075s)]] +[[gmp_int][4.68027 (0.136441s)][4.15243 (0.14809s)][3.74237 (0.150405s)][3.0483 (0.156712s)]] +[[tommath_int][10.919 (0.318314s)][9.16311 (0.326788s)][8.62554 (0.346659s)][11.6212 (0.597442s)]] +] +[table Operator & +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.0346 (0.0303431s)][[*1] (0.0427309s)][[*1] (0.0535587s)][1.06945 (0.0828084s)]] +[[cpp_int(fixed)][[*1] (0.0293284s)][1.10435 (0.04719s)][1.05262 (0.0563769s)][[*1] (0.0774309s)]] +[[gmp_int][1.86057 (0.0545675s)][1.58432 (0.0676995s)][1.69164 (0.0906018s)][1.86625 (0.144505s)]] +[[tommath_int][4.4157 (0.129506s)][3.60396 (0.154s)][2.95985 (0.158525s)][4.4032 (0.340944s)]] +] +[table Operator &(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.05874 (0.038946s)][[*1] (0.0483903s)][[*1] (0.063842s)][[*1] (0.100361s)]] +[[cpp_int(fixed)][[*1] (0.0367853s)][1.05827 (0.0512099s)][1.09114 (0.0696605s)][1.09432 (0.109826s)]] +[[gmp_int][3.92298 (0.144308s)][2.99447 (0.144903s)][2.228 (0.14224s)][1.42296 (0.142809s)]] +[[tommath_int][8.79208 (0.323419s)][7.02288 (0.339839s)][5.65271 (0.36088s)][6.27104 (0.629365s)]] +] +[table Operator << +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0248801s)][1.23196 (0.04s)][[*1] (0.0424149s)][[*1] (0.060157s)]] +[[cpp_int(fixed)][1.08931 (0.027102s)][1.40572 (0.0456418s)][1.3475 (0.0571542s)][1.24573 (0.0749397s)]] +[[gmp_int][1.05561 (0.0262636s)][[*1] (0.0324686s)][1.09914 (0.0466199s)][1.16315 (0.0699719s)]] +[[tommath_int][1.60497 (0.0399319s)][2.13048 (0.0691737s)][2.31219 (0.0980712s)][2.74695 (0.165248s)]] +] +[table Operator >> +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0213349s)][1.02127 (0.0295019s)][[*1] (0.0327116s)][1.13168 (0.0433804s)]] +[[cpp_int(fixed)][1.13514 (0.0242181s)][1.16938 (0.0337803s)][1.46999 (0.0480859s)][1.60077 (0.061362s)]] +[[gmp_int][1.26614 (0.0270129s)][[*1] (0.0288873s)][1.42219 (0.0465221s)][[*1] (0.0383329s)]] +[[tommath_int][12.0066 (0.25616s)][10.2837 (0.297067s)][9.99696 (0.327017s)][16.0943 (0.616942s)]] +] + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +Linux x86_64 results are broadly similar, except that libtommath performs much better there. + +[endsect] + +[section:rational_performance Rational Type Performance] + +Note that these tests are carefully designed to test performance of the underlying algorithms +and not memory allocation or variable copying. As usual, performance results should be taken +with a healthy dose of scepticism, and real-world performance may vary widely depending upon the +specifics of the program. In each table relative times are given first, with the best performer +given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 +operations. + +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.89417 (18.4116s)][6.87256 (47.4698s)][6.65008 (107.715s)][6.53801 (256.244s)]] +[[mpq_rational][[*1] (3.1237s)][[*1] (6.90715s)][[*1] (16.1975s)][[*1] (39.1929s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.62367 (2.46488s)][4.18291 (2.94603s)][4.726 (3.74866s)][6.1388 (5.56817s)]] +[[mpq_rational][[*1] (0.680215s)][[*1] (0.704303s)][[*1] (0.7932s)][[*1] (0.907046s)]] +] +[table Operator +(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.1527 (2.6378s)][1.31751 (3.09863s)][1.58996 (4.00714s)][2.15642 (5.75702s)]] +[[mpq_rational][[*1] (2.28837s)][[*1] (2.35189s)][[*1] (2.52028s)][[*1] (2.66971s)]] +] +[table Operator +=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.18436 (2.7059s)][1.32279 (3.11099s)][1.61398 (4.05389s)][2.20048 (5.84623s)]] +[[mpq_rational][[*1] (2.2847s)][[*1] (2.35183s)][[*1] (2.51174s)][[*1] (2.6568s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.81893 (18.3457s)][6.82209 (47.1928s)][6.64143 (107.498s)][6.51362 (255.137s)]] +[[mpq_rational][[*1] (3.15277s)][[*1] (6.91765s)][[*1] (16.1859s)][[*1] (39.1698s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.72441 (2.48756s)][4.27663 (2.98713s)][4.62109 (3.72114s)][6.17605 (5.56503s)]] +[[mpq_rational][[*1] (0.667908s)][[*1] (0.698479s)][[*1] (0.805252s)][[*1] (0.901066s)]] +] +[table Operator -(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.15627 (2.63239s)][1.32096 (3.12092s)][1.61044 (4.00106s)][2.19378 (5.7644s)]] +[[mpq_rational][[*1] (2.27663s)][[*1] (2.36262s)][[*1] (2.48445s)][[*1] (2.62761s)]] +] +[table Operator -=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.1984 (2.73444s)][1.34141 (3.15698s)][1.64159 (4.06997s)][2.23017 (5.88108s)]] +[[mpq_rational][[*1] (2.28174s)][[*1] (2.35348s)][[*1] (2.47929s)][[*1] (2.63706s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.4306 (32.5882s)][6.91805 (89.9436s)][6.94556 (207.307s)][6.88704 (492.151s)]] +[[mpq_rational][[*1] (6.00084s)][[*1] (13.0013s)][[*1] (29.8475s)][[*1] (71.4604s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.12892 (2.51376s)][2.47245 (3.07841s)][2.86832 (3.93619s)][3.94086 (6.02565s)]] +[[mpq_rational][[*1] (1.18077s)][[*1] (1.24508s)][[*1] (1.3723s)][[*1] (1.52902s)]] +] +[table Operator *(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.32254 (5.43565s)][1.56078 (6.73163s)][1.97701 (9.32522s)][2.85404 (15.1573s)]] +[[mpq_rational][[*1] (4.11002s)][[*1] (4.313s)][[*1] (4.71682s)][[*1] (5.31082s)]] +] +[table Operator *=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][6.29806 (58.1188s)][6.30556 (59.5076s)][6.3385 (62.1007s)][6.55345 (67.6905s)]] +[[mpq_rational][[*1] (9.22804s)][[*1] (9.43733s)][[*1] (9.79739s)][[*1] (10.329s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][4.4269 (66.8031s)][6.40103 (173.527s)][6.32347 (348.193s)][6.61148 (824.063s)]] +[[mpq_rational][[*1] (15.0903s)][[*1] (27.1093s)][[*1] (55.0637s)][[*1] (124.641s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.78772 (2.50984s)][2.10623 (3.10606s)][2.46986 (3.99358s)][3.37428 (5.96678s)]] +[[mpq_rational][[*1] (1.40393s)][[*1] (1.4747s)][[*1] (1.61693s)][[*1] (1.76831s)]] +] +[table Operator /(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.29695 (5.45454s)][1.55248 (6.85353s)][1.93237 (9.28765s)][2.75211 (14.8541s)]] +[[mpq_rational][[*1] (4.20568s)][[*1] (4.41458s)][[*1] (4.80635s)][[*1] (5.39734s)]] +] +[table Operator /=(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][6.19401 (58.4278s)][6.20135 (59.643s)][6.21327 (62.0338s)][6.40576 (67.6778s)]] +[[mpq_rational][[*1] (9.43295s)][[*1] (9.61774s)][[*1] (9.98407s)][[*1] (10.5652s)]] +] +[table Operator construct +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.00978288s)][[*1] (0.0100574s)][[*1] (0.0101393s)][[*1] (0.0101847s)]] +[[mpq_rational][39.1516 (0.383015s)][38.3523 (0.385725s)][37.5812 (0.381048s)][37.6007 (0.382953s)]] +] +[table Operator construct(unsigned) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.0548151s)][[*1] (0.0557542s)][[*1] (0.055825s)][[*1] (0.0552808s)]] +[[mpq_rational][7.21073 (0.395257s)][7.1016 (0.395944s)][7.02046 (0.391917s)][7.16881 (0.396297s)]] +] +[table Operator construct(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.0605156s)][[*1] (0.0616657s)][[*1] (0.0592056s)][[*1] (0.0603081s)]] +[[mpq_rational][35.1604 (2.12775s)][34.7575 (2.14335s)][35.7232 (2.11502s)][35.0437 (2.11342s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.48898 (0.0208949s)][8.49668 (0.0546688s)][10.107 (0.121897s)][10.5339 (0.310584s)]] +[[mpq_rational][[*1] (0.0038067s)][[*1] (0.00643413s)][[*1] (0.0120606s)][[*1] (0.0294843s)]] +] + +Test code was compiled with Microsoft Visual Studio 2010 with all optimisations +turned on (/Ox), and used MPIR-2.3.0 and [mpfr]-3.0.0. The tests were run on 32-bit +Windows Vista machine. + +[endsect] + +[endsect] + +[section:map Roadmap] + +[section:hist History] + +[h4 Multiprecision-2.2.3 (Boost-1.57)] + +* Changed rational to float conversions to exactly round to nearest, see [https://svn.boost.org/trac/boost/ticket/10085 10085]. +* Added improved generic float to rational conversions. +* Fixed rare bug in exponent function for __cpp_bin_float. +* Fixed various minor documentation issues. + +[h4 Multiprecision-2.2.2 (Boost-1.56)] + +* Change floating point to rational conversions to be implicit, see [@https://svn.boost.org/trac/boost/ticket/10082 10082]. +* Fix definition of checked_cpp_rational typedef. + +[h4 Multiprecision-2.2.1] + +* Fix bug in assignment from string in cpp_int, see [@https://svn.boost.org/trac/boost/ticket/9936 9936]. + +[h4 Multiprecision-2.2.0] + +* Moved to Boost.Multiprecision specific version number - we have one breaking change in Boost-1.54 +which makes this major version 2, plus two releases with new features since then. +* Added new __cpp_bin_float backend for binary floating point. +* Added MSVC-specific #include for compiler intrinsics, see [@https://svn.boost.org/trac/boost/ticket/9336 9336]. +* Fixed various typos in docs, see [@https://svn.boost.org/trac/boost/ticket/9432 9432]. +* Fixed __gmp_rational to allow move-copy from an already copied-from object, see [@https://svn.boost.org/trac/boost/ticket/9497 9497]. +* Added list of values for numeric_limits. + +[h4 Boost-1.55] + +* Added support for Boost.Serialization. +* Suppressed some GCC warnings. See [@https://svn.boost.org/trac/boost/ticket/8872 8872]. +* Fixed bug in pow for large integer arguments. See [@https://svn.boost.org/trac/boost/ticket/8809 8809]. +* Fixed bug in pow for calculation of 0[super N]. See [@https://svn.boost.org/trac/boost/ticket/8798 8798]. +* Fixed bug in fixed precision cpp_int IO code that causes conversion to string to fail when the +bit count is very small (less than CHAR_BIT). See [@https://svn.boost.org/trac/boost/ticket/8745 8745]. +* Fixed bug in cpp_int that causes left shift to fail when a fixed precision type would overflow. +See [@https://svn.boost.org/trac/boost/ticket/8741 8741]. +* Fixed some cosmetic warnings from cpp_int. See [@https://svn.boost.org/trac/boost/ticket/8748 8748]. +* Fixed calls to functions which are required to be macros in C99. See [@https://svn.boost.org/trac/boost/ticket/8732 8732]. +* Fixed bug that causes construction from INT_MIN, LONG_MIN etc to fail in cpp_int. See [@https://svn.boost.org/trac/boost/ticket/8711 8711]. + +[h4 1.54] + +* [*Breaking change] renamed `rational_adapter` to `rational_adaptor`. +* Add support for [mpfi]. +* Add logged_adaptor. +* Add support for 128-bit floats via GCC's `__float128` or Intel's `_Quad` data types. +* Add support for user-defined literals in cpp_int, improve `constexpr` support. +* Fixed bug in integer division of `cpp_int` that results in incorrect sign of `cpp_int` when both arguments are small enough +to fit in a `double_limb_type`. See [@https://svn.boost.org/trac/boost/ticket/8126 8126]. +* Fixed bug in subtraction of a single limb in `cpp_int` that results in incorrect value when the result should have a 0 +in the last limb: [@https://svn.boost.org/trac/boost/ticket/8133 8133]. +* Fixed bug in `cpp_int` where division of 0 by something doesn't get zero in the result: [@https://svn.boost.org/trac/boost/ticket/8160 8160]. +* Fixed bug in some transcendental functions that caused incorrect return values when variables are reused, for example with +`a = pow(a, b)`. See [@https://svn.boost.org/trac/boost/ticket/8326 8326]. +* Fixed some assignment operations in the mpfr and gmp backends to be safe if the target has been moved from: [@https://svn.boost.org/trac/boost/ticket/8326 8667]. +* Fixed bug in `cpp_int` that gives incorrect answer for 0%N for large N: [@https://svn.boost.org/trac/boost/ticket/8670 8670]. +* Fixed set_precision in mpfr backend so it doesn't trample over an existing value: [@https://svn.boost.org/trac/boost/ticket/8692 8692]. + +[h4 1.53] + +* First Release. +* Fix bug in [@https://svn.boost.org/trac/boost/ticket/7878 cpp_int division]. +* Fix issue [@https://svn.boost.org/trac/boost/ticket/7806 #7806]. + +[h4 Post review changes] + +* Non-expression template operators further optimised with rvalue reference support. +* Many functions made `constexp`. +* Differentiate between explicit and implicit conversions in the number constructor. +* Removed "mp_" prefix from types. +* Allowed mixed precision arithmetic. +* Changed ExpressionTemplates parameter to class `number` to use enumerated values rather than true/false. +* Changed ExpressionTemplate parameter default value to use a traits class so that the default value depends on the backend used. +* Added support for fused-multiply-add/subtract with GMP support. +* Tweaked expression template unpacking to use fewer temporaries when the LHS also appears in the RHS. +* Refactored `cpp_int_backend` based on review comments with new template parameter structure. +* Added additional template parameter to `mpfr_float_backend` to allow stack-based allocation. +* Added section on mixed precision arithmetic, and added support for operations yielding a higher precision result +than either of the arguments. +* Added overloads of integer-specific functions for built in integer types. + +[h4 Pre-review history] + +*2011-2012, John Maddock adds an expression template enabled front end to Christopher's code, +and adds support for other backends. +* 2011, Christopher Kormanyos publishes the decimal floating point code under the Boost +Software Licence. The code is published as: [@http://doi.acm.org/10.1145/1916461.1916469 +"Algorithm 910: A Portable C++ Multiple-Precision +System for Special-Function Calculations"], in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, +2011. +* 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic floating point +code. + +[endsect] + +[section:todo TODO] + + + +More a list of what ['could] be done, rather than what ['should] be done (which may be a much smaller list!). + +* Add back-end support for libdecNumber. +* Add an adaptor back-end for complex number types. +* Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. +* Add assembly level routines to cpp_int_backend. +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it, +the hard part is IO and binary-decimal conversion. +* Should there be a choice of rounding mode (probably MPFR specific)? +* We can reuse temporaries in multiple subtrees (temporary caching). +* cpp_dec_float should round to nearest. +* A 2's complement fixed precision int that uses exactly N bits and no more. + +Things requested in review: + +* The performances of mp_number<a_trivial_adaptor<float>, false>respect to +float and mp_number<a_trivial_adaptor<int>, false> and int should be +given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). +* Should we provide min/max overloads for expression templates? (Not done - we can't overload functions declared in the std namespace :-( ). +* The rounding applied when converting must be documented (Done). +* Document why we don't abstract out addition/multiplication algorithms etc. (done - FAQ) +* Document why we don't use proto (compile times) (Done). +* We can reuse temporaries in multiple subtrees (temporary caching) Moved to TODO list. +* Emphasise in the docs that ET's may reorder operations (done 2012/10/31). +* Document what happens to small fixed precision cpp_int's (done 2012/10/31). +* The use of bool in template parameters could be improved by the use of +an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled}; +enum class sign {unsigned, signed};` (Partly done 2012/09/15, done 2012/10/31). +* Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's +deliberately an implementation detail, and "optional" requirements are optimisations which can't be detected +by the user). Not done: this is an implementation detail, the exact list of requirements satisfied is purely +an optimization, not something the user can detect. +* A backend for an overflow aware integers (done 2012/10/31). +* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit +conversions. Could the explicit conversion operator be added on +compilers supporting it? (Done 2012/09/15). +* The front-end should make the differences between implicit and explicit +construction (Done 2012/09/15). +* The tutorial should add more examples concerning implicit or explicit +conversions. (Done 2012/09/15). +* The documentation must explain how move semantics helps in this domain +and what the backend needs to do to profit from this optimization. (Done 2012/09/15). +* The documentation should contain Throws specification on the mp_number +and backend requirements operations. (Done 2012/09/15). +* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) +facilities (Done 2012/09/15). +* It is unfortunate that the generic mp_number front end can not make use +constexpr as not all the backends can ensure this (done - we can go quite a way). +* literals: The library doesn't provide some kind of literals. I think that the +mp_number class should provide a way to create literals if the backend +is able to. (Done 2012/09/15). +* The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults (done 2012/09/20). +* In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary (done 2012/09/20). + + + +[h4 Pre-Review Comments] + +* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits +template argument that defaults to 0 (meaning keep going till no more space/memory). Done. +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it (Moved to TODO list). +* Should there be a choice of rounding mode (probably MPFR specific)? Moved to TODO list. +* Make the exponent type for cpp_dec_float a template parameter, maybe include support for big-integer exponents. +Open question - what should be the default - int32_t or int64_t? (done 2012/09/06) +* Document the size requirements of fixed precision ints (done 2012/09/15). +* Document std lib function accuracy (done 2012/09/15). +* Be a bit clearer on the effects of sign-magnitude representation of cpp_int - min == -max etc - done. +* Document cpp_dec_float precision, rounding, and exponent size (done 2012/09/06). +* Can we be clearer in the docs that mixed arithmetic doesn't work (no longer applicable as of 2012/09/06)? +* Document round functions behaviour better (they behave as in C++11) (added note 2012/09/06). +* Document limits on size of cpp_dec_float (done 2012/09/06). +* Add support for fused multiply add (and subtract). GMP mpz_t could use this (done 2012/09/20). + +[endsect] + +[section:faq FAQ] + +[variablelist +[[Why do I get compiler errors when passing a `number` to a template function?] + [Most likely you are actually passing an expression template type to the function and + template-argument-deduction deduces the "wrong" type. Try casting the arguments + involving expressions to the actual number type, or as a last resort turning off + expression template support in the number type you are using.]] +[[When is expression template support a performance gain?] + [As a general rule, expression template support adds a small runtime overhead + creating and unpacking the expression templates, but greatly reduces the number of + temporaries created. So it's most effective in improving performance when the cost + of creating a temporary is high: for example when creating a temporary involves a memory + allocation. It is least effective (and may even be a dis-optimisation) when temporaries + are cheap: for example if the number type is basically a thin wrapper around a native + arithmetic type. In addition, since the library makes extensive use of thin inline wrapper + functions, turning on compiler optimization is essential to achieving high performance.]] +[[Do expression templates reorder operations?] + [Yes they do, sometimes quite radically so, if this is a concern then they should be turned + off for the number type you are using.]] +[[I can't construct my number type from ['some other type], but the docs indicate that the conversion should be allowed, what's up?] + [Some conversions are ['explicit], that includes construction from a string, or constructing from any type + that may result in loss of precision (for example constructing an integer type from a float).]] +[[Why do I get an exception thrown (or the program crash due to an uncaught exception) when using the bitwise operators on a checked `cpp_int`?] + [Bitwise operations on negative values (or indeed any signed integer type) are unspecified by the standard. As a result + any attempt to carry out a bitwise operation on a negative checked-integer will result in a `std::range_error` being thrown.]] +[[Why do I get compiler errors when trying to use the complement operator?] + [Use of the complement operator on signed types is problematic as the result is unspecified by the standard, and is further + complicated by the fact that most extended precision integer types use a sign-magnitude representation rather than the 2's + complement one favored by most native integer types. As a result the complement operator is deliberately disabled for + checked `cpp_int`'s. Unchecked `cpp_int`'s give the same valued result as a 2's complement type would, but not the same bit-pattern.]] +[[Why can't I negate an unsigned type?] + [The unary negation operator is deliberately disabled for unsigned integer types as its use would almost always be a programming error.]] +[[Why doesn't the library use proto?] + [A very early version of the library did use proto, but compile times became too slow + for the library to be usable. Since the library only required a tiny fraction of what + proto has to offer anyway, a lightweight expression template mechanism was used instead. + Compile times are still too slow...]] +[[Why not abstract out addition/multiplication algorithms?] + [This was deemed not to be practical: these algorithms are intimately + tied to the actual data representation used.]] +] + +[endsect] + +[section:ack Acknowledgements] + +This library would not have happened without: + +* Christopher Kormanyos' C++ decimal number code. +* Paul Bristow for patiently testing, and commenting on the library. +* All the folks at GMP, MPFR and libtommath, for providing the "guts" that makes this library work. +* [@http://www-cs-faculty.stanford.edu/~uno/taocp.html "The Art Of Computer Programming"], +Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition +(Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. ISBN 0-201-89684-2 + +[endsect] + +[endsect] + +[section:indexes Indexes] + +''' +<index type="function_name"> +<title>Function Index</title> +</index> + +<index type="class_name"> +<title>Class Index</title> +</index> + +<index type="typedef_name"> +<title>Typedef Index</title> +</index> + +<index/> +''' + +[endsect] + + + + diff --git a/libs/multiprecision/doc/numeric_limits_32_tables.qbk b/libs/multiprecision/doc/numeric_limits_32_tables.qbk new file mode 100644 index 0000000000..06d0549078 --- /dev/null +++ b/libs/multiprecision/doc/numeric_limits_32_tables.qbk @@ -0,0 +1,94 @@ +[/ +Copyright 2013 Paul A. Bristow. +Copyright 2013 John Maddock. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). +] + +[section:limits32 Numeric limits for 32-bit platform] +These tables were generated using the following program and options: + +[pre + +Program: + numeric_limits_qbk.cpp +Mon Nov 4 18:09:06 2013 +BuildInfo: + Platform Win32 + Compiler Microsoft Visual C++ version 10.0 + MSVC version 160040219. + STL Dinkumware standard library version 520 + Boost version 1.55.0 +] + +[table:integral_constants Integer types constants (`std::numeric_limits<T>::is_integer == true` && is_exact == true) +[[type][signed][bound][modulo][round][radix][digits][digits10]] +[[bool][unsigned][bound][no][to zero][2][1][0]] +[[char][signed][bound][modulo][to zero][2][7][2]] +[[unsigned char][unsigned][bound][modulo][to zero][2][8][2]] +[[char16_t][unsigned][bound][modulo][to zero][2][16][4]] +[[char32_t][unsigned][bound][modulo][to zero][2][32][9]] +[[short][signed][bound][modulo][to zero][2][15][4]] +[[unsigned short][unsigned][bound][modulo][to zero][2][16][4]] +[[int][signed][bound][modulo][to zero][2][31][9]] +[[unsigned][unsigned][bound][modulo][to zero][2][32][9]] +[[long][signed][bound][modulo][to zero][2][31][9]] +[[unsigned long][unsigned][bound][modulo][to zero][2][32][9]] +[[long long][signed][bound][modulo][to zero][2][63][18]] +[[unsigned long long][unsigned][bound][modulo][to zero][2][64][19]] +[[int32_t][signed][bound][modulo][to zero][2][31][9]] +[[uint32_t][unsigned][bound][modulo][to zero][2][32][9]] +[[int64_t][signed][bound][modulo][to zero][2][63][18]] +[[uint64_t][unsigned][bound][modulo][to zero][2][64][19]] +[[int128_t][signed][bound][modulo][to zero][2][128][38]] +[[uint128_t][unsigned][bound][modulo][to zero][2][128][38]] +[[int256_t][signed][bound][modulo][to zero][2][256][77]] +[[uint256_t][unsigned][bound][modulo][to zero][2][256][77]] +[[cpp_int][signed][unbounded][no][to zero][2][2147483647][646392383]] +] + +[table:integral_functions Integer types functions (`std::numeric_limits<T>::is_integer == true && std::numeric_limits<T>::min() == std::numeric_limits<T>::lowest()` ) +[[function][max][min]] +[[bool][1][0]] +[[char][127][-128]] +[[unsigned char][255][0]] +[[char16_t][65535][0]] +[[char32_t][4294967295][0]] +[[short][32767][-32768]] +[[unsigned short][65535][0]] +[[int][2147483647][-2147483648]] +[[unsigned int][4294967295][0]] +[[long][2147483647][-2147483648]] +[[unsigned long][4294967295][0]] +[[long long][9223372036854775807][-9223372036854775808]] +[[unsigned long long][18446744073709551615][0]] +[[int32_t][2147483647][-2147483648]] +[[int64_t][9223372036854775807][-9223372036854775808]] +[[int128_t][340282366920938463463374607431768211455][-340282366920938463463374607431768211455]]] +[table:float_functions Floating-point types constants (`std::numeric_limits<T>::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true`) +[[type][round][radix][digits][digits10][max_digits10][min_exp][min_exp10][max_exp][max_exp10][tiny][trap]] +[[float][to nearest][2][24][6][8][-125][-37][128][38][tiny][traps]] + +[[double][to nearest][2][53][15][17][-1021][-307][1024][308][tiny][traps]] + +[[long double][to nearest][2][53][15][17][-1021][-307][1024][308][tiny][traps]] + +[[cpp_dec_float_50][indeterminate][10][50][50][80][-222953000][-67108864][222953000][67108864][no][no]] + +[[bin_128bit_double_type][to nearest][2][377][113][115][-2147482894][-646392082][2147482893][646392082][no][traps]] +] +[table:float_functions Floating-point types functions (`std::numeric_limits<T>::is_integer == false`) +[[function][float][double][long double][cpp_dec_50][cpp_bin_128]][[max][3.40282e+038][1.79769e+308][1.79769e+308][1e+67108865][1.85906e+646456766]] +[[min][1.17549e-038][2.22507e-308][2.22507e-308][1e-67108864][5.37906e-646456767]] +[[epsilon][1.19209e-007][2.22045e-016][2.22045e-016][1e-49][6.49713e-114]] +[[round_error][0.5][0.5][0.5][0.5][0.5]] +[[infinity][1.#INF][1.#INF][1.#INF][inf][inf]] +[[quiet_NaN][1.#QNAN][1.#QNAN][1.#QNAN][nan][nan]] +[[signaling_NaN][1.#QNAN][1.#QNAN][1.#QNAN][0][0]] +[[denorm_min][1.4013e-045][4.94066e-324][4.94066e-324][0][0]] +] + + +[endsect] [/section:limits32 Numeric limits for 32-bit platform] + diff --git a/libs/multiprecision/doc/numeric_limits_qbk.cpp b/libs/multiprecision/doc/numeric_limits_qbk.cpp new file mode 100644 index 0000000000..5f4f6b194f --- /dev/null +++ b/libs/multiprecision/doc/numeric_limits_qbk.cpp @@ -0,0 +1,719 @@ +// Copyright Paul A. Bristow 2013 + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +// Program to list all numeric_limits items for any type to a file in Quickbook format. + +// C standard http://www.open-std.org/jtc1/sc22/wg11/docs/n507.pdf +// SC22/WG11 N507 DRAFT INTERNATIONAL ISO/IEC STANDARD WD 10967-1 +// Information technology Language independent arithmetic Part 1: Integer and Floating point arithmetic + +/* E.3 C++ +The programming language C++ is defined by ISO/IEC 14882:1998, Programming languages C++ [18]. +An implementation should follow all the requirements of LIA-1 unless otherwise specified by +this language binding. +*/ + +// http://754r.ucbtest.org/standards/754.pdf + +// http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf + +// http://www.exploringbinary.com/using-integers-to-check-a-floating-point-approximation/ + +// http://stackoverflow.com/questions/12466745/how-to-convert-float-to-doubleboth-stored-in-ieee-754-representation-without-loss + + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant. +# pragma warning (disable : 4100) // unreferenced formal parameter. +#endif + + +#include <iostream> +#include <iomanip> +#include <string> +#include <sstream> +#include <fstream> +#include <limits> // numeric_limits + +#include <typeinfo> + +#include <boost/version.hpp> +#include <boost/config.hpp> + +// May need extra includes for other types, for example: +#include <boost/multiprecision/cpp_dec_float.hpp> // is decimal. +#include <boost/multiprecision/cpp_bin_float.hpp> // is binary. + + +// Assume that this will be run on MSVC to get the 32 or 64 bit info. +#ifdef _WIN32 + std::string bits32_64 = "32"; +std::string filename = "numeric_limits_32_tables.qbk"; +#else + std::string bits32_64 = "64"; +std::string filename = "numeric_limits_64_tables.qbk"; +#endif + +#ifdef INT32_T_MAX + int i = INT256_T_MAX; +#endif + +std::array<std::string, 16> integer_type_names = +{ +"bool", +"char", +"unsigned char", +"char16_t", +"char32_t", +"short", +"unsigned short", +"int", +"unsigned int", +"long", +"unsigned long", +"long long", +"unsigned long long", +"int32_t", +//"uint32_t", +"int64_t", +//"uint64_t", +"int128_t", +//"uint128_t" // Too big? +//"int256_t", +//"uint256_t" +//"int512_t" +}; + +std::array<std::string, 6> float_type_names = +{ + "function", "float", "double", "long double", "cpp_dec_50", "cpp_bin_128" +}; + +// Table headings for integer constants. +std::array<std::string, 8> integer_constant_heads = +{ + "type", "signed", "bound", "modulo", "round", "radix", "digits", "digits10", // "max_digits10" +}; + +// Table headings for integer functions. +std::array<std::string, 2> integer_function_heads = +{ + "max", // "lowest", assumes is same for all integer types, so not worth listing. + "min" +}; + +// Table headings for float constants. +std::array<std::string, 12> float_constant_heads = +{ + "type", // "signed", "exact", "bound", // "modulo", + "round", "radix", "digits", "digits10", "max_digits10", "min_exp", "min_exp10", "max_exp", "max_exp10", "tiny", "trap" +}; + +// Table headings for float functions. +std::array<std::string, 10> float_function_heads = +{ + "function", "max", "lowest", "min", "eps", "round", "infinity", "NaN", "sig_NaN", "denorm_min" +}; + +std::string versions() +{ // Build a string of info about Boost, platform, STL, etc. + std::stringstream mess; + //mess << "\n" << "Program:\n\" " __FILE__ << "\"\n"; // \n is mis-interpreted! + mess << "\n" << "Program:\n numeric_limits_qbk.cpp \n"; +#ifdef __TIMESTAMP__ + mess << __TIMESTAMP__; +#endif + mess << "\nBuildInfo:\n" " Platform " << BOOST_PLATFORM; + mess << "\n Compiler " BOOST_COMPILER; +#ifdef _MSC_FULL_VER + mess << "\n MSVC version "<< BOOST_STRINGIZE(_MSC_FULL_VER) << "."; +#endif + mess << "\n STL " BOOST_STDLIB; + mess << "\n Boost version " << BOOST_VERSION/100000 << "." << BOOST_VERSION/100 % 1000 << "." << BOOST_VERSION % 100 << std::endl; + return mess.str(); +} // std::string versions() + +template <typename T> +void out_round_style(std::ostream& os) +{ //! Send short string describing STD::round_style to stream os. + // os << "Round style is "; + if (std::numeric_limits<T>::round_style == std::round_indeterminate) + { + os << "indeterminate" ; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_zero) + { + os << "to zero" ; + } + else if (std::numeric_limits<T>::round_style == std::round_to_nearest) + { + os << "to nearest" ; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_infinity) + { + os << "to infin[]"; // Or << "to \u221E" << "to infinity" ; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_neg_infinity) + { + os << "to -infin[]" ; + } + else + { + os << "undefined!"; + std::cout << "std::numeric_limits<T>::round_style is undefined value!" << std::endl; + } + return; +} // out_round_style(std::ostream& os); + +template<typename T> +void integer_constants(std::string type_name, std::ostream& os) +{ //! Output a line of table integer constant values to ostream os. + os << "\n[" + "[" << type_name << "]" ; + os << "[" << (std::numeric_limits<T>::is_signed ? "signed" : "unsigned") << "]" ; + // Is always exact for integer types, so removed: + // os << "[" << (std::numeric_limits<T>::is_exact ? "exact" : "inexact") << "]" ; + os << "[" << (std::numeric_limits<T>::is_bounded ? "bound" : "unbounded") << "]" ; + os << "[" << (std::numeric_limits<T>::is_modulo ? "modulo" : "no") << "]" ; + os << "[" ; out_round_style<T>(os); os << "]" ; + os << "[" << std::numeric_limits<T>::radix << "]" ; + os << "[" << std::numeric_limits<T>::digits << "]" ; + os << "[" << std::numeric_limits<T>::digits10 << "]" ; + // Undefined for integers, so removed: + // os << "[" << std::numeric_limits<T>::max_digits10 << "]" + os << "]"; +} // void integer_constants + + +template<typename T> +void float_constants(std::string type_name, std::ostream& os) +{ //! Output a row of table values to `ostream` os. + os << "\n[" + "[" << type_name << "]" ; + //os << "[" << (std::numeric_limits<T>::is_signed ? "signed" : "unsigned") << "]" ; + //os << "[" << (std::numeric_limits<T>::is_exact ? "exact" : "inexact") << "]" ; + //os << "[" << (std::numeric_limits<T>::is_bounded ? "bound" : "no") << "]" ; + // os << "[" << (std::numeric_limits<T>::is_modulo ? "modulo" : "no") << "]" ; + os << "[" ; out_round_style<T>(os); os << "]" ; + os << "[" << std::numeric_limits<T>::radix << "]" ; + os << "[" << std::numeric_limits<T>::digits << "]" ; + os << "[" << std::numeric_limits<T>::digits10 << "]" ; + os << "[" << std::numeric_limits<T>::max_digits10 << "]"; + os << "[" << std::numeric_limits<T>::min_exponent << "]" ; + os << "[" << std::numeric_limits<T>::min_exponent10 << "]" ; + os << "[" << std::numeric_limits<T>::max_exponent << "]" ; + os << "[" << std::numeric_limits<T>::max_exponent10 << "]" ; + os << "[" << (std::numeric_limits<T>::tinyness_before ? "tiny" : "no") << "]" ; + os << "[" << (std::numeric_limits<T>::traps ? "traps" : "no") << "]" ; + os << "]" "\n"; // end of row. +} // void float_constants + +/* Types across and two functions down. + +template<typename T> +void integer_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table integer function values to `ostream` os. + os << "\n[" + "[" << type_name << "]" ; + os << "[" << std::numeric_limits<T>::max() << "]" ; + //os << "[" << std::numeric_limits<T>::lowest() << "]" ; always == min for integer types, + // so removed to save space. + os << "[" << std::numeric_limits<T>::min() << "]" + "]"; +} // void integer_functions + +*/ + +// Types down and two (or three) functions across. +template<typename T> +void integer_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table integer function values to `ostream` os. + os << "\n[" // start of row. + "[" << type_name << "]" ; + os << "[" << std::numeric_limits<T>::max() << "]" ; + // os << "[" << std::numeric_limits<T>::lowest() << "]" ; + os << "[" << std::numeric_limits<T>::min() << "]" ; + os << "]"; // end of row. +} // void integer_functions + + +template<typename T> +void float_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table float-point function values to `ostream` os. + os << "\n[" // start of row. + "[" << type_name << "]" ; + os << "[" << std::numeric_limits<T>::max() << "]" ; + os << "[" << std::numeric_limits<T>::lowest() << "]" ; + os << "[" << std::numeric_limits<T>::min() << "]" + os << "[" << std::numeric_limits<T>::epsilon() << "]" + os << "[" << std::numeric_limits<T>::round_error() << "]" + os << "[" << std::numeric_limits<T>::infinity() << "]" + os << "[" << std::numeric_limits<T>::quiet_NaN() << "]" + os << "[" << std::numeric_limits<T>::signaling_NaN() << "]" + os << "[" << std::numeric_limits<T>::denorm_min() << "]" + "]"; // end of row. +} // void float_functions + +template<typename T> +int numeric_limits_list(std::string description) +{//! Output numeric_limits for numeric_limits<T>, for example `numeric_limits_list<bool>()`. + // This is not used for Quickbook format. + // std::cout << versions() << std::endl; + + std::cout << "\n" << description << "\n" << std::endl; // int, int64_t rather than full long typeid(T).name(). + + std::cout << "Type " << typeid(T).name() << " std::numeric_limits::<" << typeid(T).name() << ">\n" << std::endl; + // ull long typeid(T).name() + + if (std::numeric_limits<T>::is_specialized == false) + { + std::cout << "type " << typeid(T).name() << " is not specialized for std::numeric_limits!" << std::endl; + //return -1; + } + + // Member constants. + + std::cout << (std::numeric_limits<T>::is_signed ? "is signed." : "unsigned.") << std::endl; + std::cout << (std::numeric_limits<T>::is_integer ? "is integer." : "not integer (fixed or float-point).") << std::endl; + std::cout << (std::numeric_limits<T>::is_exact ? "is exact." : "not exact.") << std::endl; + std::cout << (std::numeric_limits<T>::has_infinity ? "has infinity." : "no infinity.") << std::endl; + std::cout << (std::numeric_limits<T>::has_quiet_NaN ? "has quiet NaN." : "no quiet NaN.") << std::endl; + std::cout << (std::numeric_limits<T>::has_signaling_NaN ? "has signaling NaN." : "no signaling NaN.") << std::endl; + if (!std::numeric_limits<T>::is_integer) + { // is floating_point + std::cout << "Denorm style is " ; + if (std::numeric_limits<T>::has_denorm == std::denorm_absent) + { + std::cout << "denorm_absent." << std::endl; + } + else if (std::numeric_limits<T>::has_denorm == std::denorm_present) + { + std::cout << "denorm_present." << std::endl; + } + else if (std::numeric_limits<T>::has_denorm == std::denorm_indeterminate) + { + std::cout << "denorm_indeterminate." << std::endl; + } + else + { + std::cout << "std::numeric_limits<T>::has_denorm unexpected value!" << std::endl; + } + + std::cout << (std::numeric_limits<T>::has_denorm_loss ? "has denorm loss." : "no denorm loss.") << std::endl; + // true if a loss of accuracy is detected as a denormalization loss, rather than an inexact result. + + std::cout << "Round style is "; + if (std::numeric_limits<T>::round_style == std::round_indeterminate) + { + std::cout << "round_indeterminate!" << std::endl; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_zero) + { + std::cout << "round_toward_zero." << std::endl; + } + else if (std::numeric_limits<T>::round_style == std::round_to_nearest) + { + std::cout << "round_to_nearest." << std::endl; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_infinity) + { + std::cout << "round_toward_infinity." << std::endl; + } + else if (std::numeric_limits<T>::round_style == std::round_toward_neg_infinity) + { + std::cout << "round_toward_neg_infinity." << std::endl; + } + else + { + std::cout << "undefined value!" << std::endl; + } + + } // is floating_point + + std::cout << (std::numeric_limits<T>::is_iec559 ? "is IEC599." : "not IEC599.") << std::endl; + std::cout << (std::numeric_limits<T>::is_bounded ? "is bound." : "unbounded.") << std::endl; + std::cout << (std::numeric_limits<T>::is_modulo ? "is modulo." : "no modulo.") << std::endl; + std::cout << std::dec << "radix " << std::numeric_limits<T>::radix << std::endl; + std::cout << "digits " << std::numeric_limits<T>::digits << std::endl; + std::cout << "digits10 " << std::numeric_limits<T>::digits10 << std::endl; + + std::cout.precision(std::numeric_limits<T>::max_digits10); // Full precision for floating-point values like max, min ... + + std::cout << "max_digits10 " << std::numeric_limits<T>::max_digits10 << std::endl; + std::cout << "min_exponent " << std::numeric_limits<T>::min_exponent << std::endl; + std::cout << "min_exponent10 " << std::numeric_limits<T>::min_exponent10 << std::endl; + std::cout << "max_exponent " << std::numeric_limits<T>::max_exponent << std::endl; + std::cout << "max_exponent10 " << std::numeric_limits<T>::max_exponent10 << std::endl; + + std::cout << (std::numeric_limits<T>::tinyness_before ? "Can tiny values before rounding." : "no tinyness_before.") << std::endl; + // true if the type can detect tiny values before rounding; false if it cannot. + std::cout << (std::numeric_limits<T>::traps ? "traps" : "no trapping.") << std::endl; + // Whether trapping that reports on arithmetic exceptions is implemented for a type. + + std::cout << "Member functions." << std::endl; + // (assumes operator<< for type T is available). + // If floating-point then hex format may not be available. + + std::cout << "max = " << std::numeric_limits<T>::max() << std::endl; + //if (std::numeric_limits<T>::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits<T>::max() << std::endl; + //} + + std::cout << "lowest = " << std::dec << std::numeric_limits<T>::lowest() << std::endl; + //if (std::numeric_limits<T>::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits<T>::lowest() << std::endl; + //} + + std::cout << "min = " << std::dec << std::numeric_limits<T>::min() << std::endl; + //if (std::numeric_limits<T>::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits<T>::min() << std::endl; + //} + + std::cout << "epsilon = " << std::dec << std::numeric_limits<T>::epsilon() << std::endl; + //if (std::numeric_limits<T>::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits<T>::epsilon() << std::endl; + //} + // round_error is always zero for integer types. + // round_error is usually 1/2 = (T)0.5 for floating-point types. + // round_error is ? for fixed-point. + std::cout << "round_error = " << std::numeric_limits<T>::round_error() << " ULP." << std::endl; + + std::cout << "infinity = " << std::dec << std::numeric_limits<T>::infinity() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits<T>::infinity() << std::endl; + + std::cout << "quiet_NaN = " << std::dec << std::numeric_limits<T>::quiet_NaN() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits<T>::quiet_NaN() << std::endl; + + std::cout << "signaling_NaN = " << std::dec << std::numeric_limits<T>::signaling_NaN() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits<T>::signaling_NaN() << std::endl; + + // Only meaningful if (std::numeric_limits<T>::has_denorm == std::denorm_present) + // so might not bother to show if absent? + std::cout << "denorm_min = " << std::numeric_limits<T>::denorm_min() << std::endl; + std::cout << " = " << std::numeric_limits<T>::denorm_min() << std::endl; + return 0; +} + +int main() +{ + + + + try + { + using namespace boost::multiprecision; + + std::cout << versions() << std::endl; + + std::ofstream fout(filename, std::ios_base::out); + if (!fout.is_open()) + { + std::cout << "Unable to open file " << filename << " for output.\n" << std::endl; + return -1; // boost::EXIT_FAILURE; + } + fout << + "[/""\n" + "Copyright 2013 Paul A. Bristow.""\n" + "Copyright 2013 John Maddock.""\n" + "Distributed under the Boost Software License, Version 1.0.""\n" + "(See accompanying file LICENSE_1_0.txt or copy at""\n" + "http://www.boost.org/LICENSE_1_0.txt).""\n" + "]""\n" + << std::endl; + + fout << "[section:limits"<< bits32_64 << " Numeric limits for " << bits32_64 << "-bit platform]" << std::endl; + + // Output platform version info (32 or 64). + fout << "These tables were generated using the following program and options:\n\n" + "[pre""\n" + << versions() + << "]""\n" + << std::endl; + + fout << "[table:integral_constants Integer types constants (`std::numeric_limits<T>::is_integer == true` && is_exact == true)" "\n" + "["; + + for (size_t i = 0; i < integer_constant_heads.size(); i++) + { // signed, bound, modulo ... + fout << "[" << integer_constant_heads[i] << "]" ; + } + fout << "]"; + + integer_constants<bool>("bool", fout); + integer_constants<char>("char", fout); + integer_constants<unsigned char>("unsigned char", fout); + integer_constants<char16_t>("char16_t", fout); + integer_constants<char32_t>("char32_t", fout); + integer_constants<short>("short", fout); + integer_constants<unsigned short>("unsigned short", fout); + integer_constants<int>("int", fout); + integer_constants<unsigned int>("unsigned", fout); + integer_constants<long>("long", fout); + integer_constants<unsigned long>("unsigned long", fout); + integer_constants<long long>("long long", fout); + integer_constants<unsigned long long>("unsigned long long", fout); + integer_constants<int32_t>("int32_t", fout); + integer_constants<uint32_t>("uint32_t", fout); + integer_constants<int64_t>("int64_t", fout); + integer_constants<uint64_t>("uint64_t", fout); + integer_constants<int128_t>("int128_t", fout); + integer_constants<uint128_t>("uint128_t", fout); + integer_constants<int256_t>("int256_t", fout); + integer_constants<uint256_t>("uint256_t", fout); + // integer_constants<int512_t>("int512_t", fout); + //integer_constants<uint512_t>("uint512_t", fout); // Too big? + integer_constants<cpp_int>("cpp_int", fout); + + fout << "\n]\n\n"; + + + fout << "[table:integral_functions Integer types functions (`std::numeric_limits<T>::is_integer == true && std::numeric_limits<T>::min() == std::numeric_limits<T>::lowest()` )" "\n" + "["; + // Display types across the page, and 2 (or 3) functions as rows. + + fout << "[function]"; + for (size_t i = 0; i < integer_function_heads.size(); i++) + { + fout << "[" << integer_function_heads[i] << "]" ; + } + fout << "]"; // end of headings. + integer_functions<bool>("bool", fout); + //integer_functions<char>("char", fout); // Need int value not char. + fout << "\n[" // start of row. + "[" << "char"<< "]" ; + fout << "[" << static_cast<int>((std::numeric_limits<char>::max)()) << "]" ; + // fout << "[" << (std::numeric_limits<T>::lowest)() << "]" ; + fout << "[" << static_cast<int>((std::numeric_limits<char>::min)()) << "]" ; + fout << "]"; // end of row. + //integer_functions<unsigned char>("unsigned char", fout); // Need int value not char. + fout << "\n[" // start of row. + "[" << "unsigned char"<< "]" ; + fout << "[" << static_cast<int>((std::numeric_limits<unsigned char>::max)()) << "]" ; + // fout << "[" << std::numeric_limits<unsigned char>::lowest() << "]" ; + fout << "[" << static_cast<int>(std::numeric_limits<unsigned char>::min()) << "]" ; + fout << "]"; // end of row. + + integer_functions<char16_t>("char16_t", fout); + integer_functions<char32_t>("char32_t", fout); + integer_functions<short>("short", fout); + integer_functions<unsigned short>("unsigned short", fout); + integer_functions<int>("int", fout); + integer_functions<unsigned int>("unsigned int", fout); + integer_functions<long>("long", fout); + integer_functions<unsigned long>("unsigned long", fout); + integer_functions<long long>("long long", fout); + integer_functions<unsigned long long>("unsigned long long", fout); + integer_functions<int32_t>("int32_t", fout); + integer_functions<int64_t>("int64_t", fout); + integer_functions<int128_t>("int128_t", fout); + fout << "]" "\n"; // end of table; + + + //fout << "[[max]" + // << "[" << std::numeric_limits<bool>::max() << "]" + // << "[" << static_cast<int>(std::numeric_limits<char>::max()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<unsigned char>::max()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<char16_t>::max()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<char32_t>::max()) << "]" + // << "[" << std::numeric_limits<short>::max() << "]" + // << "[" << std::numeric_limits<unsigned short>::max() << "]" + // << "[" << std::numeric_limits<int>::max() << "]" + // << "[" << std::numeric_limits<unsigned int>::max() << "]" + // << "[" << std::numeric_limits<long>::max() << "]" + // << "[" << std::numeric_limits<unsigned long>::max() << "]" + // << "[" << std::numeric_limits<long long>::max() << "]" + // << "[" << std::numeric_limits<unsigned long long>::max() << "]" + // << "[" << std::numeric_limits<int32_t>::max() << "]" + // << "[" << std::numeric_limits<int64_t>::max() << "]" + // << "[" << std::numeric_limits<int128_t>::max() << "]" + // //<< "[" << std::numeric_limits<int256_t>::max() << "]" // too big? + // //<< "[" << std::numeric_limits<int512_t>::max() << "]" // too big? + // << "]" "\n"; + ///* Assume lowest() is not useful as == min for all integer types. + // */ + + //fout << "[[min]" + // << "[" << std::numeric_limits<bool>::min() << "]" + // << "[" << static_cast<int>(std::numeric_limits<char>::min()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<unsigned char>::min()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<char16_t>::min()) << "]" + // << "[" << static_cast<int>(std::numeric_limits<char32_t>::min()) << "]" + // << "[" << std::numeric_limits<short>::min() << "]" + // << "[" << std::numeric_limits<unsigned short>::min() << "]" + // << "[" << std::numeric_limits<int>::min() << "]" + // << "[" << std::numeric_limits<unsigned int>::min() << "]" + // << "[" << std::numeric_limits<long>::min() << "]" + // << "[" << std::numeric_limits<unsigned long>::min() << "]" + // << "[" << std::numeric_limits<long long>::min() << "]" + // << "[" << std::numeric_limits<unsigned long long>::min() << "]" + // << "[" << std::numeric_limits<int32_t>::min() << "]" + // << "[" << std::numeric_limits<int64_t>::min() << "]" + // << "[" << std::numeric_limits<int128_t>::min() << "]" + // // << "[" << std::numeric_limits<int256_t>::min() << "]" // too big? + // // << "[" << std::numeric_limits<int512_t>::min() << "]" // too big? + // << "]""\n"; + + + + // Floating-point + + typedef number<cpp_dec_float<50> > cpp_dec_float_50; // 50 decimal digits. + typedef number<cpp_bin_float<113> > bin_128bit_double_type; // == Binary rare long double. + + fout << + //"[table:float_functions Floating-point types constants (`std::numeric_limits<T>::is_integer == false && std::numeric_limits<T>::is_modulo == false` )" "\n" + "[table:float_functions Floating-point types constants (`std::numeric_limits<T>::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true`)" "\n" + "["; + for (size_t i = 0; i < float_constant_heads.size(); i++) + { + fout << "[" << float_constant_heads[i] << "]" ; + } + fout << "]"; // end of headings. + + float_constants<float>("float", fout); + float_constants<double>("double", fout); + float_constants<long double>("long double", fout); + float_constants<cpp_dec_float_50>("cpp_dec_float_50", fout); + float_constants<bin_128bit_double_type>("bin_128bit_double_type", fout); + fout << "]" "\n"; // end of table; + + fout << + "[table:float_functions Floating-point types functions (`std::numeric_limits<T>::is_integer == false`)" "\n" + "["; + + for (size_t i = 0; i < float_type_names.size(); i++) + { + fout << "[" << float_type_names[i] << "]" ; + } + fout << "]"; // end of headings. + + fout << "[[max]" + << "[" << std::numeric_limits<float>::max() << "]" + << "[" << std::numeric_limits<double>::max() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Perhaps to test Long double is not just a duplication of double (but need change is headings too). + << "[" << std::numeric_limits<long double>::max() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50>::max() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::max() << "]" + << "]" "\n"; // end of row. + + fout << "[[min]" + << "[" << std::numeric_limits<float>::min() << "]" + << "[" << std::numeric_limits<double>::min() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::min() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::min() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::min() << "]" + << "]" "\n"; // end of row. + + fout << "[[epsilon]" + << "[" << std::numeric_limits<float>::epsilon() << "]" + << "[" << std::numeric_limits<double>::epsilon() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::epsilon() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::epsilon() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::epsilon() << "]" + << "]" "\n"; // end of row. + + fout << "[[round_error]" + << "[" << std::numeric_limits<float>::round_error() << "]" + << "[" << std::numeric_limits<double>::round_error() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::round_error() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::round_error() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::round_error() << "]" + << "]" "\n"; // end of row. + + fout << "[[infinity]" + << "[" << std::numeric_limits<float>::infinity() << "]" + << "[" << std::numeric_limits<double>::infinity() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::infinity() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::infinity() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::infinity() << "]" + << "]" "\n"; // end of row. + + fout << "[[quiet_NaN]" + << "[" << std::numeric_limits<float>::quiet_NaN() << "]" + << "[" << std::numeric_limits<double>::quiet_NaN() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::quiet_NaN() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::quiet_NaN() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::quiet_NaN() << "]" + << "]" "\n"; // end of row. + + fout << "[[signaling_NaN]" + << "[" << std::numeric_limits<float>::signaling_NaN() << "]" + << "[" << std::numeric_limits<double>::signaling_NaN() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::signaling_NaN() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::signaling_NaN() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::signaling_NaN() << "]" + << "]" "\n"; // end of row. + + fout << "[[denorm_min]" + << "[" << std::numeric_limits<float>::denorm_min() << "]" + << "[" << std::numeric_limits<double>::denorm_min() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits<long double>::denorm_min() << "]" +//#endif + << "[" << std::numeric_limits<cpp_dec_float_50 >::denorm_min() << "]" + << "[" << std::numeric_limits<bin_128bit_double_type >::denorm_min() << "]" + << "]" "\n"; // end of row. + + + + fout << "]" "\n"; // end of table; + + + fout << "\n\n" + "[endsect] [/section:limits32 Numeric limits for 32-bit platform]" "\n" << std::endl; + + + + fout.close(); + } + catch(std::exception ex) + { + std::cout << "exception thrown: " << ex.what() << std::endl; + } + + +} // int main() + +/* + Description: Autorun "J:\Cpp\Misc\Debug\numeric_limits_qbk.exe" + + Program: I:\boost-sandbox\multiprecision.cpp_bin_float\libs\multiprecision\doc\numeric_limits_qbk.cpp + Wed Aug 28 14:17:21 2013 + BuildInfo: + Platform Win32 + Compiler Microsoft Visual C++ version 10.0 + MSVC version 160040219. + STL Dinkumware standard library version 520 + Boost version 1.55.0 + + */ + diff --git a/libs/multiprecision/example/Jamfile.v2 b/libs/multiprecision/example/Jamfile.v2 new file mode 100644 index 0000000000..b357c186fd --- /dev/null +++ b/libs/multiprecision/example/Jamfile.v2 @@ -0,0 +1,95 @@ +# \libs\math\example\jamfile.v2 +# Runs multiprecision examples. +# Copyright 2014 John Maddock +# Copyright Paul A. Bristow 2014. +# Copyright Christpher Kormanyos 2014 + +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +# bring in the rules for testing +import testing ; +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local mpfi_path = [ modules.peek : MPFI_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project + : requirements + <include>$(gmp_path) + <include>$(gmp_path)/mpfr + <include>$(gmp_path)/gmpfrxx + <include>$(mpfr_path) + <include>$(mpfi_path) + <include>$(mpfi_path)/src + <include>$(tommath_path) + <include>../include + <include>../../.. + <toolset>gcc:<cxxflags>-Wno-missing-braces + <toolset>darwin:<cxxflags>-Wno-missing-braces + <toolset>acc:<cxxflags>+W2068,2461,2236,4070 + <toolset>intel:<cxxflags>-Qwd264,239 + <toolset>msvc:<runtime-link>static + <toolset>msvc:<link>static + <toolset>msvc:<warnings>all + <toolset>msvc:<asynch-exceptions>on + <toolset>msvc:<define>_CRT_SECURE_NO_DEPRECATE + <toolset>msvc:<define>_SCL_SECURE_NO_DEPRECATE + <toolset>msvc:<define>_SCL_SECURE_NO_WARNINGS + <toolset>msvc:<define>_CRT_SECURE_NO_WARNINGS + <toolset>msvc:<cxxflags>/wd4996 + <toolset>msvc:<cxxflags>/wd4512 + <toolset>msvc:<cxxflags>/wd4610 + <toolset>msvc:<cxxflags>/wd4510 + <toolset>msvc:<cxxflags>/wd4127 + <toolset>msvc:<cxxflags>/wd4701 + <toolset>msvc:<cxxflags>/wd4127 + <toolset>msvc:<cxxflags>/wd4305 + ; + +lib gmp : : <search>$(gmp_path) ; +lib mpfr : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug ; +lib mpfi : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug <search>$(mpfi_path) <search>$(mpfi_path)/src ; +lib quadmath ; + +if $(tommath_path) +{ + lib tommath : [ GLOB $(tommath_path) : *.c ] ; + TOMMATH = tommath ; +} +else +{ + lib tommath : : <search>$(tommath_path) ; + TOMMATH = tommath ; +} + +run cpp_int_snips.cpp ; + +run cpp_dec_float_snips.cpp ; + +run cpp_bin_float_snips.cpp ; + +run debug_adaptor_snips.cpp ; +run float128_snips.cpp quadmath : : : [ check-target-builds ../config//has_float128 : : <build>no ] ; +run floating_point_examples.cpp ; +run gauss_laguerre_quadrature.cpp : : : release ; +run hypergeometric_luke_algorithms.cpp ; +run integer_examples.cpp ; +run logged_adaptor.cpp mpfi mpfr gmp : : : [ check-target-builds ../config//has_mpfi : : <build>no ] ; +run mixed_integer_arithmetic.cpp ; +run numeric_limits_snips.cpp /boost//test_exec_monitor ; +run random_snips.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run safe_prime.cpp ; + +run gmp_snips.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run mpfi_snips.cpp mpfi mpfr gmp : : : [ check-target-builds ../config//has_mpfi : : <build>no ] ; +run mpfr_snips.cpp mpfr gmp : : : [ check-target-builds ../config//has_mpfr : : <build>no ] ; +run tommath_snips.cpp $(TOMMATH) : : : [ check-target-builds ../config//has_tommath : : <build>no ] ; + + + + diff --git a/libs/multiprecision/example/cpp_bin_float_snips.cpp b/libs/multiprecision/example/cpp_bin_float_snips.cpp new file mode 100644 index 0000000000..6450440182 --- /dev/null +++ b/libs/multiprecision/example/cpp_bin_float_snips.cpp @@ -0,0 +1,32 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[cpp_bin_float_eg +#include <boost/multiprecision/cpp_bin_float.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +int main() +{ + using namespace boost::multiprecision; + + // Operations at fixed precision and full numeric_limits support: + cpp_bin_float_100 b = 2; + std::cout << std::numeric_limits<cpp_bin_float_100>::digits << std::endl; + std::cout << std::numeric_limits<cpp_bin_float_100>::digits10 << std::endl; + // We can use any C++ std lib function, lets print all the digits as well: + std::cout << std::setprecision(std::numeric_limits<cpp_bin_float_100>::max_digits10) + << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; + // And since we have an extended exponent range we can generate some really large + // numbers here (4.0238726007709377354370243e+2564): + std::cout << boost::math::tgamma(cpp_bin_float_100(1000)) << std::endl; + return 0; +} + +//] diff --git a/libs/multiprecision/example/cpp_dec_float_snips.cpp b/libs/multiprecision/example/cpp_dec_float_snips.cpp new file mode 100644 index 0000000000..faa488abab --- /dev/null +++ b/libs/multiprecision/example/cpp_dec_float_snips.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + + //[cpp_dec_float_eg +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +int main() +{ + using namespace boost::multiprecision; + + // Operations at fixed precision and full numeric_limits support: + cpp_dec_float_100 b = 2; + std::cout << std::numeric_limits<cpp_dec_float_100>::digits << std::endl; + // Note that digits10 is the same as digits, since we're base 10! : + std::cout << std::numeric_limits<cpp_dec_float_100>::digits10 << std::endl; + // We can use any C++ std lib function, lets print all the digits as well: + std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::max_digits10) + << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; + // And since we have an extended exponent range we can generate some really large + // numbers here (4.0238726007709377354370243e+2564): + std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl; + return 0; +} +//] + diff --git a/libs/multiprecision/example/cpp_int_snips.cpp b/libs/multiprecision/example/cpp_int_snips.cpp new file mode 100644 index 0000000000..e0eb92711c --- /dev/null +++ b/libs/multiprecision/example/cpp_int_snips.cpp @@ -0,0 +1,74 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_int.hpp> +#include <iostream> + +void t1() +{ +//[cpp_int_eg +//=#include <boost/multiprecision/cpp_int.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + int128_t v = 1; + + // Do some fixed precision arithmetic: + for(unsigned i = 1; i <= 20; ++i) + v *= i; + + std::cout << v << std::endl; // prints 20! + + // Repeat at arbitrary precision: + cpp_int u = 1; + for(unsigned i = 1; i <= 100; ++i) + u *= i; + + std::cout << u << std::endl; // prints 100! + +//= return 0; +//=} +//] +} + +void t3() +{ +//[cpp_rational_eg +//=#include <boost/multiprecision/cpp_int.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + cpp_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << v << std::endl; // prints 1000! / 10 + std::cout << numerator(v) << std::endl; + std::cout << denominator(v) << std::endl; + + cpp_rational w(2, 3); // component wise constructor + std::cout << w << std::endl; // prints 2/3 +//= return 0; +//=} +//] +} + + +int main() +{ + t1(); + t3(); + return 0; +} + diff --git a/libs/multiprecision/example/debug_adaptor_snips.cpp b/libs/multiprecision/example/debug_adaptor_snips.cpp new file mode 100644 index 0000000000..ca19f444ed --- /dev/null +++ b/libs/multiprecision/example/debug_adaptor_snips.cpp @@ -0,0 +1,40 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/multiprecision/debug_adaptor.hpp> +#include <iostream> + +void t1() +{ + //[debug_adaptor_eg + //=#include <boost/multiprecision/debug_adaptor.hpp> + //=#include <boost/multiprecision/cpp_dec_float.hpp> + + using namespace boost::multiprecision; + + typedef number<debug_adaptor<cpp_dec_float<50> > > fp_type; + + fp_type denom = 1; + fp_type sum = 1; + + for(unsigned i = 2; i < 50; ++i) + { + denom *= i; + sum += 1 / denom; + } + + std::cout << std::setprecision(std::numeric_limits<fp_type>::digits) << sum << std::endl; + //] +} + +int main() +{ + t1(); + return 0; +} + + + diff --git a/libs/multiprecision/example/float128_snips.cpp b/libs/multiprecision/example/float128_snips.cpp new file mode 100644 index 0000000000..c7e7d64f11 --- /dev/null +++ b/libs/multiprecision/example/float128_snips.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[float128_eg +#include <boost/multiprecision/float128.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +int main() +{ + using namespace boost::multiprecision; + + // Operations at 128-bit precision and full numeric_limits support: + float128 b = 2; + // There are 113-bits of precision: + std::cout << std::numeric_limits<float128>::digits << std::endl; + // Or 34 decimal places: + std::cout << std::numeric_limits<float128>::digits10 << std::endl; + // We can use any C++ std lib function, lets print all the digits as well: + std::cout << std::setprecision(std::numeric_limits<float128>::max_digits10) + << log(b) << std::endl; // print log(2) = 0.693147180559945309417232121458176575 + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // And since we have an extended exponent range we can generate some really large + // numbers here (4.02387260077093773543702433923004111e+2564): + std::cout << boost::math::tgamma(float128(1000)) << std::endl; + // + // We can declare constants using GCC or Intel's native types, and the Q suffix, + // these can be declared constexpr if required: + /*<-*/ +#ifndef BOOST_NO_CONSTEXPR + /*->*/ + constexpr float128 pi = 3.1415926535897932384626433832795028841971693993751058Q; + /*<-*/ +#endif + /*->*/ + return 0; +} +//] + diff --git a/libs/multiprecision/example/floating_point_examples.cpp b/libs/multiprecision/example/floating_point_examples.cpp new file mode 100644 index 0000000000..74f593f20c --- /dev/null +++ b/libs/multiprecision/example/floating_point_examples.cpp @@ -0,0 +1,697 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/math/constants/constants.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <boost/math/special_functions/bessel.hpp> +#include <iostream> +#include <iomanip> + +#if !defined(BOOST_NO_CXX11_HDR_ARRAY) && !defined(BOOST_NO_CXX11_LAMBDAS) + +#include <array> + +//[AOS1 + +/*`Generic numeric programming employs templates to use the same code for different +floating-point types and functions. Consider the area of a circle a of radius r, given by + +[:['a = [pi] * r[super 2]]] + +The area of a circle can be computed in generic programming using Boost.Math +for the constant [pi] as shown below: + +*/ + +//=#include <boost/math/constants/constants.hpp> + +template<typename T> +inline T area_of_a_circle(T r) +{ + using boost::math::constants::pi; + return pi<T>() * r * r; +} + +/*` +It is possible to use `area_of_a_circle()` with built-in floating-point types as +well as floating-point types from Boost.Multiprecision. In particular, consider a +system with 4-byte single-precision float, 8-byte double-precision double and also the +`cpp_dec_float_50` data type from Boost.Multiprecision with 50 decimal digits +of precision. + +We can compute and print the approximate area of a circle with radius 123/100 for +`float`, `double` and `cpp_dec_float_50` with the program below. + +*/ + +//] + +//[AOS3 + +/*`In the next example we'll look at calling both standard library and Boost.Math functions from within generic code. +We'll also show how to cope with template arguments which are expression-templates rather than number types.*/ + +//] + +//[JEL + +/*` +In this example we'll show several implementations of the +[@http://mathworld.wolfram.com/LambdaFunction.html Jahnke and Emden Lambda function], +each implementation a little more sophisticated than the last. + +The Jahnke-Emden Lambda function is defined by the equation: + +[:['JahnkeEmden(v, z) = [Gamma](v+1) * J[sub v](z) / (z / 2)[super v]]] + +If we were to implement this at double precision using Boost.Math's facilities for the Gamma and Bessel +function calls it would look like this: + +*/ + +double JEL1(double v, double z) +{ + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v); +} + +/*` +Calling this function as: + + std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10); + std::cout << JEL1(2.5, 0.5) << std::endl; + +Yields the output: + +[pre 9.822663964796047e-001] + +Now let's implement the function again, but this time using the multiprecision type +`cpp_dec_float_50` as the argument type: + +*/ + +boost::multiprecision::cpp_dec_float_50 + JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z) +{ + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v); +} + +/*` +The implementation is almost the same as before, but with one key difference - we can no longer call +`std::pow`, instead we must call the version inside the `boost::multiprecision` namespace. In point of +fact, we could have omitted the namespace prefix on the call to `pow` since the right overload would +have been found via [@http://en.wikipedia.org/wiki/Argument-dependent_name_lookup +argument dependent lookup] in any case. + +Note also that the first argument to `pow` along with the argument to `tgamma` in the above code +are actually expression templates. The `pow` and `tgamma` functions will handle these arguments +just fine. + +Here's an example of how the function may be called: + + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10); + std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + +Which outputs: + +[pre 9.82266396479604757017335009796882833995903762577173e-01] + +Now that we've seen some non-template examples, lets repeat the code again, but this time as a template +that can be called either with a builtin type (`float`, `double` etc), or with a multiprecision type: + +*/ + +template <class Float> +Float JEL3(Float v, Float z) +{ + using std::pow; + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v); +} + +/*` + +Once again the code is almost the same as before, but the call to `pow` has changed yet again. +We need the call to resolve to either `std::pow` (when the argument is a builtin type), or +to `boost::multiprecision::pow` (when the argument is a multiprecision type). We do that by +making the call unqualified so that versions of `pow` defined in the same namespace as type +`Float` are found via argument dependent lookup, while the `using std::pow` directive makes +the standard library versions visible for builtin floating point types. + +Let's call the function with both `double` and multiprecision arguments: + + std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10); + std::cout << JEL3(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10); + std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + +Which outputs: + +[pre +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +] + +Unfortunately there is a problem with this version: if we were to call it like this: + + boost::multiprecision::cpp_dec_float_50 v(2), z(0.5); + JEL3(v + 0.5, z); + +Then we would get a long and inscrutable error message from the compiler: the problem here is that the first +argument to `JEL3` is not a number type, but an expression template. We could obviously add a typecast to +fix the issue: + + JEL(cpp_dec_float_50(v + 0.5), z); + +However, if we want the function JEL to be truly reusable, then a better solution might be preferred. +To achieve this we can borrow some code from Boost.Math which calculates the return type of mixed-argument +functions, here's how the new code looks now: + +*/ + +template <class Float1, class Float2> +typename boost::math::tools::promote_args<Float1, Float2>::type + JEL4(Float1 v, Float2 z) +{ + using std::pow; + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v); +} + +/*` + +As you can see the two arguments to the function are now separate template types, and +the return type is computed using the `promote_args` metafunction from Boost.Math. + +Now we can call: + + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10); + std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl; + +And get 100 digits of output: + +[pre 9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01] + +As a bonus, we can now call the function not just with expression templates, but with other mixed types as well: +for example `float` and `double` or `int` and `double`, and the correct return type will be computed in each case. + +Note that while in this case we didn't have to change the body of the function, in the general case +any function like this which creates local variables internally would have to use `promote_args` +to work out what type those variables should be, for example: + + template <class Float1, class Float2> + typename boost::math::tools::promote_args<Float1, Float2>::type + JEL5(Float1 v, Float2 z) + { + using std::pow; + typedef typename boost::math::tools::promote_args<Float1, Float2>::type variable_type; + variable_type t = pow(z / 2, v); + return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / t; + } + +*/ + +//] + +//[ND1 + +/*` +In this example we'll add even more power to generic numeric programming using not only different +floating-point types but also function objects as template parameters. Consider +some well-known central difference rules for numerically computing the first derivative +of a function ['f[prime](x)] with ['x [isin] [real]]: + +[equation floating_point_eg1] + +Where the difference terms ['m[sub n]] are given by: + +[equation floating_point_eg2] + +and ['dx] is the step-size of the derivative. + +The third formula in Equation 1 is a three-point central difference rule. It calculates +the first derivative of ['f[prime](x)] to ['O(dx[super 6])], where ['dx] is the given step-size. +For example, if +the step-size is 0.01 this derivative calculation has about 6 decimal digits of precision - +just about right for the 7 decimal digits of single-precision float. +Let's make a generic template subroutine using this three-point central difference +rule. In particular: +*/ + +template<typename value_type, typename function_type> + value_type derivative(const value_type x, const value_type dx, function_type func) +{ + // Compute d/dx[func(*first)] using a three-point + // central difference rule of O(dx^6). + + const value_type dx1 = dx; + const value_type dx2 = dx1 * 2; + const value_type dx3 = dx1 * 3; + + const value_type m1 = (func(x + dx1) - func(x - dx1)) / 2; + const value_type m2 = (func(x + dx2) - func(x - dx2)) / 4; + const value_type m3 = (func(x + dx3) - func(x - dx3)) / 6; + + const value_type fifteen_m1 = 15 * m1; + const value_type six_m2 = 6 * m2; + const value_type ten_dx1 = 10 * dx1; + + return ((fifteen_m1 - six_m2) + m3) / ten_dx1; +} + +/*`The `derivative()` template function can be used to compute the first derivative +of any function to ['O(dx[super 6])]. For example, consider the first derivative of ['sin(x)] evaluated +at ['x = [pi]/3]. In other words, + +[equation floating_point_eg3] + +The code below computes the derivative in Equation 3 for float, double and boost's +multiple-precision type cpp_dec_float_50. +*/ + +//] + +//[GI1 + +/*` +Similar to the generic derivative example, we can calculate integrals in a similar manner: +*/ + +template<typename value_type, typename function_type> +inline value_type integral(const value_type a, + const value_type b, + const value_type tol, + function_type func) +{ + unsigned n = 1U; + + value_type h = (b - a); + value_type I = (func(a) + func(b)) * (h / 2); + + for(unsigned k = 0U; k < 8U; k++) + { + h /= 2; + + value_type sum(0); + for(unsigned j = 1U; j <= n; j++) + { + sum += func(a + (value_type((j * 2) - 1) * h)); + } + + const value_type I0 = I; + I = (I / 2) + (h * sum); + + const value_type ratio = I0 / I; + const value_type delta = ratio - 1; + const value_type delta_abs = ((delta < 0) ? -delta : delta); + + if((k > 1U) && (delta_abs < tol)) + { + break; + } + + n *= 2U; + } + + return I; +} + +/*` +The following sample program shows how the function can be called, we begin +by defining a function object, which when integrated should yield the Bessel J +function: +*/ + +template<typename value_type> +class cyl_bessel_j_integral_rep +{ +public: + cyl_bessel_j_integral_rep(const unsigned N, + const value_type& X) : n(N), x(X) { } + + value_type operator()(const value_type& t) const + { + // pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt] + return cos(x * sin(t) - (n * t)); + } + +private: + const unsigned n; + const value_type x; +}; + + +//] + +//[POLY + +/*` +In this example we'll look at polynomial evaluation, this is not only an important +use case, but it's one that `number` performs particularly well at because the +expression templates ['completely eliminate all temporaries] from a +[@http://en.wikipedia.org/wiki/Horner%27s_method Horner polynomial +evaluation scheme]. + +The following code evaluates `sin(x)` as a polynomial, accurate to at least 64 decimal places: + +*/ + +using boost::multiprecision::cpp_dec_float; +typedef boost::multiprecision::number<cpp_dec_float<64> > mp_type; + +mp_type mysin(const mp_type& x) +{ + // Approximation of sin(x * pi/2) for -1 <= x <= 1, using an order 63 polynomial. + static const std::array<mp_type, 32U> coefs = + {{ + mp_type("+1.5707963267948966192313216916397514420985846996875529104874722961539082031431044993140174126711"), //"), + mp_type("-0.64596409750624625365575656389794573337969351178927307696134454382929989411386887578263960484"), // ^3 + mp_type("+0.07969262624616704512050554949047802252091164235106119545663865720995702920146198554317279"), // ^5 + mp_type("-0.0046817541353186881006854639339534378594950280185010575749538605102665157913157426229824"), // ^7 + mp_type("+0.00016044118478735982187266087016347332970280754062061156858775174056686380286868007443"), // ^9 + mp_type("-3.598843235212085340458540018208389404888495232432127661083907575106196374913134E-6"), // ^11 + mp_type("+5.692172921967926811775255303592184372902829756054598109818158853197797542565E-8"), // ^13 + mp_type("-6.688035109811467232478226335783138689956270985704278659373558497256423498E-10"), // ^15 + mp_type("+6.066935731106195667101445665327140070166203261129845646380005577490472E-12"), // ^17 + mp_type("-4.377065467313742277184271313776319094862897030084226361576452003432E-14"), // ^19 + mp_type("+2.571422892860473866153865950420487369167895373255729246889168337E-16"), // ^21 + mp_type("-1.253899540535457665340073300390626396596970180355253776711660E-18"), // ^23 + mp_type("+5.15645517658028233395375998562329055050964428219501277474E-21"), // ^25 + mp_type("-1.812399312848887477410034071087545686586497030654642705E-23"), // ^27 + mp_type("+5.50728578652238583570585513920522536675023562254864E-26"), // ^29 + mp_type("-1.461148710664467988723468673933026649943084902958E-28"), // ^31 + mp_type("+3.41405297003316172502972039913417222912445427E-31"), // ^33 + mp_type("-7.07885550810745570069916712806856538290251E-34"), // ^35 + mp_type("+1.31128947968267628970845439024155655665E-36"), // ^37 + mp_type("-2.18318293181145698535113946654065918E-39"), // ^39 + mp_type("+3.28462680978498856345937578502923E-42"), // ^41 + mp_type("-4.48753699028101089490067137298E-45"), // ^43 + mp_type("+5.59219884208696457859353716E-48"), // ^45 + mp_type("-6.38214503973500471720565E-51"), // ^47 + mp_type("+6.69528558381794452556E-54"), // ^49 + mp_type("-6.47841373182350206E-57"), // ^51 + mp_type("+5.800016389666445E-60"), // ^53 + mp_type("-4.818507347289E-63"), // ^55 + mp_type("+3.724683686E-66"), // ^57 + mp_type("-2.6856479E-69"), // ^59 + mp_type("+1.81046E-72"), // ^61 + mp_type("-1.133E-75"), // ^63 + }}; + + const mp_type v = x * 2 / boost::math::constants::pi<mp_type>(); + const mp_type x2 = (v * v); + // + // Polynomial evaluation follows, if mp_type allocates memory then + // just one such allocation occurs - to initialize the variable "sum" - + // and no temporaries are created at all. + // + const mp_type sum = ((((((((((((((((((((((((((((((( + coefs[31U] + * x2 + coefs[30U]) + * x2 + coefs[29U]) + * x2 + coefs[28U]) + * x2 + coefs[27U]) + * x2 + coefs[26U]) + * x2 + coefs[25U]) + * x2 + coefs[24U]) + * x2 + coefs[23U]) + * x2 + coefs[22U]) + * x2 + coefs[21U]) + * x2 + coefs[20U]) + * x2 + coefs[19U]) + * x2 + coefs[18U]) + * x2 + coefs[17U]) + * x2 + coefs[16U]) + * x2 + coefs[15U]) + * x2 + coefs[14U]) + * x2 + coefs[13U]) + * x2 + coefs[12U]) + * x2 + coefs[11U]) + * x2 + coefs[10U]) + * x2 + coefs[9U]) + * x2 + coefs[8U]) + * x2 + coefs[7U]) + * x2 + coefs[6U]) + * x2 + coefs[5U]) + * x2 + coefs[4U]) + * x2 + coefs[3U]) + * x2 + coefs[2U]) + * x2 + coefs[1U]) + * x2 + coefs[0U]) + * v; + + return sum; +} + +/*` +Calling the function like so: + + mp_type pid4 = boost::math::constants::pi<mp_type>() / 4; + std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific; + std::cout << mysin(pid4) << std::endl; + +Yields the expected output: + +[pre 7.0710678118654752440084436210484903928483593768847403658833986900e-01] + +*/ + +//] + + +int main() +{ + using namespace boost::multiprecision; + std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10); + std::cout << JEL1(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10); + std::cout << JEL2(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits<double>::digits10); + std::cout << JEL3(2.5, 0.5) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10); + std::cout << JEL3(cpp_dec_float_50(2.5), cpp_dec_float_50(0.5)) << std::endl; + std::cout << std::scientific << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10); + std::cout << JEL4(cpp_dec_float_100(2) + 0.5, cpp_dec_float_100(0.5)) << std::endl; + + //[AOS2 + +/*=#include <iostream> +#include <iomanip> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using boost::multiprecision::cpp_dec_float_50; + +int main(int, char**) +{*/ + const float r_f(float(123) / 100); + const float a_f = area_of_a_circle(r_f); + + const double r_d(double(123) / 100); + const double a_d = area_of_a_circle(r_d); + + const cpp_dec_float_50 r_mp(cpp_dec_float_50(123) / 100); + const cpp_dec_float_50 a_mp = area_of_a_circle(r_mp); + + // 4.75292 + std::cout + << std::setprecision(std::numeric_limits<float>::digits10) + << a_f + << std::endl; + + // 4.752915525616 + std::cout + << std::setprecision(std::numeric_limits<double>::digits10) + << a_d + << std::endl; + + // 4.7529155256159981904701331745635599135018975843146 + std::cout + << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10) + << a_mp + << std::endl; +/*=}*/ + + //] + + //[ND2 +/*= +#include <iostream> +#include <iomanip> +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/math/constants/constants.hpp> + + +int main(int, char**) +{*/ + using boost::math::constants::pi; + using boost::multiprecision::cpp_dec_float_50; + // + // We'll pass a function pointer for the function object passed to derivative, + // the typecast is needed to select the correct overload of std::sin: + // + const float d_f = derivative( + pi<float>() / 3, + 0.01F, + static_cast<float(*)(float)>(std::sin) + ); + + const double d_d = derivative( + pi<double>() / 3, + 0.001, + static_cast<double(*)(double)>(std::sin) + ); + // + // In the cpp_dec_float_50 case, the sin function is multiply overloaded + // to handle expression templates etc. As a result it's hard to take its + // address without knowing about its implementation details. We'll use a + // C++11 lambda expression to capture the call. + // We also need a typecast on the first argument so we don't accidentally pass + // an expression template to a template function: + // + const cpp_dec_float_50 d_mp = derivative( + cpp_dec_float_50(pi<cpp_dec_float_50>() / 3), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50& x) -> cpp_dec_float_50 + { + return sin(x); + } + ); + + // 5.000029e-001 + std::cout + << std::setprecision(std::numeric_limits<float>::digits10) + << d_f + << std::endl; + + // 4.999999999998876e-001 + std::cout + << std::setprecision(std::numeric_limits<double>::digits10) + << d_d + << std::endl; + + // 4.99999999999999999999999999999999999999999999999999e-01 + std::cout + << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10) + << d_mp + << std::endl; +//=} + + /*` + The expected value of the derivative is 0.5. This central difference rule in this + example is ill-conditioned, meaning it suffers from slight loss of precision. With that + in mind, the results agree with the expected value of 0.5.*/ + + //] + + //[ND3 + + /*` + We can take this a step further and use our derivative function to compute + a partial derivative. For example if we take the incomplete gamma function + ['P(a, z)], and take the derivative with respect to /z/ at /(2,2)/ then we + can calculate the result as shown below, for good measure we'll compare with + the "correct" result obtained from a call to ['gamma_p_derivative], the results + agree to approximately 44 digits: + */ + + cpp_dec_float_50 gd = derivative( + cpp_dec_float_50(2), + cpp_dec_float_50(1.0E-9), + [](const cpp_dec_float_50& x) ->cpp_dec_float_50 + { + return boost::math::gamma_p(2, x); + } + ); + // 2.70670566473225383787998989944968806815263091819151e-01 + std::cout + << std::setprecision(std::numeric_limits<cpp_dec_float_50>::digits10) + << gd + << std::endl; + // 2.70670566473225383787998989944968806815253190143120e-01 + std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl; + //] + + //[GI2 + + /* The function can now be called as follows: */ +/*=int main(int, char**) +{*/ + using boost::math::constants::pi; + typedef boost::multiprecision::cpp_dec_float_50 mp_type; + + const float j2_f = + integral(0.0F, + pi<float>(), + 0.01F, + cyl_bessel_j_integral_rep<float>(2U, 1.23F)) / pi<float>(); + + const double j2_d = + integral(0.0, + pi<double>(), + 0.0001, + cyl_bessel_j_integral_rep<double>(2U, 1.23)) / pi<double>(); + + const mp_type j2_mp = + integral(mp_type(0), + pi<mp_type>(), + mp_type(1.0E-20), + cyl_bessel_j_integral_rep<mp_type>(2U, mp_type(123) / 100)) / pi<mp_type>(); + + // 0.166369 + std::cout + << std::setprecision(std::numeric_limits<float>::digits10) + << j2_f + << std::endl; + + // 0.166369383786814 + std::cout + << std::setprecision(std::numeric_limits<double>::digits10) + << j2_d + << std::endl; + + // 0.16636938378681407351267852431513159437103348245333 + std::cout + << std::setprecision(std::numeric_limits<mp_type>::digits10) + << j2_mp + << std::endl; + + // + // Print true value for comparison: + // 0.166369383786814073512678524315131594371033482453329 + std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl; +//=} + + //] + + std::cout << std::setprecision(std::numeric_limits< ::mp_type>::digits10) << std::scientific; + std::cout << mysin(boost::math::constants::pi< ::mp_type>() / 4) << std::endl; + std::cout << boost::multiprecision::sin(boost::math::constants::pi< ::mp_type>() / 4) << std::endl; + + return 0; +} + +/* + +Program output: + +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +9.822663964796047e-001 +9.82266396479604757017335009796882833995903762577173e-01 +9.8226639647960475701733500979688283399590376257717309069410413822165082248153638454147004236848917775e-01 +4.752916e+000 +4.752915525615998e+000 +4.75291552561599819047013317456355991350189758431460e+00 +5.000029e-001 +4.999999999998876e-001 +4.99999999999999999999999999999999999999999999999999e-01 +2.70670566473225383787998989944968806815263091819151e-01 +2.70670566473225383787998989944968806815253190143120e-01 +7.0710678118654752440084436210484903928483593768847403658833986900e-01 +7.0710678118654752440084436210484903928483593768847403658833986900e-01 +*/ + +#else + +int main() { return 0; } + +#endif diff --git a/libs/multiprecision/example/gauss_laguerre_quadrature.cpp b/libs/multiprecision/example/gauss_laguerre_quadrature.cpp new file mode 100644 index 0000000000..87a8bb0bc3 --- /dev/null +++ b/libs/multiprecision/example/gauss_laguerre_quadrature.cpp @@ -0,0 +1,514 @@ +#include <cmath> +#include <cstdint> +#include <functional> +#include <iomanip> +#include <iostream> +#include <numeric> +#include <boost/math/constants/constants.hpp> +#include <boost/math/special_functions/cbrt.hpp> +#include <boost/math/special_functions/factorials.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <boost/math/tools/roots.hpp> +#include <boost/noncopyable.hpp> + +#define CPP_BIN_FLOAT 1 +#define CPP_DEC_FLOAT 2 +#define CPP_MPFR_FLOAT 3 + +//#define MP_TYPE CPP_BIN_FLOAT +#define MP_TYPE CPP_DEC_FLOAT +//#define MP_TYPE CPP_MPFR_FLOAT + +namespace +{ + struct digits_characteristics + { + static const int digits10 = 300; + static const int guard_digits = 6; + }; +} + +#if (MP_TYPE == CPP_BIN_FLOAT) + #include <boost/multiprecision/cpp_bin_float.hpp> + namespace mp = boost::multiprecision; + typedef mp::number<mp::cpp_bin_float<digits_characteristics::digits10 + digits_characteristics::guard_digits>, mp::et_off> mp_type; +#elif (MP_TYPE == CPP_DEC_FLOAT) + #include <boost/multiprecision/cpp_dec_float.hpp> + namespace mp = boost::multiprecision; + typedef mp::number<mp::cpp_dec_float<digits_characteristics::digits10 + digits_characteristics::guard_digits>, mp::et_off> mp_type; +#elif (MP_TYPE == CPP_MPFR_FLOAT) + #include <boost/multiprecision/mpfr.hpp> + namespace mp = boost::multiprecision; + typedef mp::number<mp::mpfr_float_backend<digits_characteristics::digits10 + digits_characteristics::guard_digits>, mp::et_off> mp_type; +#else +#error MP_TYPE is undefined +#endif + +template<typename T> +class laguerre_function_object +{ +public: + laguerre_function_object(const int n, const T a) : order(n), + alpha(a), + p1 (0), + d2 (0) { } + + laguerre_function_object(const laguerre_function_object& other) : order(other.order), + alpha(other.alpha), + p1 (other.p1), + d2 (other.d2) { } + + ~laguerre_function_object() { } + + T operator()(const T& x) const + { + // Calculate (via forward recursion): + // * the value of the Laguerre function L(n, alpha, x), called (p2), + // * the value of the derivative of the Laguerre function (d2), + // * and the value of the corresponding Laguerre function of + // previous order (p1). + + // Return the value of the function (p2) in order to be used as a + // function object with Boost.Math root-finding. Store the values + // of the Laguerre function derivative (d2) and the Laguerre function + // of previous order (p1) in class members for later use. + + p1 = T(0); + T p2 = T(1); + d2 = T(0); + + T j_plus_alpha(alpha); + T two_j_plus_one_plus_alpha_minus_x(1 + alpha - x); + + int j; + + const T my_two(2); + + for(j = 0; j < order; ++j) + { + const T p0(p1); + + // Set the value of the previous Laguerre function. + p1 = p2; + + // Use a recurrence relation to compute the value of the Laguerre function. + p2 = ((two_j_plus_one_plus_alpha_minus_x * p1) - (j_plus_alpha * p0)) / (j + 1); + + ++j_plus_alpha; + two_j_plus_one_plus_alpha_minus_x += my_two; + } + + // Set the value of the derivative of the Laguerre function. + d2 = ((p2 * j) - (j_plus_alpha * p1)) / x; + + // Return the value of the Laguerre function. + return p2; + } + + const T& previous () const { return p1; } + const T& derivative() const { return d2; } + + static bool root_tolerance(const T& a, const T& b) + { + using std::abs; + + // The relative tolerance here is: ((a - b) * 2) / (a + b). + return (abs((a - b) * 2) < ((a + b) * boost::math::tools::epsilon<T>())); + } + +private: + const int order; + const T alpha; + mutable T p1; + mutable T d2; + + laguerre_function_object(); + + const laguerre_function_object& operator=(const laguerre_function_object&); +}; + +template<typename T> +class guass_laguerre_abscissas_and_weights : private boost::noncopyable +{ +public: + guass_laguerre_abscissas_and_weights(const int n, const T a) : order(n), + alpha(a), + valid(true), + xi (), + wi () + { + if(alpha < -20.0F) + { + // TBD: If we ever boostify this, throw a range error here. + // If so, then also document it in the docs. + std::cout << "Range error: the order of the Laguerre function must exceed -20.0." << std::endl; + } + else + { + calculate(); + } + } + + virtual ~guass_laguerre_abscissas_and_weights() { } + + const std::vector<T>& abscissas() const { return xi; } + const std::vector<T>& weights () const { return wi; } + + bool get_valid() const { return valid; } + +private: + const int order; + const T alpha; + bool valid; + + std::vector<T> xi; + std::vector<T> wi; + + void calculate() + { + using std::abs; + + std::cout << "finding approximate roots..." << std::endl; + + std::vector<boost::math::tuple<T, T> > root_estimates; + + root_estimates.reserve(static_cast<typename std::vector<boost::math::tuple<T, T> >::size_type>(order)); + + const laguerre_function_object<T> laguerre_object(order, alpha); + + // Set the initial values of the step size and the running step + // to be used for finding the estimate of the first root. + T step_size = 0.01F; + T step = step_size; + + T first_laguerre_root = 0.0F; + + bool first_laguerre_root_has_been_found = true; + + if(alpha < -1.0F) + { + // Iteratively step through the Laguerre function using a + // small step-size in order to find a rough estimate of + // the first zero. + + bool this_laguerre_value_is_negative = (laguerre_object(mp_type(0)) < 0); + + static const int j_max = 10000; + + int j; + + for(j = 0; (j < j_max) && (this_laguerre_value_is_negative != (laguerre_object(step) < 0)); ++j) + { + // Increment the step size until the sign of the Laguerre function + // switches. This indicates a zero-crossing, signalling the next root. + step += step_size; + } + + if(j >= j_max) + { + first_laguerre_root_has_been_found = false; + } + else + { + // We have found the first zero-crossing. Put a loose bracket around + // the root using a window. Here, we know that the first root lies + // between (x - step_size) < root < x. + + // Before storing the approximate root, perform a couple of + // bisection steps in order to tighten up the root bracket. + boost::uintmax_t a_couple_of_iterations = 3U; + const std::pair<T, T> + first_laguerre_root = boost::math::tools::bisect(laguerre_object, + step - step_size, + step, + laguerre_function_object<T>::root_tolerance, + a_couple_of_iterations); + + static_cast<void>(a_couple_of_iterations); + } + } + else + { + // Calculate an estimate of the 1st root of a generalized Laguerre + // function using either a Taylor series or an expansion in Bessel + // function zeros. The Bessel function zeros expansion is from Tricomi. + + // Here, we obtain an estimate of the first zero of J_alpha(x). + + T j_alpha_m1; + + if(alpha < 1.4F) + { + // For small alpha, use a short series obtained from Mathematica(R). + // Series[BesselJZero[v, 1], {v, 0, 3}] + // N[%, 12] + j_alpha_m1 = ((( 0.09748661784476F + * alpha - 0.17549359276115F) + * alpha + 1.54288974259931F) + * alpha + 2.40482555769577F); + } + else + { + // For larger alpha, use the first line of Eqs. 10.21.40 in the NIST Handbook. + const T alpha_pow_third(boost::math::cbrt(alpha)); + const T alpha_pow_minus_two_thirds(T(1) / (alpha_pow_third * alpha_pow_third)); + + j_alpha_m1 = alpha * ((((( + 0.043F + * alpha_pow_minus_two_thirds - 0.0908F) + * alpha_pow_minus_two_thirds - 0.00397F) + * alpha_pow_minus_two_thirds + 1.033150F) + * alpha_pow_minus_two_thirds + 1.8557571F) + * alpha_pow_minus_two_thirds + 1.0F); + } + + const T vf = ((order * 4.0F) + (alpha * 2.0F) + 2.0F); + const T vf2 = vf * vf; + const T j_alpha_m1_sqr = j_alpha_m1 * j_alpha_m1; + + first_laguerre_root = (j_alpha_m1_sqr * (-0.6666666666667F + ((0.6666666666667F * alpha) * alpha) + (0.3333333333333F * j_alpha_m1_sqr) + vf2)) / (vf2 * vf); + } + + if(first_laguerre_root_has_been_found) + { + bool this_laguerre_value_is_negative = (laguerre_object(mp_type(0)) < 0); + + // Re-set the initial value of the step-size based on the + // estimate of the first root. + step_size = first_laguerre_root / 2; + step = step_size; + + // Step through the Laguerre function using a step-size + // of dynamic width in order to find the zero crossings + // of the Laguerre function, providing rough estimates + // of the roots. Refine the brackets with a few bisection + // steps, and store the results as bracketed root estimates. + + while(static_cast<int>(root_estimates.size()) < order) + { + // Increment the step size until the sign of the Laguerre function + // switches. This indicates a zero-crossing, signalling the next root. + step += step_size; + + if(this_laguerre_value_is_negative != (laguerre_object(step) < 0)) + { + // We have found the next zero-crossing. + + // Change the running sign of the Laguerre function. + this_laguerre_value_is_negative = (!this_laguerre_value_is_negative); + + // We have found the first zero-crossing. Put a loose bracket around + // the root using a window. Here, we know that the first root lies + // between (x - step_size) < root < x. + + // Before storing the approximate root, perform a couple of + // bisection steps in order to tighten up the root bracket. + boost::uintmax_t a_couple_of_iterations = 3U; + const std::pair<T, T> + root_estimate_bracket = boost::math::tools::bisect(laguerre_object, + step - step_size, + step, + laguerre_function_object<T>::root_tolerance, + a_couple_of_iterations); + + static_cast<void>(a_couple_of_iterations); + + // Store the refined root estimate as a bracketed range in a tuple. + root_estimates.push_back(boost::math::tuple<T, T>(root_estimate_bracket.first, + root_estimate_bracket.second)); + + if(root_estimates.size() >= static_cast<std::size_t>(2U)) + { + // Determine the next step size. This is based on the distance between + // the previous two roots, whereby the estimates of the previous roots + // are computed by taking the average of the lower and upper range of + // the root-estimate bracket. + + const T r0 = ( boost::math::get<0>(*(root_estimates.rbegin() + 1U)) + + boost::math::get<1>(*(root_estimates.rbegin() + 1U))) / 2; + + const T r1 = ( boost::math::get<0>(*root_estimates.rbegin()) + + boost::math::get<1>(*root_estimates.rbegin())) / 2; + + const T distance_between_previous_roots = r1 - r0; + + step_size = distance_between_previous_roots / 3; + } + } + } + + const T norm_g = + ((alpha == 0) ? T(-1) + : -boost::math::tgamma(alpha + order) / boost::math::factorial<T>(order - 1)); + + xi.reserve(root_estimates.size()); + wi.reserve(root_estimates.size()); + + // Calculate the abscissas and weights to full precision. + for(std::size_t i = static_cast<std::size_t>(0U); i < root_estimates.size(); ++i) + { + std::cout << "calculating abscissa and weight for index: " << i << std::endl; + + // Calculate the abscissas using iterative root-finding. + + // Select the maximum allowed iterations, being at least 20. + // The determination of the maximum allowed iterations is + // based on the number of decimal digits in the numerical + // type T. + const int my_digits10 = static_cast<int>(static_cast<float>(boost::math::tools::digits<T>()) * 0.301F); + const boost::uintmax_t number_of_iterations_allowed = (std::max)(20, my_digits10 / 2); + + boost::uintmax_t number_of_iterations_used = number_of_iterations_allowed; + + // Perform the root-finding using ACM TOMS 748 from Boost.Math. + const std::pair<T, T> + laguerre_root_bracket = boost::math::tools::toms748_solve(laguerre_object, + boost::math::get<0>(root_estimates[i]), + boost::math::get<1>(root_estimates[i]), + laguerre_function_object<T>::root_tolerance, + number_of_iterations_used); + + // Based on the result of *each* root-finding operation, re-assess + // the validity of the Guass-Laguerre abscissas and weights object. + valid &= (number_of_iterations_used < number_of_iterations_allowed); + + // Compute the Laguerre root as the average of the values from + // the solved root bracket. + const T laguerre_root = ( laguerre_root_bracket.first + + laguerre_root_bracket.second) / 2; + + // Calculate the weight for this Laguerre root. Here, we calculate + // the derivative of the Laguerre function and the value of the + // previous Laguerre function on the x-axis at the value of this + // Laguerre root. + static_cast<void>(laguerre_object(laguerre_root)); + + // Store the abscissa and weight for this index. + xi.push_back(laguerre_root); + wi.push_back(norm_g / ((laguerre_object.derivative() * order) * laguerre_object.previous())); + } + } + } +}; + +namespace +{ + template<typename T> + struct gauss_laguerre_ai + { + public: + gauss_laguerre_ai(const T X) : x(X) + { + using std::exp; + using std::sqrt; + + zeta = ((sqrt(x) * x) * 2) / 3; + + const T zeta_times_48_pow_sixth = sqrt(boost::math::cbrt(zeta * 48)); + + factor = 1 / ((sqrt(boost::math::constants::pi<T>()) * zeta_times_48_pow_sixth) * (exp(zeta) * gamma_of_five_sixths())); + } + + gauss_laguerre_ai(const gauss_laguerre_ai& other) : x (other.x), + zeta (other.zeta), + factor(other.factor) { } + + T operator()(const T& t) const + { + using std::sqrt; + + return factor / sqrt(boost::math::cbrt(2 + (t / zeta))); + } + + private: + const T x; + T zeta; + T factor; + + static const T& gamma_of_five_sixths() + { + static const T value = boost::math::tgamma(T(5) / 6); + + return value; + } + + const gauss_laguerre_ai& operator=(const gauss_laguerre_ai&); + }; + + template<typename T> + T gauss_laguerre_airy_ai(const T x) + { + static const float digits_factor = static_cast<float>(std::numeric_limits<mp_type>::digits10) / 300.0F; + static const int laguerre_order = static_cast<int>(600.0F * digits_factor); + + static const guass_laguerre_abscissas_and_weights<T> abscissas_and_weights(laguerre_order, -T(1) / 6); + + T airy_ai_result; + + if(abscissas_and_weights.get_valid()) + { + const gauss_laguerre_ai<T> this_gauss_laguerre_ai(x); + + airy_ai_result = + std::inner_product(abscissas_and_weights.abscissas().begin(), + abscissas_and_weights.abscissas().end(), + abscissas_and_weights.weights().begin(), + T(0), + std::plus<T>(), + [&this_gauss_laguerre_ai](const T& this_abscissa, const T& this_weight) -> T + { + return this_gauss_laguerre_ai(this_abscissa) * this_weight; + }); + } + else + { + // TBD: Consider an error message. + airy_ai_result = T(0); + } + + return airy_ai_result; + } +} + +int main() +{ + // Use Gauss-Laguerre integration to compute airy_ai(120 / 7). + + // 9 digits + // 3.89904210e-22 + + // 10 digits + // 3.899042098e-22 + + // 50 digits. + // 3.8990420982303275013276114626640705170145070824318e-22 + + // 100 digits. + // 3.899042098230327501327611462664070517014507082431797677146153303523108862015228 + // 864136051942933142648e-22 + + // 200 digits. + // 3.899042098230327501327611462664070517014507082431797677146153303523108862015228 + // 86413605194293314264788265460938200890998546786740097437064263800719644346113699 + // 77010905030516409847054404055843899790277e-22 + + // 300 digits. + // 3.899042098230327501327611462664070517014507082431797677146153303523108862015228 + // 86413605194293314264788265460938200890998546786740097437064263800719644346113699 + // 77010905030516409847054404055843899790277083960877617919088116211775232728792242 + // 9346416823281460245814808276654088201413901972239996130752528e-22 + + // 500 digits. + // 3.899042098230327501327611462664070517014507082431797677146153303523108862015228 + // 86413605194293314264788265460938200890998546786740097437064263800719644346113699 + // 77010905030516409847054404055843899790277083960877617919088116211775232728792242 + // 93464168232814602458148082766540882014139019722399961307525276722937464859521685 + // 42826483602153339361960948844649799257455597165900957281659632186012043089610827 + // 78871305322190941528281744734605934497977375094921646511687434038062987482900167 + // 45127557400365419545e-22 + + // Mathematica(R) or Wolfram's Alpha: + // N[AiryAi[120 / 7], 300] + std::cout << std::setprecision(digits_characteristics::digits10) + << gauss_laguerre_airy_ai(mp_type(120) / 7) + << std::endl; +} diff --git a/libs/multiprecision/example/gmp_snips.cpp b/libs/multiprecision/example/gmp_snips.cpp new file mode 100644 index 0000000000..d3347da180 --- /dev/null +++ b/libs/multiprecision/example/gmp_snips.cpp @@ -0,0 +1,117 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/gmp.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +void t1() +{ + //[mpz_eg +//=#include <boost/multiprecision/gmp.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + mpz_int v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + + std::cout << v << std::endl; // prints 1000! + + // Access the underlying representation: + mpz_t z; + mpz_init(z); + mpz_set(z, v.backend().data()); + mpz_clear(z); +//= return 0; +//=} +//] +} + +void t2() +{ +//[mpf_eg +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/math/special_functions/gamma.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + // Operations at variable precision and limited standard library support: + mpf_float a = 2; + mpf_float::default_precision(1000); + std::cout << mpf_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full standard library support: + mpf_float_100 b = 2; + std::cout << std::numeric_limits<mpf_float_100>::digits << std::endl; + // We can use any C++ std lib function: + std::cout << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; + + // Access the underlying representation: + mpf_t f; + mpf_init(f); + mpf_set(f, a.backend().data()); + mpf_clear(f); +//= return 0; +//=} +//] +} + +void t3() +{ +//[mpq_eg +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/multiprecision/gmp.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + mpq_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << v << std::endl; // prints 1000! / 10 + std::cout << numerator(v) << std::endl; + std::cout << denominator(v) << std::endl; + + mpq_rational w(2, 3); // component wise constructor + std::cout << w << std::endl; // prints 2/3 + + // Access the underlying data: + mpq_t q; + mpq_init(q); + mpq_set(q, v.backend().data()); + mpq_clear(q); +//= return 0; +//=} +//] +} + +int main() +{ + t1(); + t2(); + t3(); + return 0; +} + diff --git a/libs/multiprecision/example/hypergeometric_luke_algorithms.cpp b/libs/multiprecision/example/hypergeometric_luke_algorithms.cpp new file mode 100644 index 0000000000..f7ff1c4b1b --- /dev/null +++ b/libs/multiprecision/example/hypergeometric_luke_algorithms.cpp @@ -0,0 +1,803 @@ + +/////////////////////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2013 - 2014. +// Copyright John Maddock 2013. +// Distributed under the Boost Software License, +// Version 1.0. (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 +// + +#include <algorithm> +#include <cstdint> +#include <deque> +#include <functional> +#include <iostream> +#include <limits> +#include <numeric> +#include <vector> +#include <boost/math/constants/constants.hpp> +#include <boost/noncopyable.hpp> + +//#define USE_CPP_BIN_FLOAT +#define USE_CPP_DEC_FLOAT +//#define USE_MPFR + +#if !defined(DIGIT_COUNT) +#define DIGIT_COUNT 100 +#endif + +#define HAS_STD_CHRONO + +#if defined(HAS_STD_CHRONO) + #include <chrono> + #define STD_CHRONO std::chrono +#else + #include <boost/chrono.hpp> + #define STD_CHRONO boost::chrono +#endif + +#if defined(USE_CPP_BIN_FLOAT) + #include <boost/multiprecision/cpp_bin_float.hpp> + typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<DIGIT_COUNT + 10> > mp_type; +#elif defined(USE_CPP_DEC_FLOAT) + #include <boost/multiprecision/cpp_dec_float.hpp> + typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<DIGIT_COUNT + 10> > mp_type; +#elif defined(USE_MPFR) + #include <boost/multiprecision/mpfr.hpp> + typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<DIGIT_COUNT + 10> > mp_type; +#else + #error no multiprecision floating type is defined +#endif + +template <class clock_type> +struct stopwatch +{ +public: + typedef typename clock_type::duration duration_type; + + stopwatch() : m_start(clock_type::now()) { } + + stopwatch(const stopwatch& other) : m_start(other.m_start) { } + + stopwatch& operator=(const stopwatch& other) + { + m_start = other.m_start; + return *this; + } + + ~stopwatch() { } + + duration_type elapsed() const + { + return (clock_type::now() - m_start); + } + + void reset() + { + m_start = clock_type::now(); + } + +private: + typename clock_type::time_point m_start; +}; + +namespace my_math +{ + template<class T> T chebyshev_t(const std::int32_t n, const T& x); + + template<class T> T chebyshev_t(const std::uint32_t n, const T& x, std::vector<T>* vp); + + template<class T> bool isneg(const T& x) { return (x < T(0)); } + + template<class T> const T& zero() { static const T value_zero(0); return value_zero; } + template<class T> const T& one () { static const T value_one (1); return value_one; } + template<class T> const T& two () { static const T value_two (2); return value_two; } +} + +namespace orthogonal_polynomial_series +{ + template<typename T> static inline T orthogonal_polynomial_template(const T& x, const std::uint32_t n, std::vector<T>* const vp = static_cast<std::vector<T>*>(0u)) + { + // Compute the value of an orthogonal chebyshev polinomial. + // Use stable upward recursion. + + if(vp != nullptr) + { + vp->clear(); + vp->reserve(static_cast<std::size_t>(n + 1u)); + } + + T y0 = my_math::one<T>(); + + if(vp != nullptr) { vp->push_back(y0); } + + if(n == static_cast<std::uint32_t>(0u)) + { + return y0; + } + + T y1 = x; + + if(vp != nullptr) { vp->push_back(y1); } + + if(n == static_cast<std::uint32_t>(1u)) + { + return y1; + } + + T a = my_math::two <T>(); + T b = my_math::zero<T>(); + T c = my_math::one <T>(); + + T yk; + + // Calculate higher orders using the recurrence relation. + // The direction of stability is upward recursion. + for(std::int32_t k = static_cast<std::int32_t>(2); k <= static_cast<std::int32_t>(n); ++k) + { + yk = (((a * x) + b) * y1) - (c * y0); + + y0 = y1; + y1 = yk; + + if(vp != nullptr) { vp->push_back(yk); } + } + + return yk; + } +} + +template<class T> T my_math::chebyshev_t(const std::int32_t n, const T& x) +{ + if(my_math::isneg(x)) + { + const bool b_negate = ((n % static_cast<std::int32_t>(2)) != static_cast<std::int32_t>(0)); + + const T y = chebyshev_t(n, -x); + + return (!b_negate ? y : -y); + } + + if(n < static_cast<std::int32_t>(0)) + { + const std::int32_t nn = static_cast<std::int32_t>(-n); + + return chebyshev_t(nn, x); + } + else + { + return orthogonal_polynomial_series::orthogonal_polynomial_template(x, static_cast<std::uint32_t>(n)); + } +} + +template<class T> T my_math::chebyshev_t(const std::uint32_t n, const T& x, std::vector<T>* const vp) { return orthogonal_polynomial_series::orthogonal_polynomial_template(x, static_cast<std::int32_t>(n), vp); } + +namespace util +{ + template <class T> float digit_scale() + { + const int d = ((std::max)(std::numeric_limits<T>::digits10, 15)); + return static_cast<float>(d) / 300.0F; + } +} + +namespace examples +{ + namespace nr_006 + { + template<typename T> class hypergeometric_pfq_base : private boost::noncopyable + { + public: + virtual ~hypergeometric_pfq_base() { } + + virtual void ccoef() const = 0; + + virtual T series() const + { + using my_math::chebyshev_t; + + // Compute the Chebyshev coefficients. + // Get the values of the shifted Chebyshev polynomials. + std::vector<T> chebyshev_t_shifted_values; + const T z_shifted = ((Z / W) * static_cast<std::int32_t>(2)) - static_cast<std::int32_t>(1); + + chebyshev_t(static_cast<std::uint32_t>(C.size()), + z_shifted, + &chebyshev_t_shifted_values); + + // Luke: C ---------- COMPUTE SCALE FACTOR ---------- + // Luke: C + // Luke: C ---------- SCALE THE COEFFICIENTS ---------- + // Luke: C + + // The coefficient scaling is preformed after the Chebyshev summation, + // and it is carried out with a single division operation. + bool b_neg = false; + + const T scale = std::accumulate(C.begin(), + C.end(), + T(0), + [&b_neg](T& scale_sum, const T& ck) -> T + { + ((!b_neg) ? (scale_sum += ck) : (scale_sum -= ck)); + b_neg = (!b_neg); + return scale_sum; + }); + + // Compute the result of the series expansion using unscaled coefficients. + const T sum = std::inner_product(C.begin(), + C.end(), + chebyshev_t_shifted_values.begin(), + T(0)); + + // Return the properly scaled result. + return sum / scale; + } + + protected: + const T Z; + const T W; + mutable std::deque<T> C; + + hypergeometric_pfq_base(const T& z, + const T& w) : Z(z), + W(w), + C(0u) { } + + virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 500.0F); } + }; + + template<typename T> class ccoef4_hypergeometric_0f1 : public hypergeometric_pfq_base<T> + { + public: + ccoef4_hypergeometric_0f1(const T& c, + const T& z, + const T& w) : hypergeometric_pfq_base<T>(z, w), + CP(c) { } + + virtual ~ccoef4_hypergeometric_0f1() { } + + virtual void ccoef() const + { + // See Luke 1977 page 80. + const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1)); + const std::int32_t N2 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(2)); + + // Luke: C ---------- START COMPUTING COEFFICIENTS USING ---------- + // Luke: C ---------- BACKWARD RECURRENCE SCHEME ---------- + // Luke: C + T A3(0); + T A2(0); + T A1(boost::math::tools::root_epsilon<T>()); + + hypergeometric_pfq_base<T>::C.resize(1u, A1); + + std::int32_t X1 = N2; + + T C1 = T(1) - CP; + + const T Z1 = T(4) / hypergeometric_pfq_base<T>::W; + + for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k) + { + const T DIVFAC = T(1) / X1; + + --X1; + + // The terms have been slightly re-arranged resulting in lower complexity. + // Parentheses have been added to avoid reliance on operator precedence. + const T term = (A2 - ((A3 * DIVFAC) * X1)) + + ((A2 * X1) * ((1 + (C1 + X1)) * Z1)) + + ((A1 * X1) * ((DIVFAC - (C1 * Z1)) + (X1 * Z1))); + + hypergeometric_pfq_base<T>::C.push_front(term); + + A3 = A2; + A2 = A1; + A1 = hypergeometric_pfq_base<T>::C.front(); + } + + hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2); + } + + private: + const T CP; + }; + + template<typename T> class ccoef1_hypergeometric_1f0 : public hypergeometric_pfq_base<T> + { + public: + ccoef1_hypergeometric_1f0(const T& a, + const T& z, + const T& w) : hypergeometric_pfq_base<T>(z, w), + AP(a) { } + + virtual ~ccoef1_hypergeometric_1f0() { } + + virtual void ccoef() const + { + // See Luke 1977 page 67. + const std::int32_t N1 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(1)); + const std::int32_t N2 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(2)); + + // Luke: C ---------- START COMPUTING COEFFICIENTS USING ---------- + // Luke: C ---------- BACKWARD RECURRENCE SCHEME ---------- + // Luke: C + T A2(0); + T A1(boost::math::tools::root_epsilon<T>()); + + hypergeometric_pfq_base<T>::C.resize(1u, A1); + + std::int32_t X1 = N2; + + T V1 = T(1) - AP; + + // Here, we have corrected what appears to be an error in Luke's code. + + // Luke's original code listing has: + // AFAC = 2 + FOUR/W + // But it appears as though the correct form is: + // AFAC = 2 - FOUR/W. + + const T AFAC = 2 - (T(4) / hypergeometric_pfq_base<T>::W); + + for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k) + { + --X1; + + // The terms have been slightly re-arranged resulting in lower complexity. + // Parentheses have been added to avoid reliance on operator precedence. + const T term = -(((X1 * AFAC) * A1) + ((X1 + V1) * A2)) / (X1 - V1); + + hypergeometric_pfq_base<T>::C.push_front(term); + + A2 = A1; + A1 = hypergeometric_pfq_base<T>::C.front(); + } + + hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2); + } + + private: + const T AP; + + virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 1600.0F); } + }; + + template<typename T> class ccoef3_hypergeometric_1f1 : public hypergeometric_pfq_base<T> + { + public: + ccoef3_hypergeometric_1f1(const T& a, + const T& c, + const T& z, + const T& w) : hypergeometric_pfq_base<T>(z, w), + AP(a), + CP(c) { } + + virtual ~ccoef3_hypergeometric_1f1() { } + + virtual void ccoef() const + { + // See Luke 1977 page 74. + const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1)); + const std::int32_t N2 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(2)); + + // Luke: C ---------- START COMPUTING COEFFICIENTS USING ---------- + // Luke: C ---------- BACKWARD RECURRENCE SCHEME ---------- + // Luke: C + T A3(0); + T A2(0); + T A1(boost::math::tools::root_epsilon<T>()); + + hypergeometric_pfq_base<T>::C.resize(1u, A1); + + std::int32_t X = N1; + std::int32_t X1 = N2; + + T XA = X + AP; + T X3A = (X + 3) - AP; + + const T Z1 = T(4) / hypergeometric_pfq_base<T>::W; + + for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k) + { + --X; + --X1; + --XA; + --X3A; + + const T X3A_over_X2 = X3A / static_cast<std::int32_t>(X + 2); + + // The terms have been slightly re-arranged resulting in lower complexity. + // Parentheses have been added to avoid reliance on operator precedence. + const T PART1 = A1 * (((X + CP) * Z1) - X3A_over_X2); + const T PART2 = A2 * (Z1 * ((X + 3) - CP) + (XA / X1)); + const T PART3 = A3 * X3A_over_X2; + + const T term = (((PART1 + PART2) + PART3) * X1) / XA; + + hypergeometric_pfq_base<T>::C.push_front(term); + + A3 = A2; + A2 = A1; + A1 = hypergeometric_pfq_base<T>::C.front(); + } + + hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2); + } + + private: + const T AP; + const T CP; + }; + + template<typename T> class ccoef6_hypergeometric_1f2 : public hypergeometric_pfq_base<T> + { + public: + ccoef6_hypergeometric_1f2(const T& a, + const T& b, + const T& c, + const T& z, + const T& w) : hypergeometric_pfq_base<T>(z, w), + AP(a), + BP(b), + CP(c) { } + + virtual ~ccoef6_hypergeometric_1f2() { } + + virtual void ccoef() const + { + // See Luke 1977 page 85. + const std::int32_t N1 = static_cast<std::int32_t>(this->N() + static_cast<std::int32_t>(1)); + + // Luke: C ---------- START COMPUTING COEFFICIENTS USING ---------- + // Luke: C ---------- BACKWARD RECURRENCE SCHEME ---------- + // Luke: C + T A4(0); + T A3(0); + T A2(0); + T A1(boost::math::tools::root_epsilon<T>()); + + hypergeometric_pfq_base<T>::C.resize(1u, A1); + + std::int32_t X = N1; + T PP = X + AP; + + const T Z1 = T(4) / hypergeometric_pfq_base<T>::W; + + for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k) + { + --X; + --PP; + + const std::int32_t TWO_X = static_cast<std::int32_t>(X * 2); + const std::int32_t X_PLUS_1 = static_cast<std::int32_t>(X + 1); + const std::int32_t X_PLUS_3 = static_cast<std::int32_t>(X + 3); + const std::int32_t X_PLUS_4 = static_cast<std::int32_t>(X + 4); + + const T QQ = T(TWO_X + 3) / static_cast<std::int32_t>(TWO_X + static_cast<std::int32_t>(5)); + const T SS = (X + BP) * (X + CP); + + // The terms have been slightly re-arranged resulting in lower complexity. + // Parentheses have been added to avoid reliance on operator precedence. + const T PART1 = A1 * (((PP - (QQ * (PP + 1))) * 2) + (SS * Z1)); + const T PART2 = (A2 * (X + 2)) * ((((TWO_X + 1) * PP) / X_PLUS_1) - ((QQ * 4) * (PP + 1)) + (((TWO_X + 3) * (PP + 2)) / X_PLUS_3) + ((Z1 * 2) * (SS - (QQ * (X_PLUS_1 + BP)) * (X_PLUS_1 + CP)))); + const T PART3 = A3 * ((((X_PLUS_3 - AP) - (QQ * (X_PLUS_4 - AP))) * 2) + (((QQ * Z1) * (X_PLUS_4 - BP)) * (X_PLUS_4 - CP))); + const T PART4 = ((A4 * QQ) * (X_PLUS_4 - AP)) / X_PLUS_3; + + const T term = (((PART1 - PART2) + (PART3 - PART4)) * X_PLUS_1) / PP; + + hypergeometric_pfq_base<T>::C.push_front(term); + + A4 = A3; + A3 = A2; + A2 = A1; + A1 = hypergeometric_pfq_base<T>::C.front(); + } + + hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2); + } + + private: + const T AP; + const T BP; + const T CP; + }; + + template<typename T> class ccoef2_hypergeometric_2f1 : public hypergeometric_pfq_base<T> + { + public: + ccoef2_hypergeometric_2f1(const T& a, + const T& b, + const T& c, + const T& z, + const T& w) : hypergeometric_pfq_base<T>(z, w), + AP(a), + BP(b), + CP(c) { } + + virtual ~ccoef2_hypergeometric_2f1() { } + + virtual void ccoef() const + { + // See Luke 1977 page 59. + const std::int32_t N1 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(1)); + const std::int32_t N2 = static_cast<std::int32_t>(N() + static_cast<std::int32_t>(2)); + + // Luke: C ---------- START COMPUTING COEFFICIENTS USING ---------- + // Luke: C ---------- BACKWARD RECURRENCE SCHEME ---------- + // Luke: C + T A3(0); + T A2(0); + T A1(boost::math::tools::root_epsilon<T>()); + + hypergeometric_pfq_base<T>::C.resize(1u, A1); + + std::int32_t X = N1; + std::int32_t X1 = N2; + std::int32_t X3 = static_cast<std::int32_t>((X * 2) + 3); + + T X3A = (X + 3) - AP; + T X3B = (X + 3) - BP; + + const T Z1 = T(4) / hypergeometric_pfq_base<T>::W; + + for(std::int32_t k = static_cast<std::int32_t>(0); k < N1; ++k) + { + --X; + --X1; + --X3A; + --X3B; + X3 -= 2; + + const std::int32_t X_PLUS_2 = static_cast<std::int32_t>(X + 2); + + const T XAB = T(1) / ((X + AP) * (X + BP)); + + // The terms have been slightly re-arranged resulting in lower complexity. + // Parentheses have been added to avoid reliance on operator precedence. + const T PART1 = (A1 * X1) * (2 - (((AP + X1) * (BP + X1)) * ((T(X3) / X_PLUS_2) * XAB)) + ((CP + X) * (XAB * Z1))); + const T PART2 = (A2 * XAB) * ((X3A * X3B) - (X3 * ((X3A + X3B) - 1)) + (((3 - CP) + X) * (X1 * Z1))); + const T PART3 = (A3 * X1) * (X3A / X_PLUS_2) * (X3B * XAB); + + const T term = (PART1 + PART2) - PART3; + + hypergeometric_pfq_base<T>::C.push_front(term); + + A3 = A2; + A2 = A1; + A1 = hypergeometric_pfq_base<T>::C.front(); + } + + hypergeometric_pfq_base<T>::C.front() /= static_cast<std::int32_t>(2); + } + + private: + const T AP; + const T BP; + const T CP; + + virtual std::int32_t N() const { return static_cast<std::int32_t>(util::digit_scale<T>() * 1600.0F); } + }; + + template<class T> T luke_ccoef4_hypergeometric_0f1(const T& a, const T& x); + template<class T> T luke_ccoef1_hypergeometric_1f0(const T& a, const T& x); + template<class T> T luke_ccoef3_hypergeometric_1f1(const T& a, const T& b, const T& x); + template<class T> T luke_ccoef6_hypergeometric_1f2(const T& a, const T& b, const T& c, const T& x); + template<class T> T luke_ccoef2_hypergeometric_2f1(const T& a, const T& b, const T& c, const T& x); + } +} + +template<class T> +T examples::nr_006::luke_ccoef4_hypergeometric_0f1(const T& a, const T& x) +{ + const ccoef4_hypergeometric_0f1<T> hypergeometric_0f1_object(a, x, T(-20)); + + hypergeometric_0f1_object.ccoef(); + + return hypergeometric_0f1_object.series(); +} + +template<class T> +T examples::nr_006::luke_ccoef1_hypergeometric_1f0(const T& a, const T& x) +{ + const ccoef1_hypergeometric_1f0<T> hypergeometric_1f0_object(a, x, T(-20)); + + hypergeometric_1f0_object.ccoef(); + + return hypergeometric_1f0_object.series(); +} + +template<class T> +T examples::nr_006::luke_ccoef3_hypergeometric_1f1(const T& a, const T& b, const T& x) +{ + const ccoef3_hypergeometric_1f1<T> hypergeometric_1f1_object(a, b, x, T(-20)); + + hypergeometric_1f1_object.ccoef(); + + return hypergeometric_1f1_object.series(); +} + +template<class T> +T examples::nr_006::luke_ccoef6_hypergeometric_1f2(const T& a, const T& b, const T& c, const T& x) +{ + const ccoef6_hypergeometric_1f2<T> hypergeometric_1f2_object(a, b, c, x, T(-20)); + + hypergeometric_1f2_object.ccoef(); + + return hypergeometric_1f2_object.series(); +} + +template<class T> +T examples::nr_006::luke_ccoef2_hypergeometric_2f1(const T& a, const T& b, const T& c, const T& x) +{ + const ccoef2_hypergeometric_2f1<T> hypergeometric_2f1_object(a, b, c, x, T(-20)); + + hypergeometric_2f1_object.ccoef(); + + return hypergeometric_2f1_object.series(); +} + +int main() +{ + stopwatch<STD_CHRONO::high_resolution_clock> my_stopwatch; + float total_time = 0.0F; + + std::vector<mp_type> hypergeometric_0f1_results(20U); + std::vector<mp_type> hypergeometric_1f0_results(20U); + std::vector<mp_type> hypergeometric_1f1_results(20U); + std::vector<mp_type> hypergeometric_2f1_results(20U); + std::vector<mp_type> hypergeometric_1f2_results(20U); + + const mp_type a(mp_type(3) / 7); + const mp_type b(mp_type(2) / 3); + const mp_type c(mp_type(1) / 4); + + std::int_least16_t i; + + std::cout << "test hypergeometric_0f1." << std::endl; + i = 1U; + my_stopwatch.reset(); + + // Generate a table of values of Hypergeometric0F1. + // Compare with the Mathematica command: + // Table[N[HypergeometricPFQ[{}, {3/7}, -(i*EulerGamma)], 100], {i, 1, 20, 1}] + std::for_each(hypergeometric_0f1_results.begin(), + hypergeometric_0f1_results.end(), + [&i, &a](mp_type& new_value) + { + const mp_type x(-(boost::math::constants::euler<mp_type>() * i)); + + new_value = examples::nr_006::luke_ccoef4_hypergeometric_0f1(a, x); + + ++i; + }); + + total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count(); + + // Print the values of Hypergeometric0F1. + std::for_each(hypergeometric_0f1_results.begin(), + hypergeometric_0f1_results.end(), + [](const mp_type& h) + { + std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl; + }); + + std::cout << "test hypergeometric_1f0." << std::endl; + i = 1U; + my_stopwatch.reset(); + + // Generate a table of values of Hypergeometric1F0. + // Compare with the Mathematica command: + // Table[N[HypergeometricPFQ[{3/7}, {}, -(i*EulerGamma)], 100], {i, 1, 20, 1}] + std::for_each(hypergeometric_1f0_results.begin(), + hypergeometric_1f0_results.end(), + [&i, &a](mp_type& new_value) + { + const mp_type x(-(boost::math::constants::euler<mp_type>() * i)); + + new_value = examples::nr_006::luke_ccoef1_hypergeometric_1f0(a, x); + + ++i; + }); + + total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count(); + + // Print the values of Hypergeometric1F0. + std::for_each(hypergeometric_1f0_results.begin(), + hypergeometric_1f0_results.end(), + [](const mp_type& h) + { + std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl; + }); + + std::cout << "test hypergeometric_1f1." << std::endl; + i = 1U; + my_stopwatch.reset(); + + // Generate a table of values of Hypergeometric1F1. + // Compare with the Mathematica command: + // Table[N[HypergeometricPFQ[{3/7}, {2/3}, -(i*EulerGamma)], 100], {i, 1, 20, 1}] + std::for_each(hypergeometric_1f1_results.begin(), + hypergeometric_1f1_results.end(), + [&i, &a, &b](mp_type& new_value) + { + const mp_type x(-(boost::math::constants::euler<mp_type>() * i)); + + new_value = examples::nr_006::luke_ccoef3_hypergeometric_1f1(a, b, x); + + ++i; + }); + + total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count(); + + // Print the values of Hypergeometric1F1. + std::for_each(hypergeometric_1f1_results.begin(), + hypergeometric_1f1_results.end(), + [](const mp_type& h) + { + std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl; + }); + + std::cout << "test hypergeometric_1f2." << std::endl; + i = 1U; + my_stopwatch.reset(); + + // Generate a table of values of Hypergeometric1F2. + // Compare with the Mathematica command: + // Table[N[HypergeometricPFQ[{3/7}, {2/3, 1/4}, -(i*EulerGamma)], 100], {i, 1, 20, 1}] + std::for_each(hypergeometric_1f2_results.begin(), + hypergeometric_1f2_results.end(), + [&i, &a, &b, &c](mp_type& new_value) + { + const mp_type x(-(boost::math::constants::euler<mp_type>() * i)); + + new_value = examples::nr_006::luke_ccoef6_hypergeometric_1f2(a, b, c, x); + + ++i; + }); + + total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count(); + + // Print the values of Hypergeometric1F2. + std::for_each(hypergeometric_1f2_results.begin(), + hypergeometric_1f2_results.end(), + [](const mp_type& h) + { + std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl; + }); + + std::cout << "test hypergeometric_2f1." << std::endl; + i = 1U; + my_stopwatch.reset(); + + // Generate a table of values of Hypergeometric2F1. + // Compare with the Mathematica command: + // Table[N[HypergeometricPFQ[{3/7, 2/3}, {1/4}, -(i * EulerGamma)], 100], {i, 1, 20, 1}] + std::for_each(hypergeometric_2f1_results.begin(), + hypergeometric_2f1_results.end(), + [&i, &a, &b, &c](mp_type& new_value) + { + const mp_type x(-(boost::math::constants::euler<mp_type>() * i)); + + new_value = examples::nr_006::luke_ccoef2_hypergeometric_2f1(a, b, c, x); + + ++i; + }); + + total_time += STD_CHRONO::duration_cast<STD_CHRONO::duration<float> >(my_stopwatch.elapsed()).count(); + + // Print the values of Hypergeometric2F1. + std::for_each(hypergeometric_2f1_results.begin(), + hypergeometric_2f1_results.end(), + [](const mp_type& h) + { + std::cout << std::setprecision(DIGIT_COUNT) << h << std::endl; + }); + + std::cout << "Total execution time = " << std::setprecision(3) << total_time << "s" << std::endl; +} diff --git a/libs/multiprecision/example/integer_examples.cpp b/libs/multiprecision/example/integer_examples.cpp new file mode 100644 index 0000000000..67187978d9 --- /dev/null +++ b/libs/multiprecision/example/integer_examples.cpp @@ -0,0 +1,230 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_int.hpp> +#include <iostream> +#include <iomanip> +#include <vector> + +//[FAC1 + +/*` +In this simple example, we'll write a routine to print out all of the factorials +which will fit into a 128-bit integer. At the end of the routine we do some +fancy iostream formatting of the results: +*/ +/*= +#include <boost/multiprecision/cpp_int.hpp> +#include <iostream> +#include <iomanip> +#include <vector> +*/ + +void print_factorials() +{ + using boost::multiprecision::cpp_int; + // + // Print all the factorials that will fit inside a 128-bit integer. + // + // Begin by building a big table of factorials, once we know just how + // large the largest is, we'll be able to "pretty format" the results. + // + // Calculate the largest number that will fit inside 128 bits, we could + // also have used numeric_limits<int128_t>::max() for this value: + cpp_int limit = (cpp_int(1) << 128) - 1; + // + // Our table of values: + std::vector<cpp_int> results; + // + // Initial values: + unsigned i = 1; + cpp_int factorial = 1; + // + // Cycle through the factorials till we reach the limit: + while(factorial < limit) + { + results.push_back(factorial); + ++i; + factorial *= i; + } + // + // Lets see how many digits the largest factorial was: + unsigned digits = results.back().str().size(); + // + // Now print them out, using right justification, while we're at it + // we'll indicate the limit of each integer type, so begin by defining + // the limits for 16, 32, 64 etc bit integers: + cpp_int limits[] = { + (cpp_int(1) << 16) - 1, + (cpp_int(1) << 32) - 1, + (cpp_int(1) << 64) - 1, + (cpp_int(1) << 128) - 1, + }; + std::string bit_counts[] = { "16", "32", "64", "128" }; + unsigned current_limit = 0; + for(unsigned j = 0; j < results.size(); ++j) + { + if(limits[current_limit] < results[j]) + { + std::string message = "Limit of " + bit_counts[current_limit] + " bit integers"; + std::cout << std::setfill('.') << std::setw(digits+1) << std::right << message << std::setfill(' ') << std::endl; + ++current_limit; + } + std::cout << std::setw(digits + 1) << std::right << results[j] << std::endl; + } +} + +/*` +The output from this routine is: +[pre + 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 +................Limit of 16 bit integers + 362880 + 3628800 + 39916800 + 479001600 +................Limit of 32 bit integers + 6227020800 + 87178291200 + 1307674368000 + 20922789888000 + 355687428096000 + 6402373705728000 + 121645100408832000 + 2432902008176640000 +................Limit of 64 bit integers + 51090942171709440000 + 1124000727777607680000 + 25852016738884976640000 + 620448401733239439360000 + 15511210043330985984000000 + 403291461126605635584000000 + 10888869450418352160768000000 + 304888344611713860501504000000 + 8841761993739701954543616000000 + 265252859812191058636308480000000 + 8222838654177922817725562880000000 + 263130836933693530167218012160000000 + 8683317618811886495518194401280000000 + 295232799039604140847618609643520000000 +] +*/ + +//] + +//[BITOPS + +/*` +In this example we'll show how individual bits within an integer may be manipulated, +we'll start with an often needed calculation of ['2[super n] - 1], which we could obviously +implement like this: +*/ + +using boost::multiprecision::cpp_int; + +cpp_int b1(unsigned n) +{ + cpp_int r(1); + return (r << n) - 1; +} + +/*` +Calling: + + std::cout << std::hex << std::showbase << b1(200) << std::endl; + +Yields as expected: + +[pre 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF] + +However, we could equally just set the n'th bit in the result, like this: +*/ + +cpp_int b2(unsigned n) +{ + cpp_int r(0); + return --bit_set(r, n); +} + +/*` +Note how the `bit_set` function sets the specified bit in its argument and then returns a reference to the result - +which we can then simply decrement. The result from a call to `b2` is the same as that to `b1`. + +We can equally test bits, so for example the n'th bit of the result returned from `b2` shouldn't be set +unless we increment it first: + + assert(!bit_test(b1(200), 200)); // OK + assert(bit_test(++b1(200), 200)); // OK + +And of course if we flip the n'th bit after increment, then we should get back to zero: + + assert(!bit_flip(++b1(200), 200)); // OK +*/ + +//] + +int main() +{ + print_factorials(); + + std::cout << std::hex << std::showbase << b1(200) << std::endl; + std::cout << std::hex << std::showbase << b2(200) << std::endl; + assert(!bit_test(b1(200), 200)); // OK + assert(bit_test(++b1(200), 200)); // OK + assert(!bit_flip(++b1(200), 200)); // OK + return 0; +} + +/* + +Program output: + + 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 +................Limit of 16 bit integers + 362880 + 3628800 + 39916800 + 479001600 +................Limit of 32 bit integers + 6227020800 + 87178291200 + 1307674368000 + 20922789888000 + 355687428096000 + 6402373705728000 + 121645100408832000 + 2432902008176640000 +................Limit of 64 bit integers + 51090942171709440000 + 1124000727777607680000 + 25852016738884976640000 + 620448401733239439360000 + 15511210043330985984000000 + 403291461126605635584000000 + 10888869450418352160768000000 + 304888344611713860501504000000 + 8841761993739701954543616000000 + 265252859812191058636308480000000 + 8222838654177922817725562880000000 + 263130836933693530167218012160000000 + 8683317618811886495518194401280000000 + 295232799039604140847618609643520000000 + 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF + 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF + */ diff --git a/libs/multiprecision/example/logged_adaptor.cpp b/libs/multiprecision/example/logged_adaptor.cpp new file mode 100644 index 0000000000..e6270af6ec --- /dev/null +++ b/libs/multiprecision/example/logged_adaptor.cpp @@ -0,0 +1,119 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[logged_adaptor + +#include <boost/multiprecision/mpfi.hpp> +#include <boost/multiprecision/logged_adaptor.hpp> +#include <iostream> +#include <iomanip> +// +// Begin by overloading log_postfix_event so we can capture each arithmetic event as it happens: +// +namespace boost{ namespace multiprecision{ + +template <unsigned D> +inline void log_postfix_event(const mpfi_float_backend<D>& val, const char* event_description) +{ + // Print out the (relative) diameter of the interval: + using namespace boost::multiprecision; + number<mpfr_float_backend<D> > diam; + mpfi_diam(diam.backend().data(), val.data()); + std::cout << "Diameter was " << diam << " after operation: " << event_description << std::endl; +} +template <unsigned D, class T> +inline void log_postfix_event(const mpfi_float_backend<D>&, const T&, const char* event_description) +{ + // This version is never called in this example. +} + +}} + + +int main() +{ + using namespace boost::multiprecision; + typedef number<logged_adaptor<mpfi_float_backend<17> > > logged_type; + // + // Test case deliberately introduces cancellation error, relative size of interval + // gradually gets larger after each operation: + // + logged_type a = 1; + a /= 10; + + for(unsigned i = 0; i < 13; ++i) + { + logged_type b = a * 9; + b /= 10; + a -= b; + } + std::cout << "Final value was: " << a << std::endl; + return 0; +} + +//] + +/* +//[logged_adaptor_output + +Diameter was nan after operation: Default construct +Diameter was 0 after operation: Assignment from arithmetic type +Diameter was 4.33681e-18 after operation: /= +Diameter was nan after operation: Default construct +Diameter was 7.70988e-18 after operation: * +Diameter was 9.63735e-18 after operation: /= +Diameter was 1.30104e-16 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 1.30104e-16 after operation: * +Diameter was 1.38537e-16 after operation: /= +Diameter was 2.54788e-15 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 2.54788e-15 after operation: * +Diameter was 2.54863e-15 after operation: /= +Diameter was 4.84164e-14 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 4.84164e-14 after operation: * +Diameter was 4.84221e-14 after operation: /= +Diameter was 9.19962e-13 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 9.19962e-13 after operation: * +Diameter was 9.19966e-13 after operation: /= +Diameter was 1.74793e-11 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 1.74793e-11 after operation: * +Diameter was 1.74793e-11 after operation: /= +Diameter was 3.32107e-10 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 3.32107e-10 after operation: * +Diameter was 3.32107e-10 after operation: /= +Diameter was 6.31003e-09 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 6.31003e-09 after operation: * +Diameter was 6.31003e-09 after operation: /= +Diameter was 1.19891e-07 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 1.19891e-07 after operation: * +Diameter was 1.19891e-07 after operation: /= +Diameter was 2.27792e-06 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 2.27792e-06 after operation: * +Diameter was 2.27792e-06 after operation: /= +Diameter was 4.32805e-05 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 4.32805e-05 after operation: * +Diameter was 4.32805e-05 after operation: /= +Diameter was 0.00082233 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 0.00082233 after operation: * +Diameter was 0.00082233 after operation: /= +Diameter was 0.0156243 after operation: -= +Diameter was nan after operation: Default construct +Diameter was 0.0156243 after operation: * +Diameter was 0.0156243 after operation: /= +Diameter was 0.296861 after operation: -= +Final value was: {8.51569e-15,1.14843e-14} + +//] +*/ diff --git a/libs/multiprecision/example/mixed_integer_arithmetic.cpp b/libs/multiprecision/example/mixed_integer_arithmetic.cpp new file mode 100644 index 0000000000..48155115cc --- /dev/null +++ b/libs/multiprecision/example/mixed_integer_arithmetic.cpp @@ -0,0 +1,55 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +//[mixed_eg +#include <boost/multiprecision/cpp_int.hpp> + +int main() +{ + using namespace boost::multiprecision; + + boost::uint64_t i = (std::numeric_limits<boost::uint64_t>::max)(); + boost::uint64_t j = 1; + + uint128_t ui128; + uint256_t ui256; + // + // Start by performing arithmetic on 64-bit integers to yield 128-bit results: + // + std::cout << std::hex << std::showbase << i << std::endl; + std::cout << std::hex << std::showbase << add(ui128, i, j) << std::endl; + std::cout << std::hex << std::showbase << multiply(ui128, i, i) << std::endl; + // + // The try squaring a 128-bit integer to yield a 256-bit result: + // + ui128 = (std::numeric_limits<uint128_t>::max)(); + std::cout << std::hex << std::showbase << multiply(ui256, ui128, ui128) << std::endl; + + return 0; +} +//] + +/* + +Program output: + +//[mixed_output + +0xffffffffffffffff +0x10000000000000000 +0xFFFFFFFFFFFFFFFE0000000000000001 +0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE00000000000000000000000000000001 + +//] +*/ + diff --git a/libs/multiprecision/example/mpfi_snips.cpp b/libs/multiprecision/example/mpfi_snips.cpp new file mode 100644 index 0000000000..c3580a1941 --- /dev/null +++ b/libs/multiprecision/example/mpfi_snips.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[mpfi_eg +#include <boost/multiprecision/mpfi.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +int main() +{ + using namespace boost::multiprecision; + + // Operations at variable precision and no numeric_limits support: + mpfi_float a = 2; + mpfi_float::default_precision(1000); + std::cout << mpfi_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full numeric_limits support: + mpfi_float_100 b = 2; + std::cout << std::numeric_limits<mpfi_float_100>::digits << std::endl; + // We can use any C++ std lib function: + std::cout << log(b) << std::endl; // print log(2) + + // Access the underlying data: + mpfi_t r; + mpfi_init(r); + mpfi_set(r, b.backend().data()); + + // Construct some explicit intervals and perform set operations: + mpfi_float_50 i1(1, 2), i2(1.5, 2.5); + std::cout << intersect(i1, i2) << std::endl; + std::cout << hull(i1, i2) << std::endl; + std::cout << overlap(i1, i2) << std::endl; + std::cout << subset(i1, i2) << std::endl; + mpfi_clear(r); + return 0; +} +//] + diff --git a/libs/multiprecision/example/mpfr_snips.cpp b/libs/multiprecision/example/mpfr_snips.cpp new file mode 100644 index 0000000000..ccb5c9a4d7 --- /dev/null +++ b/libs/multiprecision/example/mpfr_snips.cpp @@ -0,0 +1,40 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[mpfr_eg +#include <boost/multiprecision/mpfr.hpp> +#include <boost/math/special_functions/gamma.hpp> +#include <iostream> + +int main() +{ + using namespace boost::multiprecision; + + // Operations at variable precision and no numeric_limits support: + mpfr_float a = 2; + mpfr_float::default_precision(1000); + std::cout << mpfr_float::default_precision() << std::endl; + std::cout << sqrt(a) << std::endl; // print root-2 + + // Operations at fixed precision and full numeric_limits support: + mpfr_float_100 b = 2; + std::cout << std::numeric_limits<mpfr_float_100>::digits << std::endl; + // We can use any C++ std lib function: + std::cout << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; + + // Access the underlying data: + mpfr_t r; + mpfr_init(r); + mpfr_set(r, b.backend().data(), GMP_RNDN); + mpfr_clear(r); + return 0; +} +//] + + diff --git a/libs/multiprecision/example/numeric_limits_snips.cpp b/libs/multiprecision/example/numeric_limits_snips.cpp new file mode 100644 index 0000000000..fbdc5c5e70 --- /dev/null +++ b/libs/multiprecision/example/numeric_limits_snips.cpp @@ -0,0 +1,435 @@ +// Copyright Paul A. Bristow 2013 +// Copyright John Maddock 2013 +// Copyright Christopher Kormanyos + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +// Examples of numeric_limits usage as snippets for multiprecision documentation. + +// Includes text as Quickbook comments. + +#include <iostream> +#include <iomanip> +#include <string> +#include <sstream> +#include <limits> // numeric_limits +#include <iomanip> +#include <locale> +#include <boost/assert.hpp> + +#include <boost/math/constants/constants.hpp> +#include <boost/math/special_functions/nonfinite_num_facets.hpp> + + + +#include <boost/math/special_functions/factorials.hpp> +#include <boost/math/special_functions/next.hpp> +#include <boost/math/tools/precision.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> // is decimal. +#include <boost/multiprecision/cpp_bin_float.hpp> // is binary. + +#include <boost/test/unit_test.hpp> // Boost.Test +#include <boost/test/floating_point_comparison.hpp> + +int test_main(int argc, char**const argv) +{ + try + { + +// Example of portable way to get std::numeric_limits<T>::max_digits10. + +//[max_digits10_1 +/*`For example, to be portable, including older platforms: +*/ + + typedef float T; // Any type: `double`, cpp_dec_float_50, bin_128bit_double_type ... + +#if defined(BOOST_NO_CXX11_NUMERIC_LIMITS) + std::cout.precision(2 + std::numeric_limits<T>::digits * 3010U/10000U); +#else +# if (_MSC_VER <= 1600) // Correct wrong value for float. + std::cout.precision(2 + std::numeric_limits<T>::digits * 3010U/10000U); +# else + std::cout.precision(std::numeric_limits<T>::max_digits10); +# endif +#endif + + std::cout << "std::cout.precision = " << std::cout.precision() << std::endl; + + double x = 1.2345678901234567889; + + std::cout << "x = " << x << std::endl; // + +/*`which should output: + + std::cout.precision = 9 + x = 1.23456789 +*/ + +//] [/max_digits10_1] + + { +//[max_digits10_2 + + double write = 2./3; // Any arbitrary value that cannot be represented exactly. + double read = 0; + std::stringstream s; + s.precision(std::numeric_limits<double>::digits10); // or `float64_t` for 64-bit IEE754 double. + s << write; + s >> read; + if(read != write) + { + std::cout << std::setprecision(std::numeric_limits<double>::digits10) + << read << " != " << write << std::endl; + } + +//] [/max_digits10_2] + // 0.666666666666667 != 0.666666666666667 + } + + { +//[max_digits10_3 + + double pi = boost::math::double_constants::pi; + std::cout.precision(std::numeric_limits<double>::max_digits10); + std::cout << pi << std::endl; // 3.1415926535897931 + +//] [/max_digits10_3] + } + { +//[max_digits10_4 +/*`and similarly for a much higher precision type: +*/ + + using namespace boost::multiprecision; + + typedef number<cpp_dec_float<50> > cpp_dec_float_50; // 50 decimal digits. + + using boost::multiprecision::cpp_dec_float_50; + + cpp_dec_float_50 pi = boost::math::constants::pi<cpp_dec_float_50>(); + std::cout.precision(std::numeric_limits<cpp_dec_float_50>::max_digits10); + std::cout << pi << std::endl; + // 3.141592653589793238462643383279502884197169399375105820974944592307816406 +//] [/max_digits10_4] + } + + { +//[max_digits10_5 + + for (int i = 2; i < 15; i++) + { + std::cout << std::setw(std::numeric_limits<int>::max_digits10) + << boost::math::factorial<double>(i) << std::endl; + } + +//] [/max_digits10_5] + } + + } + catch(std::exception ex) + { + std::cout << "Caught Exception " << ex.what() << std::endl; + } + + { +//[max_digits10_6 + + typedef double T; + + bool denorm = std::numeric_limits<T>::denorm_min() < std::numeric_limits<T>::min(); + BOOST_ASSERT(denorm); + +//] [/max_digits10_6] + } + + { + unsigned char c = 256; + std::cout << "char c = " << (int)c << std::endl; + } + + { +//[digits10_1 + std::cout + << std::setw(std::numeric_limits<short>::digits10 +1 +1) // digits10+1, and +1 for sign. + << std::showpos << (std::numeric_limits<short>::max)() // +32767 + << std::endl + << std::setw(std::numeric_limits<short>::digits10 +1 +1) + << (std::numeric_limits<short>::min)() << std::endl; // -32767 +//] [/digits10_1] + } + + { +//[digits10_2 + std::cout + << std::setw(std::numeric_limits<unsigned short>::digits10 +1 +1) // digits10+1, and +1 for sign. + << std::showpos << (std::numeric_limits<unsigned short>::max)() // 65535 + << std::endl + << std::setw(std::numeric_limits<unsigned short>::digits10 +1 +1) // digits10+1, and +1 for sign. + << (std::numeric_limits<unsigned short>::min)() << std::endl; // 0 +//] [/digits10_2] + } + + std::cout <<std::noshowpos << std::endl; + + { +//[digits10_3 + std::cout.precision(std::numeric_limits<double>::max_digits10); + double d = 1e15; + double dp1 = d+1; + std::cout << d << "\n" << dp1 << std::endl; + // 1000000000000000 + // 1000000000000001 + std::cout << dp1 - d << std::endl; // 1 +//] [/digits10_3] + } + + { +//[digits10_4 + std::cout.precision(std::numeric_limits<double>::max_digits10); + double d = 1e16; + double dp1 = d+1; + std::cout << d << "\n" << dp1 << std::endl; + // 10000000000000000 + // 10000000000000000 + std::cout << dp1 - d << std::endl; // 0 !!! +//] [/digits10_4] + } + + { +//[epsilon_1 + std::cout.precision(std::numeric_limits<double>::max_digits10); + double d = 1.; + double eps = std::numeric_limits<double>::epsilon(); + double dpeps = d+eps; + std::cout << std::showpoint // Ensure all trailing zeros are shown. + << d << "\n" // 1.0000000000000000 + << dpeps << std::endl; // 2.2204460492503131e-016 + std::cout << dpeps - d // 1.0000000000000002 + << std::endl; +//] [epsilon_1] + } + + { +//[epsilon_2 + double one = 1.; + double nad = boost::math::float_next(one); + std::cout << nad << "\n" // 1.0000000000000002 + << nad - one // 2.2204460492503131e-016 + << std::endl; +//] [epsilon_2] + } + { +//[epsilon_3 + std::cout.precision(std::numeric_limits<double>::max_digits10); + double d = 1.; + double eps = std::numeric_limits<double>::epsilon(); + double dpeps = d + eps/2; + + std::cout << std::showpoint // Ensure all trailing zeros are shown. + << dpeps << "\n" // 1.0000000000000000 + << eps/2 << std::endl; // 1.1102230246251565e-016 + std::cout << dpeps - d // 0.00000000000000000 + << std::endl; +//] [epsilon_3] + } + + { + typedef double RealType; +//[epsilon_4 +/*`A tolerance might be defined using this version of epsilon thus: +*/ + RealType tolerance = boost::math::tools::epsilon<RealType>() * 2; +//] [epsilon_4] + } + + { +//[digits10_5 + -(std::numeric_limits<double>::max)() == std::numeric_limits<double>::lowest(); +//] [/digits10_5] + } + + { +//[denorm_min_1 + std::cout.precision(std::numeric_limits<double>::max_digits10); + if (std::numeric_limits<double>::has_denorm == std::denorm_present) + { + double d = std::numeric_limits<double>::denorm_min(); + + std::cout << d << std::endl; // 4.9406564584124654e-324 + + int exponent; + + double significand = frexp(d, &exponent); + std::cout << "exponent = " << std::hex << exponent << std::endl; // fffffbcf + std::cout << "significand = " << std::hex << significand << std::endl; // 0.50000000000000000 + } + else + { + std::cout << "No denormalization. " << std::endl; + } +//] [denorm_min_1] + } + + { +//[round_error_1 + double round_err = std::numeric_limits<double>::epsilon() // 2.2204460492503131e-016 + * std::numeric_limits<double>::round_error(); // 1/2 + std::cout << round_err << std::endl; // 1.1102230246251565e-016 +//] [/round_error_1] + } + + { + typedef double T; +//[tolerance_1 +/*`For example, if we want a tolerance that might suit about 9 arithmetical operations, +say sqrt(9) = 3, we could define: +*/ + + T tolerance = 3 * std::numeric_limits<T>::epsilon(); + +/*`This is very widely used in Boost.Math testing +with Boost.Test's macro `BOOST_CHECK_CLOSE_FRACTION` +*/ + + T expected = 1.0; + T calculated = 1.0 + std::numeric_limits<T>::epsilon(); + + BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance); + +//] [/tolerance_1] + } + + { +//[tolerance_2 + + using boost::multiprecision::number; + using boost::multiprecision::cpp_dec_float; + using boost::multiprecision::et_off; + + typedef number<cpp_dec_float<50>, et_off > cpp_dec_float_50; // 50 decimal digits. +/*`[note that Boost.Test does not yet allow floating-point comparisons with expression templates on, +so the default expression template parameter has been replaced by `et_off`.] +*/ + + cpp_dec_float_50 tolerance = 3 * std::numeric_limits<cpp_dec_float_50>::epsilon(); + cpp_dec_float_50 expected = boost::math::constants::two_pi<cpp_dec_float_50>(); + cpp_dec_float_50 calculated = 2 * boost::math::constants::pi<cpp_dec_float_50>(); + + BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance); + +//] [/tolerance_2] + } + + { +//[tolerance_3 + + using boost::multiprecision::cpp_bin_float_quad; + + cpp_bin_float_quad tolerance = 3 * std::numeric_limits<cpp_bin_float_quad>::epsilon(); + cpp_bin_float_quad expected = boost::math::constants::two_pi<cpp_bin_float_quad>(); + cpp_bin_float_quad calculated = 2 * boost::math::constants::pi<cpp_bin_float_quad>(); + + BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance); + +//] [/tolerance_3] + } + + { +//[nan_1] + +/*`NaN can be used with binary multiprecision types like `cpp_bin_float_quad`: +*/ + using boost::multiprecision::cpp_bin_float_quad; + + if (std::numeric_limits<cpp_bin_float_quad>::has_quiet_NaN == true) + { + cpp_bin_float_quad tolerance = 3 * std::numeric_limits<cpp_bin_float_quad>::epsilon(); + + cpp_bin_float_quad NaN = std::numeric_limits<cpp_bin_float_quad>::quiet_NaN(); + std::cout << "cpp_bin_float_quad NaN is " << NaN << std::endl; // cpp_bin_float_quad NaN is nan + + cpp_bin_float_quad expected = NaN; + cpp_bin_float_quad calculated = 2 * NaN; + // Comparisons of NaN's always fail: + bool b = expected == calculated; + std::cout << b << std::endl; + BOOST_CHECK_NE(expected, expected); + BOOST_CHECK_NE(expected, calculated); + } + else + { + std::cout << "Type " << typeid(cpp_bin_float_quad).name() << " does not have NaNs!" << std::endl; + } + +//] [/nan_1] + } + + { +//[facet_1] + +/*` +See [@boost:/libs/math/example/nonfinite_facet_sstream.cpp] +and we also need + + #include <boost/math/special_functions/nonfinite_num_facets.hpp> + +Then we can equally well use a multiprecision type cpp_bin_float_quad: + +*/ + using boost::multiprecision::cpp_bin_float_quad; + + typedef cpp_bin_float_quad T; + + using boost::math::nonfinite_num_put; + using boost::math::nonfinite_num_get; + { + std::locale old_locale; + std::locale tmp_locale(old_locale, new nonfinite_num_put<char>); + std::locale new_locale(tmp_locale, new nonfinite_num_get<char>); + std::stringstream ss; + ss.imbue(new_locale); + T inf = std::numeric_limits<T>::infinity(); + ss << inf; // Write out. + assert(ss.str() == "inf"); + T r; + ss >> r; // Read back in. + assert(inf == r); // Confirms that the floating-point values really are identical. + std::cout << "infinity output was " << ss.str() << std::endl; + std::cout << "infinity input was " << r << std::endl; + } + +/*` + infinity output was inf + infinity input was inf + +Similarly we can do the same with NaN (except that we cannot use `assert`) +*/ + { + std::locale old_locale; + std::locale tmp_locale(old_locale, new nonfinite_num_put<char>); + std::locale new_locale(tmp_locale, new nonfinite_num_get<char>); + std::stringstream ss; + ss.imbue(new_locale); + T n; + T NaN = std::numeric_limits<T>::quiet_NaN(); + ss << NaN; // Write out. + assert(ss.str() == "nan"); + std::cout << "NaN output was " << ss.str() << std::endl; + ss >> n; // Read back in. + std::cout << "NaN input was " << n << std::endl; + } +/*` + NaN output was nan + NaN input was nan + +*/ +//] [/facet_1] + } + + return 0; + +} // int main() diff --git a/libs/multiprecision/example/random_snips.cpp b/libs/multiprecision/example/random_snips.cpp new file mode 100644 index 0000000000..c083bf2f21 --- /dev/null +++ b/libs/multiprecision/example/random_snips.cpp @@ -0,0 +1,134 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/random.hpp> +#include <iostream> +#include <iomanip> + +void t1() +{ +//[random_eg1 +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/multiprecision/random.hpp> +//= +//=int main() +//={ + using namespace boost::multiprecision; + using namespace boost::random; + + // + // Declare our random number generator type, the underlying generator + // is the Mersenne twister mt19937 engine, and 256 bits are generated: + // + typedef independent_bits_engine<mt19937, 256, mpz_int> generator_type; + generator_type gen; + // + // Generate some values: + // + std::cout << std::hex << std::showbase; + for(unsigned i = 0; i < 10; ++i) + std::cout << gen() << std::endl; +//= return 0; +//=} +//] +} + +void t2() +{ +//[random_eg2 +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/multiprecision/random.hpp> +//= +//=int main() +//={ + using namespace boost::multiprecision; + using namespace boost::random; + + // + // Generate integers in a given range using uniform_int, + // the underlying generator is invoked multiple times + // to generate enough bits: + // + mt19937 mt; + uniform_int_distribution<mpz_int> ui(0, mpz_int(1) << 256); + // + // Generate the numbers: + // + std::cout << std::hex << std::showbase; + for(unsigned i = 0; i < 10; ++i) + std::cout << ui(mt) << std::endl; + +//= return 0; +//=} +//] +} + +void t3() +{ +//[random_eg3 +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/multiprecision/random.hpp> +//= +//=int main() +//={ + using namespace boost::multiprecision; + using namespace boost::random; + // + // We need an underlying generator with at least as many bits as the + // floating point type to generate numbers in [0, 1) with all the bits + // in the floating point type randomly filled: + // + uniform_01<mpf_float_50> uf; + independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen; + // + // Generate the values: + // + std::cout << std::setprecision(50); + for(unsigned i = 0; i < 20; ++i) + std::cout << uf(gen) << std::endl; +//= return 0; +//=} +//] +} + +void t4() +{ +//[random_eg4 +//=#include <boost/multiprecision/gmp.hpp> +//=#include <boost/multiprecision/random.hpp> +//= +//=int main() +//={ + using namespace boost::multiprecision; + using namespace boost::random; + // + // We can repeat the above example, with other distributions: + // + uniform_real_distribution<mpf_float_50> ur(-20, 20); + gamma_distribution<mpf_float_50> gd(20); + independent_bits_engine<mt19937, 50L*1000L/301L, mpz_int> gen; + // + // Generate some values: + // + std::cout << std::setprecision(50); + for(unsigned i = 0; i < 20; ++i) + std::cout << ur(gen) << std::endl; + for(unsigned i = 0; i < 20; ++i) + std::cout << gd(gen) << std::endl; +//= return 0; +//=} +//] +} + +int main() +{ + t1(); + t2(); + t3(); + t4(); + return 0; +} + diff --git a/libs/multiprecision/example/safe_prime.cpp b/libs/multiprecision/example/safe_prime.cpp new file mode 100644 index 0000000000..71adf4f34a --- /dev/null +++ b/libs/multiprecision/example/safe_prime.cpp @@ -0,0 +1,45 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +//[safe_prime + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/miller_rabin.hpp> +#include <iostream> +#include <iomanip> + +int main() +{ + using namespace boost::random; + using namespace boost::multiprecision; + + typedef cpp_int int_type; + mt11213b base_gen(clock()); + independent_bits_engine<mt11213b, 256, int_type> gen(base_gen); + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. + // + mt19937 gen2(clock()); + + for(unsigned i = 0; i < 100000; ++i) + { + int_type n = gen(); + if(miller_rabin_test(n, 25, gen2)) + { + // Value n is probably prime, see if (n-1)/2 is also prime: + std::cout << "We have a probable prime with value: " << std::hex << std::showbase << n << std::endl; + if(miller_rabin_test((n-1)/2, 25, gen2)) + { + std::cout << "We have a safe prime with value: " << std::hex << std::showbase << n << std::endl; + return 0; + } + } + } + std::cout << "Ooops, no safe primes were found" << std::endl; + return 1; +} + +//] diff --git a/libs/multiprecision/example/tommath_snips.cpp b/libs/multiprecision/example/tommath_snips.cpp new file mode 100644 index 0000000000..63a78b22ef --- /dev/null +++ b/libs/multiprecision/example/tommath_snips.cpp @@ -0,0 +1,84 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/tommath.hpp> +#include <iostream> + +void t1() +{ +//[tommath_eg +//=#include <boost/multiprecision/tommath.hpp> +//=#include <iostream> +//= +//=int main() +//={ + boost::multiprecision::tom_int v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + + std::cout << v << std::endl; // prints 1000! + std::cout << std::hex << v << std::endl; // prints 1000! in hex format + + try{ + std::cout << std::hex << -v << std::endl; // Ooops! can't print a negative value in hex format! + } + catch(const std::runtime_error& e) + { + std::cout << e.what() << std::endl; + } + + try{ + // v is not a 2's complement type, bitwise operations are only supported + // on positive values: + v = -v & 2; + } + catch(const std::runtime_error& e) + { + std::cout << e.what() << std::endl; + } + +//= return 0; +//=} +//] +} + +void t3() +{ +//[mp_rat_eg +//=#include <boost/multiprecision/tommath.hpp> +//=#include <iostream> +//= +//=int main() +//={ + using namespace boost::multiprecision; + + tom_rational v = 1; + + // Do some arithmetic: + for(unsigned i = 1; i <= 1000; ++i) + v *= i; + v /= 10; + + std::cout << v << std::endl; // prints 1000! / 10 + std::cout << numerator(v) << std::endl; + std::cout << denominator(v) << std::endl; + + tom_rational w(2, 3); // Component wise constructor + std::cout << w << std::endl; // prints 2/3 + +//= return 0; +//=} +//] +} + +int main() +{ + t1(); + t3(); + return 0; +} + diff --git a/libs/multiprecision/index.html b/libs/multiprecision/index.html new file mode 100644 index 0000000000..df7430bd0e --- /dev/null +++ b/libs/multiprecision/index.html @@ -0,0 +1,15 @@ +<html> + <head> + <meta http-equiv="refresh" content="0; URL=doc/html/index.html"> + </head> + <body> + <P> + Automatic redirection failed, please go to <a href="doc/html/index.html">doc/html/index.html</a>. + </P> + <P>Copyright John Maddock 2001</P> + <P>Distributed under the Boost Software License, Version 1.0. (See accompanying file <A href="../../LICENSE_1_0.txt"> + LICENSE_1_0.txt</A> or copy at <A href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</A>).</P> + </body> +</html> + + diff --git a/libs/multiprecision/meta/libraries.json b/libs/multiprecision/meta/libraries.json new file mode 100644 index 0000000000..ce2f2eb180 --- /dev/null +++ b/libs/multiprecision/meta/libraries.json @@ -0,0 +1,16 @@ +{ + "key": "multiprecision", + "name": "Multiprecision", + "authors": [ + "John Maddock", + "Christopher Kormanyos" + ], + "description": "Extended precision arithmetic types for floating point, integer andrational arithmetic.", + "category": [ + "Math" + ], + "maintainers": [ + "John Maddock <john -at- johnmaddock.co.uk>", + "christopher Kormanyos <e_float -at- yahoo.com>" + ] +} diff --git a/libs/multiprecision/performance/Jamfile.v2 b/libs/multiprecision/performance/Jamfile.v2 new file mode 100644 index 0000000000..fbd6731561 --- /dev/null +++ b/libs/multiprecision/performance/Jamfile.v2 @@ -0,0 +1,133 @@ +# copyright John Maddock 2012 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project : requirements + <target-os>freebsd:<linkflags>"-lrt" + <target-os>linux:<linkflags>"-lrt" + <toolset>pgi:<linkflags>"-lrt" + <include>$(gmp_path) + <include>$(gmp_path)/mpfr + <include>$(gmp_path)/gmpfrxx + <include>$(mpfr_path) + <include>$(tommath_path) + <include>../../.. + <search>$(gmp_path) + <search>$(mpfr_path) + <search>$(mpfr_path)/build.vc10/lib/Win32/Debug + <search>$(tommath_path) + <link>static + <define>BOOST_ALL_NO_LIB + <debug-symbols>off + ; + + +lib gmp ; +lib mpfr ; + +if $(tommath_path) +{ + TOMMATH = [ GLOB $(tommath_path) : *.c ] ; +} +else +{ + lib tommath ; + TOMMATH = tommath ; +} + +exe performance_test : performance_test.cpp /boost/system//boost_system + : release + [ check-target-builds ../config//has_gmp : <define>TEST_MPF <define>TEST_MPZ <source>gmp : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <source>mpfr : ] + [ check-target-builds ../config//has_tommath : <define>TEST_TOMMATH <source>$(TOMMATH) : ] + <define>TEST_CPP_DEC_FLOAT + <define>TEST_CPP_INT + ; + +exe miller_rabin_performance : miller_rabin_performance.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : release + [ check-target-builds ../config//has_gmp : <define>TEST_MPF <define>TEST_MPZ <source>gmp : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <source>mpfr : ] + #[ check-target-builds ../config//has_tommath : <define>TEST_TOMMATH <source>$(TOMMATH) : ] + <define>TEST_CPP_DEC_FLOAT + <define>TEST_CPP_INT + ; + +exe sf_performance : sf_performance.cpp sf_performance_basic.cpp sf_performance_bessel.cpp + sf_performance_bessel1.cpp sf_performance_bessel2.cpp sf_performance_bessel3.cpp + sf_performance_bessel4.cpp sf_performance_bessel5.cpp sf_performance_bessel6.cpp + sf_performance_nct.cpp sf_performance_nct1.cpp + sf_performance_nct2.cpp sf_performance_nct3.cpp sf_performance_nct4.cpp + sf_performance_nct5.cpp sf_performance_nct6.cpp + sf_performance_poly.cpp + /boost/system//boost_system /boost/chrono//boost_chrono /boost/thread//boost_thread + : release + [ check-target-builds ../config//has_gmp : <define>TEST_MPF <define>TEST_MPZ <source>gmp : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <source>mpfr : ] + <define>TEST_CPP_DEC_FLOAT + <toolset>msvc:<cxxflags>-bigobj + ; + +exe delaunay_test : delaunay_test.cpp /boost/system//boost_system /boost/chrono//boost_chrono ; + +obj obj_linpack_benchmark_mpfr : linpack-benchmark.cpp + : release + [ check-target-builds ../config//has_mpfr : : <build>no ] + <define>TEST_MPFR_50 + ; + +obj obj_linpack_benchmark_mpf : linpack-benchmark.cpp + : release + [ check-target-builds ../config//has_gmp : : <build>no ] + <define>TEST_MPF_50 + ; + +obj obj_linpack_benchmark_cpp_float : linpack-benchmark.cpp + : release + <define>TEST_CPP_DEC_FLOAT + ; + +obj obj_linpack_benchmark_double : linpack-benchmark.cpp + : release + ; + +lib f2c ; + +exe linpack_benchmark_mpfr : obj_linpack_benchmark_mpfr mpfr f2c gmp + : release + [ check-target-builds ../config//has_mpfr : : <build>no ] + <define>TEST_MPFR_50 + ; + +exe linpack_benchmark_mpf : obj_linpack_benchmark_mpf gmp f2c + : release + [ check-target-builds ../config//has_gmp : : <build>no ] + <define>TEST_MPF_50 + ; + +exe linpack_benchmark_cpp_float : obj_linpack_benchmark_cpp_float f2c + : release + <define>TEST_CPP_DEC_FLOAT + ; + +exe linpack_benchmark_double : obj_linpack_benchmark_double f2c + : release + ; + +install miller_rabin_install : miller_rabin_performance : <location>. ; +install performance_test_install : performance_test : <location>. ; +install sf_performance_install : sf_performance : <location>. ; +install . : linpack_benchmark_double linpack_benchmark_cpp_float linpack_benchmark_mpf linpack_benchmark_mpfr ; +install delaunay_install : delaunay_test : <location>. ; + + + diff --git a/libs/multiprecision/performance/arithmetic_backend.hpp b/libs/multiprecision/performance/arithmetic_backend.hpp new file mode 100644 index 0000000000..a0574d193b --- /dev/null +++ b/libs/multiprecision/performance/arithmetic_backend.hpp @@ -0,0 +1,600 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_FLOAT_BACKEND_HPP +#define BOOST_MATH_FLOAT_BACKEND_HPP + +#include <iostream> +#include <iomanip> +#include <sstream> +#include <boost/cstdint.hpp> +#include <boost/lexical_cast.hpp> +#include <boost/math/concepts/real_concept.hpp> +#include <boost/multiprecision/number.hpp> +#include <boost/math/common_factor_rt.hpp> + +namespace boost{ +namespace multiprecision{ +namespace backends{ + +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable:4389 4244 4018 4244 4127) +#endif + +template <class Arithmetic> +struct arithmetic_backend +{ + typedef mpl::list<short, int, long, long long> signed_types; + typedef mpl::list<unsigned short, unsigned, unsigned long, unsigned long long> unsigned_types; + typedef mpl::list<float, double, long double> float_types; + typedef int exponent_type; + + arithmetic_backend(){} + arithmetic_backend(const arithmetic_backend& o) + { + m_value = o.m_value; + } + template <class A> + arithmetic_backend(const A& o, const typename enable_if<is_arithmetic<A> >::type* = 0) : m_value(o) {} + template <class A> + arithmetic_backend(const arithmetic_backend<A>& o) : m_value(o.data()) {} + arithmetic_backend& operator = (const arithmetic_backend& o) + { + m_value = o.m_value; + return *this; + } + template <class A> + typename enable_if<is_arithmetic<A>, arithmetic_backend&>::type operator = (A i) + { + m_value = i; + return *this; + } + template <class A> + arithmetic_backend& operator = (const arithmetic_backend<A>& i) + { + m_value = i.data(); + return *this; + } + arithmetic_backend& operator = (const char* s) + { + try + { + m_value = boost::lexical_cast<Arithmetic>(s); + } + catch(const bad_lexical_cast&) + { + throw std::runtime_error(std::string("Unable to interpret the string provided: \"") + s + std::string("\" as a compatible number type.")); + } + return *this; + } + void swap(arithmetic_backend& o) + { + std::swap(m_value, o.m_value); + } + std::string str(std::streamsize digits, std::ios_base::fmtflags f)const + { + std::stringstream ss; + ss.flags(f); + ss << std::setprecision(digits ? digits : std::numeric_limits<Arithmetic>::digits10 + 4) << m_value; + return ss.str(); + } + void do_negate(const mpl::true_&) + { + m_value = 1 + ~m_value; + } + void do_negate(const mpl::false_&) + { + m_value = -m_value; + } + void negate() + { + do_negate(is_unsigned<Arithmetic>()); + } + int compare(const arithmetic_backend& o)const + { + return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); + } + template <class A> + typename enable_if<is_arithmetic<A>, int>::type compare(A i)const + { + return m_value > static_cast<Arithmetic>(i) ? 1 : (m_value < static_cast<Arithmetic>(i) ? -1 : 0); + } + Arithmetic& data() { return m_value; } + const Arithmetic& data()const { return m_value; } +private: + Arithmetic m_value; +}; + +template <class R, class Arithmetic> +inline void eval_convert_to(R* result, const arithmetic_backend<Arithmetic>& backend) +{ + *result = backend.data(); +} + +template <class Arithmetic> +inline bool eval_eq(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + return a.data() == b.data(); +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2>, bool>::type eval_eq(const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + return a.data() == static_cast<Arithmetic>(b); +} +template <class Arithmetic> +inline bool eval_lt(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + return a.data() < b.data(); +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2>, bool>::type eval_lt(const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + return a.data() < static_cast<Arithmetic>(b); +} +template <class Arithmetic> +inline bool eval_gt(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + return a.data() > b.data(); +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2>, bool>::type eval_gt(const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + return a.data() > static_cast<Arithmetic>(b); +} + +template <class Arithmetic> +inline void eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + result.data() += o.data(); +} +template <class Arithmetic> +inline void eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + result.data() -= o.data(); +} +template <class Arithmetic> +inline void eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + result.data() *= o.data(); +} +template <class Arithmetic> +inline typename enable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + result.data() /= o.data(); +} +template <class Arithmetic> +inline typename disable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + if(!o.data()) + BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); + result.data() /= o.data(); +} + +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_add(arithmetic_backend<Arithmetic>& result, const A2& o) +{ + result.data() += o; +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_subtract(arithmetic_backend<Arithmetic>& result, const A2& o) +{ + result.data() -= o; +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_multiply(arithmetic_backend<Arithmetic>& result, const A2& o) +{ + result.data() *= o; +} +template <class Arithmetic, class A2> +inline typename enable_if_c<(is_arithmetic<A2>::value && !std::numeric_limits<Arithmetic>::has_infinity)>::type + eval_divide(arithmetic_backend<Arithmetic>& result, const A2& o) +{ + if(!o) + BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); + result.data() /= o; +} +template <class Arithmetic, class A2> +inline typename enable_if_c<(is_arithmetic<A2>::value && std::numeric_limits<Arithmetic>::has_infinity)>::type + eval_divide(arithmetic_backend<Arithmetic>& result, const A2& o) +{ + result.data() /= o; +} + +template <class Arithmetic> +inline void eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = a.data() + b.data(); +} +template <class Arithmetic> +inline void eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = a.data() - b.data(); +} +template <class Arithmetic> +inline void eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = a.data() * b.data(); +} +template <class Arithmetic> +inline typename enable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = a.data() / b.data(); +} +template <class Arithmetic> +inline typename disable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + if(!b.data()) + BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); + result.data() = a.data() / b.data(); +} + +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + result.data() = a.data() + b; +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + result.data() = a.data() - b; +} +template <class Arithmetic, class A2> +inline typename enable_if<is_arithmetic<A2> >::type eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + result.data() = a.data() * b; +} +template <class Arithmetic, class A2> +inline typename enable_if_c<(is_arithmetic<A2>::value && !std::numeric_limits<Arithmetic>::has_infinity)>::type + eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + if(!b) + BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); + result.data() = a.data() / b; +} +template <class Arithmetic, class A2> +inline typename enable_if_c<(is_arithmetic<A2>::value && std::numeric_limits<Arithmetic>::has_infinity)>::type + eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) +{ + result.data() = a.data() / b; +} + +template <class Arithmetic> +inline bool eval_is_zero(const arithmetic_backend<Arithmetic>& val) +{ + return val.data() == 0; +} + +template <class Arithmetic> +inline typename enable_if_c< + (!std::numeric_limits<Arithmetic>::is_specialized + || std::numeric_limits<Arithmetic>::is_signed), int>::type + eval_get_sign(const arithmetic_backend<Arithmetic>& val) +{ + return val.data() == 0 ? 0 : val.data() < 0 ? -1 : 1; +} +template <class Arithmetic> +inline typename disable_if_c< + (std::numeric_limits<Arithmetic>::is_specialized + || std::numeric_limits<Arithmetic>::is_signed), int>::type + eval_get_sign(const arithmetic_backend<Arithmetic>& val) +{ + return val.data() == 0 ? 0 : 1; +} + +template <class T> +inline typename enable_if<is_unsigned<T>, T>::type abs(T v) { return v; } + +template <class Arithmetic> +inline void eval_abs(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + using std::abs; + using boost::multiprecision::backends::abs; + result.data() = abs(o.data()); +} + +template <class Arithmetic> +inline void eval_fabs(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + result.data() = std::abs(o.data()); +} + +template <class Arithmetic> +inline void eval_floor(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = floor(o.data()); +} + +template <class Arithmetic> +inline void eval_ceil(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = ceil(o.data()); +} + +template <class Arithmetic> +inline void eval_sqrt(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = sqrt(o.data()); +} + +template <class Arithmetic> +inline int eval_fpclassify(const arithmetic_backend<Arithmetic>& o) +{ + return (boost::math::fpclassify)(o.data()); +} + +template <class Arithmetic> +inline void eval_trunc(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = trunc(o.data()); +} + +template <class Arithmetic> +inline void eval_round(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = round(o.data()); +} + +template <class Arithmetic> +inline void eval_frexp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, int* v) +{ + BOOST_MATH_STD_USING + result.data() = frexp(a.data(), v); +} + +template <class Arithmetic> +inline void eval_ldexp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, int v) +{ + BOOST_MATH_STD_USING + result.data() = ldexp(a.data(), v); +} + +template <class Arithmetic> +inline void eval_exp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = exp(o.data()); +} + +template <class Arithmetic> +inline void eval_log(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = log(o.data()); +} + +template <class Arithmetic> +inline void eval_log10(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = log10(o.data()); +} + +template <class Arithmetic> +inline void eval_sin(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = sin(o.data()); +} + +template <class Arithmetic> +inline void eval_cos(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = cos(o.data()); +} + +template <class Arithmetic> +inline void eval_tan(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = tan(o.data()); +} + +template <class Arithmetic> +inline void eval_acos(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = acos(o.data()); +} + +template <class Arithmetic> +inline void eval_asin(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = asin(o.data()); +} + +template <class Arithmetic> +inline void eval_atan(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = atan(o.data()); +} + +template <class Arithmetic> +inline void eval_sinh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = sinh(o.data()); +} + +template <class Arithmetic> +inline void eval_cosh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = cosh(o.data()); +} + +template <class Arithmetic> +inline void eval_tanh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) +{ + BOOST_MATH_STD_USING + result.data() = tanh(o.data()); +} + +template <class Arithmetic> +inline void eval_fmod(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + BOOST_MATH_STD_USING + result.data() = fmod(a.data(), b.data()); +} + +template <class Arithmetic> +inline void eval_pow(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + BOOST_MATH_STD_USING + result.data() = pow(a.data(), b.data()); +} + +template <class Arithmetic> +inline void eval_atan2(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + BOOST_MATH_STD_USING + result.data() = atan2(a.data(), b.data()); +} + +template <class Arithmetic, class I> +inline void eval_left_shift(arithmetic_backend<Arithmetic>& result, I val) +{ + result.data() <<= val; +} + +template <class Arithmetic, class I> +inline void eval_right_shift(arithmetic_backend<Arithmetic>& result, I val) +{ + result.data() >>= val; +} + +template <class Arithmetic> +inline void eval_modulus(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) +{ + result.data() %= a.data(); +} + +template <class Arithmetic> +inline void eval_bitwise_and(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) +{ + result.data() &= a.data(); +} + +template <class Arithmetic> +inline void eval_bitwise_or(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) +{ + result.data() |= a.data(); +} + +template <class Arithmetic> +inline void eval_bitwise_xor(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) +{ + result.data() ^= a.data(); +} + +template <class Arithmetic> +inline void eval_complement(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) +{ + result.data() = ~a.data(); +} + +template <class Arithmetic> +inline void eval_gcd(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = boost::math::gcd(a.data(), b.data()); +} + +template <class Arithmetic> +inline void eval_lcm(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) +{ + result.data() = boost::math::lcm(a.data(), b.data()); +} + +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif + +} // namespace backends + +using boost::multiprecision::backends::arithmetic_backend; + +template <class Arithmetic> +struct number_category<arithmetic_backend<Arithmetic> > : public mpl::int_<is_integral<Arithmetic>::value ? number_kind_integer : number_kind_floating_point>{}; + +namespace detail{ + +template <class Backend> +struct double_precision_type; + +template<class Arithmetic, boost::multiprecision::expression_template_option ET> +struct double_precision_type<number<arithmetic_backend<Arithmetic>, ET> > +{ + typedef number<arithmetic_backend<typename double_precision_type<Arithmetic>::type>, ET> type; +}; +template<> +struct double_precision_type<arithmetic_backend<boost::int32_t> > +{ + typedef arithmetic_backend<boost::int64_t> type; +}; + +} + +}} // namespaces + +namespace boost{ namespace math{ namespace tools{ + +template <> +inline double real_cast<double, concepts::real_concept>(concepts::real_concept r) +{ + return static_cast<double>(r.value()); +} + +}}} + + +namespace std{ + +template <class Arithmetic, boost::multiprecision::expression_template_option ExpressionTemplates> +class numeric_limits<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates > > : public std::numeric_limits<Arithmetic> +{ + typedef std::numeric_limits<Arithmetic> base_type; + typedef boost::multiprecision::number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates> number_type; +public: + BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } +}; + +template<> +class numeric_limits<boost::math::concepts::real_concept> : public std::numeric_limits<long double> +{ + typedef std::numeric_limits<long double> base_type; + typedef boost::math::concepts::real_concept number_type; +public: + static const number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } + static const number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } + static const number_type lowest() BOOST_NOEXCEPT { return -(max)(); } + static const number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } + static const number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } + static const number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } + static const number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } + static const number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } + static const number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } +}; + +} + +#include <boost/multiprecision/detail/integer_ops.hpp> + +#endif diff --git a/libs/multiprecision/performance/delaunay_test.cpp b/libs/multiprecision/performance/delaunay_test.cpp new file mode 100644 index 0000000000..d6fff13529 --- /dev/null +++ b/libs/multiprecision/performance/delaunay_test.cpp @@ -0,0 +1,295 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. +// Copyright 2012 Phil Endecott +// Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include "arithmetic_backend.hpp" +#include <boost/chrono.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int_distribution.hpp> + +#include <fstream> +#include <iomanip> + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +// Custom 128-bit maths used for exact calculation of the Delaunay test. +// Only the few operators actually needed here are implemented. + +struct int128_t { + int64_t high; + uint64_t low; + + int128_t() {} + int128_t(int32_t i): high(i>>31), low(static_cast<int64_t>(i)) {} + int128_t(uint32_t i): high(0), low(i) {} + int128_t(int64_t i): high(i>>63), low(i) {} + int128_t(uint64_t i): high(0), low(i) {} +}; + +inline int128_t operator<<(int128_t val, int amt) +{ + int128_t r; + r.low = val.low << amt; + r.high = val.low >> (64-amt); + r.high |= val.high << amt; + return r; +} + +inline int128_t& operator+=(int128_t& l, int128_t r) +{ + l.low += r.low; + bool carry = l.low < r.low; + l.high += r.high; + if (carry) ++l.high; + return l; +} + +inline int128_t operator-(int128_t val) +{ + val.low = ~val.low; + val.high = ~val.high; + val.low += 1; + if (val.low == 0) val.high += 1; + return val; +} + +inline int128_t operator+(int128_t l, int128_t r) +{ + l += r; + return l; +} + +inline bool operator<(int128_t l, int128_t r) +{ + if (l.high != r.high) return l.high < r.high; + return l.low < r.low; +} + + +inline int128_t mult_64x64_to_128(int64_t a, int64_t b) +{ + // Make life simple by dealing only with positive numbers: + bool neg = false; + if (a<0) { neg = !neg; a = -a; } + if (b<0) { neg = !neg; b = -b; } + + // Divide input into 32-bit halves: + uint32_t ah = a >> 32; + uint32_t al = a & 0xffffffff; + uint32_t bh = b >> 32; + uint32_t bl = b & 0xffffffff; + + // Long multiplication, with 64-bit temporaries: + + // ah al + // * bh bl + // ---------------- + // al*bl (t1) + // + ah*bl (t2) + // + al*bh (t3) + // + ah*bh (t4) + // ---------------- + + uint64_t t1 = static_cast<uint64_t>(al)*bl; + uint64_t t2 = static_cast<uint64_t>(ah)*bl; + uint64_t t3 = static_cast<uint64_t>(al)*bh; + uint64_t t4 = static_cast<uint64_t>(ah)*bh; + + int128_t r(t1); + r.high = t4; + r += int128_t(t2) << 32; + r += int128_t(t3) << 32; + + if (neg) r = -r; + + return r; +} + +template <class R, class T> +BOOST_FORCEINLINE void mul_2n(R& r, const T& a, const T& b) +{ + r = a; + r *= b; +} + +template <class B, boost::multiprecision::expression_template_option ET, class T> +BOOST_FORCEINLINE void mul_2n(boost::multiprecision::number<B, ET>& r, const T& a, const T& b) +{ + multiply(r, a, b); +} + +BOOST_FORCEINLINE void mul_2n(int128_t& r, const boost::int64_t& a, const boost::int64_t& b) +{ + r = mult_64x64_to_128(a, b); +} + +template <class Traits> +inline bool delaunay_test(int32_t ax, int32_t ay, int32_t bx, int32_t by, + int32_t cx, int32_t cy, int32_t dx, int32_t dy) +{ + // Test whether the quadrilateral ABCD's diagonal AC should be flipped to BD. + // This is the Cline & Renka method. + // Flip if the sum of the angles ABC and CDA is greater than 180 degrees. + // Equivalently, flip if sin(ABC + CDA) < 0. + // Trig identity: cos(ABC) * sin(CDA) + sin(ABC) * cos(CDA) < 0 + // We can use scalar and vector products to find sin and cos, and simplify + // to the following code. + // Numerical robustness is important. This code addresses it by performing + // exact calculations with large integer types. + // + // NOTE: This routine is limited to inputs with up to 30 BIT PRECISION, which + // is to say all inputs must be in the range [INT_MIN/2, INT_MAX/2]. + + typedef typename Traits::i64_t i64; + typedef typename Traits::i128_t i128; + + i64 cos_abc, t; + mul_2n(cos_abc, (ax-bx), (cx-bx)); // subtraction yields 31-bit values, multiplied to give 62-bit values + mul_2n(t, (ay-by), (cy-by)); + cos_abc += t; // addition yields 63 bit value, leaving one left for the sign + + i64 cos_cda; + mul_2n(cos_cda, (cx-dx), (ax-dx)); + mul_2n(t, (cy-dy), (ay-dy)); + cos_cda += t; + + if (cos_abc >= 0 && cos_cda >= 0) return false; + if (cos_abc < 0 && cos_cda < 0) return true; + + i64 sin_abc; + mul_2n(sin_abc, (ax-bx), (cy-by)); + mul_2n(t, (cx-bx), (ay-by)); + sin_abc -= t; + + i64 sin_cda; + mul_2n(sin_cda, (cx-dx), (ay-dy)); + mul_2n(t, (ax-dx), (cy-dy)); + sin_cda -= t; + + i128 sin_sum, t128; + mul_2n(sin_sum, sin_abc, cos_cda); // 63-bit inputs multiplied to 126-bit output + mul_2n(t128, cos_abc, sin_cda); + sin_sum += t128; // Addition yields 127 bit result, leaving one bit for the sign + + return sin_sum < 0; +} + + +struct dt_dat { + int32_t ax, ay, bx, by, cx, cy, dx, dy; +}; + +typedef std::vector<dt_dat> data_t; +data_t data; + +template <class Traits> +void do_calc(const char* name) +{ + std::cout << "Running calculations for: " << name << std::endl; + + stopwatch<boost::chrono::high_resolution_clock> w; + + boost::uint64_t flips = 0; + boost::uint64_t calcs = 0; + + for(int j = 0; j < 1000; ++j) + { + for(data_t::const_iterator i = data.begin(); i != data.end(); ++i) + { + const dt_dat& d = *i; + bool flip = delaunay_test<Traits>(d.ax,d.ay, d.bx,d.by, d.cx,d.cy, d.dx,d.dy); + if (flip) ++flips; + ++calcs; + } + } + double t = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + + std::cout << "Number of calculations = " << calcs << std::endl; + std::cout << "Number of flips = " << flips << std::endl; + std::cout << "Total execution time = " << t << std::endl; + std::cout << "Time per calculation = " << t / calcs << std::endl << std::endl; +} + +template <class I64, class I128> +struct test_traits +{ + typedef I64 i64_t; + typedef I128 i128_t; +}; + + +dt_dat generate_quadrilateral() +{ + static boost::random::mt19937 gen; + static boost::random::uniform_int_distribution<> dist(INT_MIN/2, INT_MAX/2); + + dt_dat result; + + result.ax = dist(gen); + result.ay = dist(gen); + result.bx = boost::random::uniform_int_distribution<>(result.ax, INT_MAX/2)(gen); // bx is to the right of ax. + result.by = dist(gen); + result.cx = dist(gen); + result.cy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX/2)(gen); // cy is below at least one of ay and by. + result.dx = boost::random::uniform_int_distribution<>(result.cx, INT_MAX/2)(gen); // dx is to the right of cx. + result.dy = boost::random::uniform_int_distribution<>(result.cx > result.bx ? result.by : result.ay, INT_MAX/2)(gen); // cy is below at least one of ay and by. + + return result; +} + +static void load_data() +{ + for(unsigned i = 0; i < 100000; ++i) + data.push_back(generate_quadrilateral()); +} + + +int main() +{ + using namespace boost::multiprecision; + std::cout << "loading data...\n"; + load_data(); + + std::cout << "calculating...\n"; + + do_calc<test_traits<boost::int64_t, boost::int64_t> >("int64_t, int64_t"); + do_calc<test_traits<number<arithmetic_backend<boost::int64_t>, et_off>, number<arithmetic_backend<boost::int64_t>, et_off> > >("arithmetic_backend<int64_t>, arithmetic_backend<int64_t>"); + do_calc<test_traits<boost::int64_t, number<arithmetic_backend<boost::int64_t>, et_off> > >("int64_t, arithmetic_backend<int64_t>"); + do_calc<test_traits<number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off>, number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off> > >("multiprecision::int64_t, multiprecision::int64_t"); + + do_calc<test_traits<boost::int64_t, ::int128_t> >("int64_t, int128_t"); + do_calc<test_traits<boost::int64_t, boost::multiprecision::int128_t> >("int64_t, boost::multiprecision::int128_t"); + do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128, 128, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_on> > >("int64_t, int128_t (ET)"); + do_calc<test_traits<number<cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, et_off>, boost::multiprecision::int128_t > >("multiprecision::int64_t, multiprecision::int128_t"); + + do_calc<test_traits<boost::int64_t, cpp_int> >("int64_t, cpp_int"); + do_calc<test_traits<boost::int64_t, number<cpp_int_backend<>, et_off> > >("int64_t, cpp_int (no ET's)"); + do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128> > > >("int64_t, cpp_int(128-bit cache)"); + do_calc<test_traits<boost::int64_t, number<cpp_int_backend<128>, et_off> > >("int64_t, cpp_int (128-bit Cache no ET's)"); + + return 0; +} + diff --git a/libs/multiprecision/performance/linpack-benchmark.cpp b/libs/multiprecision/performance/linpack-benchmark.cpp new file mode 100644 index 0000000000..104ac4c904 --- /dev/null +++ b/libs/multiprecision/performance/linpack-benchmark.cpp @@ -0,0 +1,1278 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +/* 1000d.f -- translated by f2c (version 20050501). +You must link the resulting object file with libf2c: +on Microsoft Windows system, link with libf2c.lib; +on Linux or Unix systems, link with .../path/to/libf2c.a -lm +or, if you install libf2c.a in a standard place, with -lf2c -lm +-- in that order, at the end of the command line, as in +cc *.o -lf2c -lm +Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + +http://www.netlib.org/f2c/libf2c.zip +*/ +#include <iostream> +#include <iomanip> +#include <cmath> + +#if defined(TEST_GMPXX) +#include <gmpxx.h> +typedef mpf_class real_type; +#elif defined(TEST_MPFRXX) +#include <gmpfrxx.h> +typedef mpfr_class real_type; +#elif defined(TEST_CPP_DEC_FLOAT) +#include <boost/multiprecision/cpp_dec_float.hpp> +typedef boost::multiprecision::cpp_dec_float_50 real_type; +#elif defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +typedef boost::multiprecision::mpfr_float_50 real_type; +#elif defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +typedef boost::multiprecision::mpf_float_50 real_type; +#elif defined(NATIVE_FLOAT128) +#include <boost/multiprecision/float128.hpp> +typedef __float128 real_type; + +std::ostream& operator<<(std::ostream& os, const __float128& f) +{ + return os << boost::multiprecision::float128(f); +} + +#include <boost/type_traits/has_left_shift.hpp> + +namespace boost{ + +template<> +struct has_left_shift<std::basic_ostream<char>, __float128> : public mpl::true_ {}; + +template<> +double lexical_cast<double, __float128>(const __float128& f) +{ return f; } + +} + +#elif defined(TEST_FLOAT128) +#include <boost/multiprecision/float128.hpp> +typedef boost::multiprecision::float128 real_type; +#else +typedef double real_type; +#endif + +#include <boost/lexical_cast.hpp> + +#ifndef CAST_TO_RT +# define CAST_TO_RT(x) x +#endif + +extern "C" { +#include "f2c.h" + integer s_wsfe(cilist *), e_wsfe(void), do_fio(integer *, char *, ftnlen), + s_wsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), + e_wsle(void); + /* Subroutine */ int s_stop(char *, ftnlen); + +#undef abs +#undef dabs +#define dabs abs +#undef dmin +#undef dmax +#define dmin min +#define dmax max + +} +#include <time.h> + +using std::min; +using std::max; + +/* Table of constant values */ + +static integer c__0 = 0; +static real_type c_b7 = CAST_TO_RT(1); +static integer c__1 = 1; +static integer c__9 = 9; + +inline double second_(void) +{ + return ((double)(clock())) / CLOCKS_PER_SEC; +} + +int dgefa_(real_type *, integer *, integer *, integer *, integer *), dgesl_(real_type *, integer *, integer *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); +int matgen_(real_type *, integer *, integer *, real_type *, real_type *); +real_type epslon_(real_type *); +real_type ran_(integer *); +int dscal_(integer *, real_type *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +integer idamax_(integer *, real_type *, integer *); +real_type ddot_(integer *, real_type *, integer *, real_type *, integer *); +int daxpy_(integer *, real_type *, real_type *, integer *, real_type *, integer *); +int dmxpy_(integer *, real_type *, integer *, integer *, real_type *, real_type *); + +extern "C" int MAIN__() +{ +#ifdef TEST_MPF_50 + std::cout << "Testing number<mpf_float<50> >" << std::endl; +#elif defined(TEST_MPFR_50) + std::cout << "Testing number<mpf_float<50> >" << std::endl; +#elif defined(TEST_GMPXX) + std::cout << "Testing mpf_class at 50 decimal degits" << std::endl; + mpf_set_default_prec(((50 + 1) * 1000L) / 301L); +#elif defined(TEST_MPFRXX) + std::cout << "Testing mpfr_class at 50 decimal degits" << std::endl; + mpfr_set_default_prec(((50 + 1) * 1000L) / 301L); +#elif defined(TEST_CPP_DEC_FLOAT) + std::cout << "Testing number<cpp_dec_float<50> >" << std::endl; +#elif defined(NATIVE_FLOAT128) + std::cout << "Testing __float128" << std::endl; +#elif defined(TEST_FLOAT128) + std::cout << "Testing number<float128_backend, et_off>" << std::endl; +#else + std::cout << "Testing double" << std::endl; +#endif + + + /* Format strings */ + static char fmt_1[] = "(\002 Please send the results of this run to:\002" + "//\002 Jack J. Dongarra\002/\002 Computer Science Department\002/" + "\002 University of Tennessee\002/\002 Knoxville, Tennessee 37996" + "-1300\002//\002 Fax: 615-974-8296\002//\002 Internet: dongarra@c" + "s.utk.edu\002/)"; + static char fmt_40[] = "(\002 norm. resid resid mac" + "hep\002,\002 x(1) x(n)\002)"; + static char fmt_50[] = "(1p5e16.8)"; + static char fmt_60[] = "(//\002 times are reported for matrices of or" + "der \002,i5)"; + static char fmt_70[] = "(6x,\002factor\002,5x,\002solve\002,6x,\002tota" + "l\002,5x,\002mflops\002,7x,\002unit\002,6x,\002ratio\002)"; + static char fmt_80[] = "(\002 times for array with leading dimension o" + "f\002,i4)"; + static char fmt_110[] = "(6(1pe11.3))"; + + /* System generated locals */ + integer i__1; + real_type d__1, d__2, d__3; + + /* Builtin functions */ + + /* Local variables */ + static real_type a[1001000] /* was [1001][1000] */, b[1000]; + static integer i__, n; + static real_type x[1000]; + static double t1; + static integer lda; + static double ops; + static real_type eps; + static integer info; + static double time[6], cray, total; + static integer ipvt[1000]; + static real_type resid, norma; + static real_type normx; + static real_type residn; + + /* Fortran I/O blocks */ + static cilist io___4 = { 0, 6, 0, fmt_1, 0 }; + static cilist io___20 = { 0, 6, 0, fmt_40, 0 }; + static cilist io___21 = { 0, 6, 0, fmt_50, 0 }; + static cilist io___22 = { 0, 6, 0, fmt_60, 0 }; + static cilist io___23 = { 0, 6, 0, fmt_70, 0 }; + static cilist io___24 = { 0, 6, 0, fmt_80, 0 }; + static cilist io___25 = { 0, 6, 0, fmt_110, 0 }; + static cilist io___26 = { 0, 6, 0, 0, 0 }; + + + lda = 1001; + + /* this program was updated on 10/12/92 to correct a */ + /* problem with the random number generator. The previous */ + /* random number generator had a short period and produced */ + /* singular matrices occasionally. */ + + n = 1000; + cray = .056f; + s_wsfe(&io___4); + e_wsfe(); + /* Computing 3rd power */ + d__1 = (real_type) n; + /* Computing 2nd power */ + d__2 = (real_type) n; + ops = boost::lexical_cast<double>(real_type(d__1 * (d__1 * d__1) * 2. / 3. + d__2 * d__2 * 2.)); + + matgen_(a, &lda, &n, b, &norma); + + /* ****************************************************************** */ + /* ****************************************************************** */ + /* you should replace the call to dgefa and dgesl */ + /* by calls to your linear equation solver. */ + /* ****************************************************************** */ + /* ****************************************************************** */ + + t1 = second_(); + dgefa_(a, &lda, &n, ipvt, &info); + time[0] = second_() - t1; + t1 = second_(); + dgesl_(a, &lda, &n, ipvt, b, &c__0); + time[1] = second_() - t1; + total = time[0] + time[1]; + /* ****************************************************************** */ + /* ****************************************************************** */ + + /* compute a residual to verify results. */ + + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__ - 1] = b[i__ - 1]; + /* L10: */ + } + matgen_(a, &lda, &n, b, &norma); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ - 1] = -b[i__ - 1]; + /* L20: */ + } + dmxpy_(&n, b, &n, &lda, x, a); + resid = CAST_TO_RT(0); + normx = CAST_TO_RT(0); + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + /* Computing MAX */ + d__2 = resid, d__3 = (d__1 = b[i__ - 1], abs(d__1)); + resid = (max)(d__2,d__3); + /* Computing MAX */ + d__2 = normx, d__3 = (d__1 = x[i__ - 1], abs(d__1)); + normx = (max)(d__2,d__3); + /* L30: */ + } + eps = epslon_(&c_b7); + residn = resid / (n * norma * normx * eps); + s_wsfe(&io___20); + e_wsfe(); + s_wsfe(&io___21); + /* + do_fio(&c__1, (char *)&residn, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&resid, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&eps, (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[0], (ftnlen)sizeof(real_type)); + do_fio(&c__1, (char *)&x[n - 1], (ftnlen)sizeof(real_type)); + */ + std::cout << std::setw(12) << std::setprecision(5) << residn << " " << resid << " " << eps << " " << x[0] << " " << x[n-1] << std::endl; + e_wsfe(); + + s_wsfe(&io___22); + do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___23); + e_wsfe(); + + time[2] = total; + time[3] = ops / (total * 1e6); + time[4] = 2. / time[3]; + time[5] = total / cray; + s_wsfe(&io___24); + do_fio(&c__1, (char *)&lda, (ftnlen)sizeof(integer)); + e_wsfe(); + s_wsfe(&io___25); + for (i__ = 1; i__ <= 6; ++i__) { + // do_fio(&c__1, (char *)&time[i__ - 1], (ftnlen)sizeof(real_type)); + std::cout << std::setw(12) << std::setprecision(5) << time[i__ - 1]; + } + e_wsfe(); + s_wsle(&io___26); + do_lio(&c__9, &c__1, " end of tests -- this version dated 10/12/92", ( + ftnlen)44); + e_wsle(); + + s_stop("", (ftnlen)0); + return 0; +} /* MAIN__ */ + +/* Subroutine */ int matgen_(real_type *a, integer *lda, integer *n, + real_type *b, real_type *norma) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + real_type d__1, d__2; + + /* Local variables */ + static integer i__, j; + static integer init[4]; + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --b; + + /* Function Body */ + init[0] = 1; + init[1] = 2; + init[2] = 3; + init[3] = 1325; + *norma = CAST_TO_RT(0); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = ran_(init) - .5f; + /* Computing MAX */ + d__2 = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + *norma = (max)(d__2,*norma); + /* L20: */ + } + /* L30: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__] = CAST_TO_RT(0); + /* L35: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__] += a[i__ + j * a_dim1]; + /* L40: */ + } + /* L50: */ + } + return 0; +} /* matgen_ */ + +/* Subroutine */ int dgefa_(real_type *a, integer *lda, integer *n, integer * + ipvt, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + static integer j, k, l; + static real_type t; + static integer kp1, nm1; + + + /* dgefa factors a double precision matrix by gaussian elimination. */ + + /* dgefa is usually called by dgeco, but it can be called */ + /* directly with a saving in time if rcond is not needed. */ + /* (time for dgeco) = (1 + 9/n)*(time for dgefa) . */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the matrix to be factored. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* on return */ + + /* a an upper triangular matrix and the multipliers */ + /* which were used to obtain it. */ + /* the factorization can be written a = l*u where */ + /* l is a product of permutation and unit lower */ + /* triangular matrices and u is upper triangular. */ + + /* ipvt integer(n) */ + /* an integer vector of pivot indices. */ + + /* info integer */ + /* = 0 normal value. */ + /* = k if u(k,k) .eq. 0.0 . this is not an error */ + /* condition for this subroutine, but it does */ + /* indicate that dgesl or dgedi will divide by zero */ + /* if called. use rcond in dgeco for a reliable */ + /* indication of singularity. */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,dscal,idamax */ + + /* internal variables */ + + + + /* gaussian elimination with partial pivoting */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + + /* Function Body */ + *info = 0; + nm1 = *n - 1; + if (nm1 < 1) { + goto L70; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + kp1 = k + 1; + + /* find l = pivot index */ + + i__2 = *n - k + 1; + l = idamax_(&i__2, &a[k + k * a_dim1], &c__1) + k - 1; + ipvt[k] = l; + + /* zero pivot implies this column already triangularized */ + + if (a[l + k * a_dim1] == 0.) { + goto L40; + } + + /* interchange if necessary */ + + if (l == k) { + goto L10; + } + t = a[l + k * a_dim1]; + a[l + k * a_dim1] = a[k + k * a_dim1]; + a[k + k * a_dim1] = t; +L10: + + /* compute multipliers */ + + t = -1. / a[k + k * a_dim1]; + i__2 = *n - k; + dscal_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1); + + /* row elimination with column indexing */ + + i__2 = *n; + for (j = kp1; j <= i__2; ++j) { + t = a[l + j * a_dim1]; + if (l == k) { + goto L20; + } + a[l + j * a_dim1] = a[k + j * a_dim1]; + a[k + j * a_dim1] = t; +L20: + i__3 = *n - k; + daxpy_(&i__3, &t, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + j * + a_dim1], &c__1); + /* L30: */ + } + goto L50; +L40: + *info = k; +L50: + /* L60: */ + ; + } +L70: + ipvt[*n] = *n; + if (a[*n + *n * a_dim1] == 0.) { + *info = *n; + } + return 0; +} /* dgefa_ */ + +/* Subroutine */ int dgesl_(real_type *a, integer *lda, integer *n, integer * + ipvt, real_type *b, integer *job) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + static integer k, l; + static real_type t; + static integer kb, nm1; + + + /* dgesl solves the double precision system */ + /* a * x = b or trans(a) * x = b */ + /* using the factors computed by dgeco or dgefa. */ + + /* on entry */ + + /* a double precision(lda, n) */ + /* the output from dgeco or dgefa. */ + + /* lda integer */ + /* the leading dimension of the array a . */ + + /* n integer */ + /* the order of the matrix a . */ + + /* ipvt integer(n) */ + /* the pivot vector from dgeco or dgefa. */ + + /* b double precision(n) */ + /* the right hand side vector. */ + + /* job integer */ + /* = 0 to solve a*x = b , */ + /* = nonzero to solve trans(a)*x = b where */ + /* trans(a) is the transpose. */ + + /* on return */ + + /* b the solution vector x . */ + + /* error condition */ + + /* a division by zero will occur if the input factor contains a */ + /* zero on the diagonal. technically this indicates singularity */ + /* but it is often caused by improper arguments or improper */ + /* setting of lda . it will not occur if the subroutines are */ + /* called correctly and if dgeco has set rcond .gt. 0.0 */ + /* or dgefa has set info .eq. 0 . */ + + /* to compute inverse(a) * c where c is a matrix */ + /* with p columns */ + /* call dgeco(a,lda,n,ipvt,rcond,z) */ + /* if (rcond is too small) go to ... */ + /* do 10 j = 1, p */ + /* call dgesl(a,lda,n,ipvt,c(1,j),0) */ + /* 10 continue */ + + /* linpack. this version dated 08/14/78 . */ + /* cleve moler, university of new mexico, argonne national lab. */ + + /* subroutines and functions */ + + /* blas daxpy,ddot */ + + /* internal variables */ + + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipvt; + --b; + + /* Function Body */ + nm1 = *n - 1; + if (*job != 0) { + goto L50; + } + + /* job = 0 , solve a * x = b */ + /* first solve l*y = b */ + + if (nm1 < 1) { + goto L30; + } + i__1 = nm1; + for (k = 1; k <= i__1; ++k) { + l = ipvt[k]; + t = b[l]; + if (l == k) { + goto L10; + } + b[l] = b[k]; + b[k] = t; +L10: + i__2 = *n - k; + daxpy_(&i__2, &t, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + /* L20: */ + } +L30: + + /* now solve u*x = y */ + + i__1 = *n; + for (kb = 1; kb <= i__1; ++kb) { + k = *n + 1 - kb; + b[k] /= a[k + k * a_dim1]; + t = -b[k]; + i__2 = k - 1; + daxpy_(&i__2, &t, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + /* L40: */ + } + goto L100; +L50: + + /* job = nonzero, solve trans(a) * x = b */ + /* first solve trans(u)*y = b */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + t = ddot_(&i__2, &a[k * a_dim1 + 1], &c__1, &b[1], &c__1); + b[k] = (b[k] - t) / a[k + k * a_dim1]; + /* L60: */ + } + + /* now solve trans(l)*x = y */ + + if (nm1 < 1) { + goto L90; + } + i__1 = nm1; + for (kb = 1; kb <= i__1; ++kb) { + k = *n - kb; + i__2 = *n - k; + b[k] += ddot_(&i__2, &a[k + 1 + k * a_dim1], &c__1, &b[k + 1], &c__1); + l = ipvt[k]; + if (l == k) { + goto L70; + } + t = b[l]; + b[l] = b[k]; + b[k] = t; +L70: + /* L80: */ + ; + } +L90: +L100: + return 0; +} /* dgesl_ */ + +/* Subroutine */ int daxpy_(integer *n, real_type *da, real_type *dx, + integer *incx, real_type *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + + + /* constant times a vector plus a vector. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*da == 0.) { + return 0; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] += *da * dx[ix]; + ix += *incx; + iy += *incy; + /* L10: */ + } + return 0; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 4; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] += *da * dx[i__]; + /* L30: */ + } + if (*n < 4) { + return 0; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 4) { + dy[i__] += *da * dx[i__]; + dy[i__ + 1] += *da * dx[i__ + 1]; + dy[i__ + 2] += *da * dx[i__ + 2]; + dy[i__ + 3] += *da * dx[i__ + 3]; + /* L50: */ + } + return 0; +} /* daxpy_ */ + +real_type ddot_(integer *n, real_type *dx, integer *incx, real_type *dy, + integer *incy) +{ + /* System generated locals */ + integer i__1; + real_type ret_val; + + /* Local variables */ + static integer i__, m, ix, iy, mp1; + static real_type dtemp; + + + /* forms the dot product of two vectors. */ + /* uses unrolled loops for increments equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + ret_val = CAST_TO_RT(0); + dtemp = CAST_TO_RT(0); + if (*n <= 0) { + return ret_val; + } + if (*incx == 1 && *incy == 1) { + goto L20; + } + + /* code for unequal increments or equal increments */ + /* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; + /* L10: */ + } + ret_val = dtemp; + return ret_val; + + /* code for both increments equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; + /* L30: */ + } + if (*n < 5) { + goto L60; + } +L40: + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ + i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + + 4] * dy[i__ + 4]; + /* L50: */ + } +L60: + ret_val = dtemp; + return ret_val; +} /* ddot_ */ + +/* Subroutine */ int dscal_(integer *n, real_type *da, real_type *dx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + static integer i__, m, mp1, nincx; + + + /* scales a vector by a constant. */ + /* uses unrolled loops for increment equal to one. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; + /* L10: */ + } + return 0; + + /* code for increment equal to 1 */ + + + /* clean-up loop */ + +L20: + m = *n % 5; + if (m == 0) { + goto L40; + } + i__2 = m; + for (i__ = 1; i__ <= i__2; ++i__) { + dx[i__] = *da * dx[i__]; + /* L30: */ + } + if (*n < 5) { + return 0; + } +L40: + mp1 = m + 1; + i__2 = *n; + for (i__ = mp1; i__ <= i__2; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; + /* L50: */ + } + return 0; +} /* dscal_ */ + +integer idamax_(integer *n, real_type *dx, integer *incx) +{ + /* System generated locals */ + integer ret_val, i__1; + real_type d__1; + + /* Local variables */ + static integer i__, ix; + static real_type dmax__; + + + /* finds the index of element having max. dabsolute value. */ + /* jack dongarra, linpack, 3/11/78. */ + + + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0; + if (*n < 1) { + return ret_val; + } + ret_val = 1; + if (*n == 1) { + return ret_val; + } + if (*incx == 1) { + goto L20; + } + + /* code for increment not equal to 1 */ + + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { + goto L5; + } + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); +L5: + ix += *incx; + /* L10: */ + } + return ret_val; + + /* code for increment equal to 1 */ + +L20: + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { + goto L30; + } + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); +L30: + ; + } + return ret_val; +} /* idamax_ */ + +real_type epslon_(real_type *x) +{ +#if defined(TEST_MPF_100) || defined(TEST_MPFR_100) || defined(TEST_GMPXX) || defined(TEST_MPFRXX) + return std::ldexp(1.0, 1 - ((100 + 1) * 1000L) / 301L); +#elif defined(TEST_CPP_DEC_FLOAT_BN) + return std::pow(10.0, 1-std::numeric_limits<efx::cpp_dec_float_50>::digits10); +#elif defined(NATIVE_FLOAT128) + return FLT128_EPSILON; +#else + return CAST_TO_RT(std::numeric_limits<real_type>::epsilon()); +#endif +} /* epslon_ */ + +/* Subroutine */ int mm_(real_type *a, integer *lda, integer *n1, integer * + n3, real_type *b, integer *ldb, integer *n2, real_type *c__, + integer *ldc) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j; + + + /* purpose: */ + /* multiply matrix b times matrix c and store the result in matrix a. */ + + /* parameters: */ + + /* a double precision(lda,n3), matrix of n1 rows and n3 columns */ + + /* lda integer, leading dimension of array a */ + + /* n1 integer, number of rows in matrices a and b */ + + /* n3 integer, number of columns in matrices a and c */ + + /* b double precision(ldb,n2), matrix of n1 rows and n2 columns */ + + /* ldb integer, leading dimension of array b */ + + /* n2 integer, number of columns in matrix b, and number of rows in */ + /* matrix c */ + + /* c double precision(ldc,n3), matrix of n2 rows and n3 columns */ + + /* ldc integer, leading dimension of array c */ + + /* ---------------------------------------------------------------------- */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + i__1 = *n3; + for (j = 1; j <= i__1; ++j) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = CAST_TO_RT(0); + /* L10: */ + } + dmxpy_(n2, &a[j * a_dim1 + 1], n1, ldb, &c__[j * c_dim1 + 1], &b[ + b_offset]); + /* L20: */ + } + + return 0; +} /* mm_ */ + +/* Subroutine */ int dmxpy_(integer *n1, real_type *y, integer *n2, integer * + ldm, real_type *x, real_type *m) +{ + /* System generated locals */ + integer m_dim1, m_offset, i__1, i__2; + + /* Local variables */ + static integer i__, j, jmin; + + + /* purpose: */ + /* multiply matrix m times vector x and add the result to vector y. */ + + /* parameters: */ + + /* n1 integer, number of elements in vector y, and number of rows in */ + /* matrix m */ + + /* y double precision(n1), vector of length n1 to which is added */ + /* the product m*x */ + + /* n2 integer, number of elements in vector x, and number of columns */ + /* in matrix m */ + + /* ldm integer, leading dimension of array m */ + + /* x double precision(n2), vector of length n2 */ + + /* m double precision(ldm,n2), matrix of n1 rows and n2 columns */ + + /* ---------------------------------------------------------------------- */ + + /* cleanup odd vector */ + + /* Parameter adjustments */ + --y; + m_dim1 = *ldm; + m_offset = 1 + m_dim1; + m -= m_offset; + --x; + + /* Function Body */ + j = *n2 % 2; + if (j >= 1) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] += x[j] * m[i__ + j * m_dim1]; + /* L10: */ + } + } + + /* cleanup odd group of two vectors */ + + j = *n2 % 4; + if (j >= 2) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[ + i__ + j * m_dim1]; + /* L20: */ + } + } + + /* cleanup odd group of four vectors */ + + j = *n2 % 8; + if (j >= 4) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 3] * m[i__ + (j - 3) * m_dim1] + x[j - 2] + * m[i__ + (j - 2) * m_dim1] + x[j - 1] * m[i__ + (j - 1) * + m_dim1] + x[j] * m[i__ + j * m_dim1]; + /* L30: */ + } + } + + /* cleanup odd group of eight vectors */ + + j = *n2 % 16; + if (j >= 8) { + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = y[i__] + x[j - 7] * m[i__ + (j - 7) * m_dim1] + x[j - 6] + * m[i__ + (j - 6) * m_dim1] + x[j - 5] * m[i__ + (j - 5) * + m_dim1] + x[j - 4] * m[i__ + (j - 4) * m_dim1] + x[j - 3] + * m[i__ + (j - 3) * m_dim1] + x[j - 2] * m[i__ + (j - 2) + * m_dim1] + x[j - 1] * m[i__ + (j - 1) * m_dim1] + x[j] * + m[i__ + j * m_dim1]; + /* L40: */ + } + } + + /* main loop - groups of sixteen vectors */ + + jmin = j + 16; + i__1 = *n2; + for (j = jmin; j <= i__1; j += 16) { + i__2 = *n1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] = y[i__] + x[j - 15] * m[i__ + (j - 15) * m_dim1] + x[j - + 14] * m[i__ + (j - 14) * m_dim1] + x[j - 13] * m[i__ + (j + - 13) * m_dim1] + x[j - 12] * m[i__ + (j - 12) * m_dim1] + + x[j - 11] * m[i__ + (j - 11) * m_dim1] + x[j - 10] * m[ + i__ + (j - 10) * m_dim1] + x[j - 9] * m[i__ + (j - 9) * + m_dim1] + x[j - 8] * m[i__ + (j - 8) * m_dim1] + x[j - 7] + * m[i__ + (j - 7) * m_dim1] + x[j - 6] * m[i__ + (j - 6) * + m_dim1] + x[j - 5] * m[i__ + (j - 5) * m_dim1] + x[j - 4] + * m[i__ + (j - 4) * m_dim1] + x[j - 3] * m[i__ + (j - 3) + * m_dim1] + x[j - 2] * m[i__ + (j - 2) * m_dim1] + x[j - + 1] * m[i__ + (j - 1) * m_dim1] + x[j] * m[i__ + j * + m_dim1]; + /* L50: */ + } + /* L60: */ + } + return 0; +} /* dmxpy_ */ + +real_type ran_(integer *iseed) +{ + /* System generated locals */ + real_type ret_val; + + /* Local variables */ + static integer it1, it2, it3, it4; + + + /* modified from the LAPACK auxiliary routine 10/12/92 JD */ + /* -- LAPACK auxiliary routine (version 1.0) -- */ + /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ + /* Courant Institute, Argonne National Lab, and Rice University */ + /* February 29, 1992 */ + + /* .. Array Arguments .. */ + /* .. */ + + /* Purpose */ + /* ======= */ + + /* DLARAN returns a random double number from a uniform (0,1) */ + /* distribution. */ + + /* Arguments */ + /* ========= */ + + /* ISEED (input/output) INTEGER array, dimension (4) */ + /* On entry, the seed of the random number generator; the array */ + /* elements must be between 0 and 4095, and ISEED(4) must be */ + /* odd. */ + /* On exit, the seed is updated. */ + + /* Further Details */ + /* =============== */ + + /* This routine uses a multiplicative congruential method with modulus */ + /* 2**48 and multiplier 33952834046453 (see G.S.Fishman, */ + /* 'Multiplicative congruential random number generators with modulus */ + /* 2**b: an exhaustive analysis for b = 32 and a partial analysis for */ + /* b = 48', Math. Comp. 189, pp 331-344, 1990). */ + + /* 48-bit integers are stored in 4 integer array elements with 12 bits */ + /* per element. Hence the routine is portable across machines with */ + /* integers of 32 bits or more. */ + + /* .. Parameters .. */ + /* .. */ + /* .. Local Scalars .. */ + /* .. */ + /* .. Intrinsic Functions .. */ + /* .. */ + /* .. Executable Statements .. */ + + /* multiply the seed by the multiplier modulo 2**48 */ + + /* Parameter adjustments */ + --iseed; + + /* Function Body */ + it4 = iseed[4] * 2549; + it3 = it4 / 4096; + it4 -= it3 << 12; + it3 = it3 + iseed[3] * 2549 + iseed[4] * 2508; + it2 = it3 / 4096; + it3 -= it2 << 12; + it2 = it2 + iseed[2] * 2549 + iseed[3] * 2508 + iseed[4] * 322; + it1 = it2 / 4096; + it2 -= it1 << 12; + it1 = it1 + iseed[1] * 2549 + iseed[2] * 2508 + iseed[3] * 322 + iseed[4] + * 494; + it1 %= 4096; + + /* return updated seed */ + + iseed[1] = it1; + iseed[2] = it2; + iseed[3] = it3; + iseed[4] = it4; + + /* convert 48-bit integer to a double number in the interval (0,1) */ + + ret_val = ((real_type) it1 + ((real_type) it2 + ((real_type) it3 + ( + real_type) it4 * 2.44140625e-4) * 2.44140625e-4) * 2.44140625e-4) + * 2.44140625e-4; + return ret_val; + + /* End of RAN */ + +} /* ran_ */ + +/* + +Double results: +~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +6.4915 7.207e-013 2.2204e-016 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +1.443 0.003 1.446 462.43 0.004325 25.821 + + +mpf_class results: +~~~~~~~~~~~~~~~~~~ + +norm. resid resid machep x(1) x(n) +3.6575e-05 5.2257e-103 2.8575e-101 1 1 + + + +times are reported for matrices of order 1000 +factor solve total mflops unit ratio +times for array with leading dimension of1001 +266.45 0.798 267.24 2.5021 0.79933 4772.2 + + +number<gmp_float<100> >: +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 0.36575e-4 0.52257e-102 0.28575e-100 0.1e1 0.1e1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 279.96 0.84 280.8 2.3813 0.83988 5014.3 + +boost::multiprecision::ef::cpp_dec_float_50: +~~~~~~~~~~~~~~~~~~~~~~~~~ + + norm. resid resid machep x(1) x(n) + 2.551330735e-16 1.275665107e-112 1e-99 1 1 + + + + times are reported for matrices of order 1000 + factor solve total mflops unit ratio + times for array with leading dimension of1001 + 363.89 1.074 364.97 1.8321 1.0916 6517.3 +*/ diff --git a/libs/multiprecision/performance/miller_rabin_performance.cpp b/libs/multiprecision/performance/miller_rabin_performance.cpp new file mode 100644 index 0000000000..e4ca6a500a --- /dev/null +++ b/libs/multiprecision/performance/miller_rabin_performance.cpp @@ -0,0 +1,167 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_CHRONO_HEADER_ONLY + +#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_MPZ +# define TEST_TOMMATH +# define TEST_CPP_INT +#endif + +#ifdef TEST_MPZ +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_TOMMATH +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_CPP_INT +#include <boost/multiprecision/cpp_int.hpp> +#endif +#include <boost/multiprecision/miller_rabin.hpp> +#include <boost/chrono.hpp> +#include <map> + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +#ifdef TEST_MPZ +boost::chrono::duration<double> test_miller_rabin_gmp() +{ + using namespace boost::random; + using namespace boost::multiprecision; + + stopwatch<boost::chrono::high_resolution_clock> c; + + independent_bits_engine<mt11213b, 256, mpz_int> gen; + + for(unsigned i = 0; i < 1000; ++i) + { + mpz_int n = gen(); + mpz_probab_prime_p(n.backend().data(), 25); + } + return c.elapsed(); +} +#endif + +std::map<std::string, double> results; +double min_time = (std::numeric_limits<double>::max)(); + +template <class IntType> +boost::chrono::duration<double> test_miller_rabin(const char* name) +{ + using namespace boost::random; + + stopwatch<boost::chrono::high_resolution_clock> c; + + independent_bits_engine<mt11213b, 256, IntType> gen; + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. + // + mt19937 gen2; + unsigned result_count = 0; + + for(unsigned i = 0; i < 1000; ++i) + { + IntType n = gen(); + if(boost::multiprecision::miller_rabin_test(n, 25, gen2)) + ++result_count; + } + boost::chrono::duration<double> t = c.elapsed(); + double d = t.count(); + if(d < min_time) + min_time = d; + results[name] = d; + std::cout << "Time for " << std::setw(30) << std::left << name << " = " << d << std::endl; + std::cout << "Number of primes found = " << result_count << std::endl; + return t; +} + +void generate_quickbook() +{ + std::cout << "[table\n[[Integer Type][Relative Performance (Actual time in parenthesis)]]\n"; + + std::map<std::string, double>::const_iterator i(results.begin()), j(results.end()); + + while(i != j) + { + double rel = i->second / min_time; + std::cout << "[[" << i->first << "][" << rel << "(" << i->second << "s)]]\n"; + ++i; + } + + std::cout << "]\n"; +} + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST_CPP_INT + test_miller_rabin<number<cpp_int_backend<>, et_off> >("cpp_int (no Expression templates)"); + test_miller_rabin<cpp_int>("cpp_int"); + test_miller_rabin<number<cpp_int_backend<128> > >("cpp_int (128-bit cache)"); + test_miller_rabin<number<cpp_int_backend<256> > >("cpp_int (256-bit cache)"); + test_miller_rabin<number<cpp_int_backend<512> > >("cpp_int (512-bit cache)"); + test_miller_rabin<number<cpp_int_backend<1024> > >("cpp_int (1024-bit cache)"); + test_miller_rabin<int1024_t>("int1024_t"); + test_miller_rabin<checked_int1024_t>("checked_int1024_t"); +#endif +#ifdef TEST_MPZ + test_miller_rabin<number<gmp_int, et_off> >("mpz_int (no Expression templates)"); + test_miller_rabin<mpz_int>("mpz_int"); + std::cout << "Time for mpz_int (native Miller Rabin Test) = " << test_miller_rabin_gmp() << std::endl; +#endif +#ifdef TEST_TOMMATH + test_miller_rabin<number<boost::multiprecision::tommath_int, et_off> >("tom_int (no Expression templates)"); + test_miller_rabin<boost::multiprecision::tom_int>("tom_int"); +#endif + + generate_quickbook(); + + return 0; +} + diff --git a/libs/multiprecision/performance/performance_test-gcc-linux.log b/libs/multiprecision/performance/performance_test-gcc-linux.log new file mode 100644 index 0000000000..83b150044c --- /dev/null +++ b/libs/multiprecision/performance/performance_test-gcc-linux.log @@ -0,0 +1,718 @@ +gmp_float 50 + 0.0180885 +gmp_float 50 - 0.0227712 +gmp_float 50 * 0.0567584 +gmp_float 50 / 0.289062 +gmp_float 50 str 0.00354863 +gmp_float 50 +(int)0.0129337 +gmp_float 50 -(int)0.0256267 +gmp_float 50 *(int)0.0197258 +gmp_float 50 /(int)0.087785 +gmp_float 100 + 0.0196977 +gmp_float 100 - 0.024745 +gmp_float 100 * 0.0972 +gmp_float 100 / 0.393792 +gmp_float 100 str 0.00528245 +gmp_float 100 +(int)0.0154802 +gmp_float 100 -(int)0.0242376 +gmp_float 100 *(int)0.0251239 +gmp_float 100 /(int)0.100588 +gmp_float 500 + 0.034133 +gmp_float 500 - 0.0411447 +gmp_float 500 * 0.938779 +gmp_float 500 / 1.5973 +gmp_float 500 str 0.0406575 +gmp_float 500 +(int)0.0220839 +gmp_float 500 -(int)0.0310849 +gmp_float 500 *(int)0.046899 +gmp_float 500 /(int)0.240511 +gmp_int 128 + 0.0236625 +gmp_int 128 - 0.0255431 +gmp_int 128 * 0.0164612 +gmp_int 128 / 0.20205 +gmp_int 128 str 0.000397397 +gmp_int 128 +(int)0.00907029 +gmp_int 128 -(int)0.0120936 +gmp_int 128 *(int)0.0139764 +gmp_int 128 /(int)0.061181 +gmp_int 128 % 0.167724 +gmp_int 128 | 0.0126627 +gmp_int 128 & 0.0129377 +gmp_int 128 ^ 0.0136018 +gmp_int 128 << 0.0109566 +gmp_int 128 >> 0.0107283 +gmp_int 128 %(int)0.0408971 +gmp_int 128 |(int)0.0463637 +gmp_int 128 &(int)0.0502028 +gmp_int 128 ^(int)0.047593 +gmp_int 128 gcd 0.452707 +gmp_int 256 + 0.0257277 +gmp_int 256 - 0.0314085 +gmp_int 256 * 0.0495293 +gmp_int 256 / 0.242695 +gmp_int 256 str 0.000617745 +gmp_int 256 +(int)0.0129046 +gmp_int 256 -(int)0.0163165 +gmp_int 256 *(int)0.0153128 +gmp_int 256 /(int)0.0730963 +gmp_int 256 % 0.203102 +gmp_int 256 | 0.0149383 +gmp_int 256 & 0.0170717 +gmp_int 256 ^ 0.0160796 +gmp_int 256 << 0.0146023 +gmp_int 256 >> 0.010293 +gmp_int 256 %(int)0.0525884 +gmp_int 256 |(int)0.0501017 +gmp_int 256 &(int)0.0508389 +gmp_int 256 ^(int)0.0498771 +gmp_int 256 gcd 2.17179 +gmp_int 512 + 0.0283556 +gmp_int 512 - 0.0398509 +gmp_int 512 * 0.104633 +gmp_int 512 / 0.294206 +gmp_int 512 str 0.00125749 +gmp_int 512 +(int)0.0156938 +gmp_int 512 -(int)0.0204795 +gmp_int 512 *(int)0.0190714 +gmp_int 512 /(int)0.09638 +gmp_int 512 % 0.23687 +gmp_int 512 | 0.0244134 +gmp_int 512 & 0.0209509 +gmp_int 512 ^ 0.0266707 +gmp_int 512 << 0.0178981 +gmp_int 512 >> 0.0122496 +gmp_int 512 %(int)0.0655264 +gmp_int 512 |(int)0.0536497 +gmp_int 512 &(int)0.0532932 +gmp_int 512 ^(int)0.0540655 +gmp_int 512 gcd 4.86569 +gmp_int 1024 + 0.0417292 +gmp_int 1024 - 0.0504965 +gmp_int 1024 * 0.330741 +gmp_int 1024 / 0.376529 +gmp_int 1024 str 0.00295526 +gmp_int 1024 +(int)0.0258726 +gmp_int 1024 -(int)0.0235972 +gmp_int 1024 *(int)0.0326542 +gmp_int 1024 /(int)0.148103 +gmp_int 1024 % 0.301177 +gmp_int 1024 | 0.0262977 +gmp_int 1024 & 0.0235786 +gmp_int 1024 ^ 0.0254182 +gmp_int 1024 << 0.0206225 +gmp_int 1024 >> 0.012848 +gmp_int 1024 %(int)0.0765616 +gmp_int 1024 |(int)0.0495613 +gmp_int 1024 &(int)0.0512979 +gmp_int 1024 ^(int)0.0491785 +gmp_int 1024 gcd 10.2899 +cpp_int 128 + 0.0226262 +cpp_int 128 - 0.0256171 +cpp_int 128 * 0.0363846 +cpp_int 128 / 0.227187 +cpp_int 128 str 0.000703371 +cpp_int 128 +(int)0.0156956 +cpp_int 128 -(int)0.0122229 +cpp_int 128 *(int)0.0257193 +cpp_int 128 /(int)0.129609 +cpp_int 128 % 0.226534 +cpp_int 128 | 0.0242976 +cpp_int 128 & 0.0244482 +cpp_int 128 ^ 0.0243197 +cpp_int 128 << 0.0182175 +cpp_int 128 >> 0.0215535 +cpp_int 128 %(int)0.181554 +cpp_int 128 |(int)0.0454215 +cpp_int 128 &(int)0.0426893 +cpp_int 128 ^(int)0.0404509 +cpp_int 128 gcd 4.16823 +cpp_int 256 + 0.0275581 +cpp_int 256 - 0.0305114 +cpp_int 256 * 0.100083 +cpp_int 256 / 0.467116 +cpp_int 256 str 0.00181769 +cpp_int 256 +(int)0.017033 +cpp_int 256 -(int)0.0143035 +cpp_int 256 *(int)0.0294836 +cpp_int 256 /(int)0.303922 +cpp_int 256 % 0.435207 +cpp_int 256 | 0.0281237 +cpp_int 256 & 0.028049 +cpp_int 256 ^ 0.0280192 +cpp_int 256 << 0.0210768 +cpp_int 256 >> 0.0175781 +cpp_int 256 %(int)0.279274 +cpp_int 256 |(int)0.0323883 +cpp_int 256 &(int)0.0338674 +cpp_int 256 ^(int)0.0299941 +cpp_int 256 gcd 8.51244 +cpp_int 512 + 0.033691 +cpp_int 512 - 0.0422701 +cpp_int 512 * 0.343683 +cpp_int 512 / 0.755608 +cpp_int 512 str 0.00434022 +cpp_int 512 +(int)0.0196755 +cpp_int 512 -(int)0.0171212 +cpp_int 512 *(int)0.039305 +cpp_int 512 /(int)0.535727 +cpp_int 512 % 0.719958 +cpp_int 512 | 0.0339623 +cpp_int 512 & 0.0342017 +cpp_int 512 ^ 0.033929 +cpp_int 512 << 0.0269161 +cpp_int 512 >> 0.0216914 +cpp_int 512 %(int)0.53345 +cpp_int 512 |(int)0.0324562 +cpp_int 512 &(int)0.0424884 +cpp_int 512 ^(int)0.0323887 +cpp_int 512 gcd 19.489 +cpp_int 1024 + 0.0456764 +cpp_int 1024 - 0.0574919 +cpp_int 1024 * 1.28548 +cpp_int 1024 / 1.30086 +cpp_int 1024 str 0.0122363 +cpp_int 1024 +(int)0.0241476 +cpp_int 1024 -(int)0.0212992 +cpp_int 1024 *(int)0.0540818 +cpp_int 1024 /(int)1.00179 +cpp_int 1024 % 1.27181 +cpp_int 1024 | 0.0457886 +cpp_int 1024 & 0.0456006 +cpp_int 1024 ^ 0.0456494 +cpp_int 1024 << 0.0394128 +cpp_int 1024 >> 0.0294462 +cpp_int 1024 %(int)0.962651 +cpp_int 1024 |(int)0.0372077 +cpp_int 1024 &(int)0.0577198 +cpp_int 1024 ^(int)0.0372218 +cpp_int 1024 gcd 47.7651 +cpp_int(fixed) 128 + 0.0183948 +cpp_int(fixed) 128 - 0.0182905 +cpp_int(fixed) 128 * 0.0201727 +cpp_int(fixed) 128 / 0.206852 +cpp_int(fixed) 128 str 0.000630107 +cpp_int(fixed) 128 +(int)0.00967714 +cpp_int(fixed) 128 -(int)0.00810627 +cpp_int(fixed) 128 *(int)0.0183201 +cpp_int(fixed) 128 /(int)0.111309 +cpp_int(fixed) 128 % 0.204164 +cpp_int(fixed) 128 | 0.0136789 +cpp_int(fixed) 128 & 0.0143848 +cpp_int(fixed) 128 ^ 0.0137773 +cpp_int(fixed) 128 << 0.0131154 +cpp_int(fixed) 128 >> 0.00912176 +cpp_int(fixed) 128 %(int)0.115583 +cpp_int(fixed) 128 |(int)0.0164462 +cpp_int(fixed) 128 &(int)0.0169816 +cpp_int(fixed) 128 ^(int)0.014607 +cpp_int(fixed) 128 gcd 2.87326 +cpp_int(fixed) 256 + 0.0217614 +cpp_int(fixed) 256 - 0.0208437 +cpp_int(fixed) 256 * 0.0385279 +cpp_int(fixed) 256 / 0.321272 +cpp_int(fixed) 256 str 0.00149991 +cpp_int(fixed) 256 +(int)0.0102395 +cpp_int(fixed) 256 -(int)0.00923316 +cpp_int(fixed) 256 *(int)0.021549 +cpp_int(fixed) 256 /(int)0.219146 +cpp_int(fixed) 256 % 0.321039 +cpp_int(fixed) 256 | 0.0154596 +cpp_int(fixed) 256 & 0.0156443 +cpp_int(fixed) 256 ^ 0.015493 +cpp_int(fixed) 256 << 0.0169546 +cpp_int(fixed) 256 >> 0.0114138 +cpp_int(fixed) 256 %(int)0.238857 +cpp_int(fixed) 256 |(int)0.015725 +cpp_int(fixed) 256 &(int)0.021641 +cpp_int(fixed) 256 ^(int)0.0163443 +cpp_int(fixed) 256 gcd 6.68597 +cpp_int(fixed) 512 + 0.0284799 +cpp_int(fixed) 512 - 0.028304 +cpp_int(fixed) 512 * 0.119904 +cpp_int(fixed) 512 / 0.616699 +cpp_int(fixed) 512 str 0.00415653 +cpp_int(fixed) 512 +(int)0.0122821 +cpp_int(fixed) 512 -(int)0.0110103 +cpp_int(fixed) 512 *(int)0.0283635 +cpp_int(fixed) 512 /(int)0.451373 +cpp_int(fixed) 512 % 0.620217 +cpp_int(fixed) 512 | 0.0189862 +cpp_int(fixed) 512 & 0.0192657 +cpp_int(fixed) 512 ^ 0.018973 +cpp_int(fixed) 512 << 0.0188263 +cpp_int(fixed) 512 >> 0.0152103 +cpp_int(fixed) 512 %(int)0.491398 +cpp_int(fixed) 512 |(int)0.0182191 +cpp_int(fixed) 512 &(int)0.0277722 +cpp_int(fixed) 512 ^(int)0.0182565 +cpp_int(fixed) 512 gcd 16.1788 +cpp_int(fixed) 1024 + 0.0396571 +cpp_int(fixed) 1024 - 0.0413187 +cpp_int(fixed) 1024 * 0.371065 +cpp_int(fixed) 1024 / 1.09072 +cpp_int(fixed) 1024 str 0.011546 +cpp_int(fixed) 1024 +(int)0.0254102 +cpp_int(fixed) 1024 -(int)0.020939 +cpp_int(fixed) 1024 *(int)0.0494233 +cpp_int(fixed) 1024 /(int)0.870306 +cpp_int(fixed) 1024 % 1.09888 +cpp_int(fixed) 1024 | 0.0393824 +cpp_int(fixed) 1024 & 0.0397966 +cpp_int(fixed) 1024 ^ 0.0394082 +cpp_int(fixed) 1024 << 0.0392477 +cpp_int(fixed) 1024 >> 0.0214742 +cpp_int(fixed) 1024 %(int)0.941513 +cpp_int(fixed) 1024 |(int)0.0304613 +cpp_int(fixed) 1024 &(int)0.0497983 +cpp_int(fixed) 1024 ^(int)0.0333848 +cpp_int(fixed) 1024 gcd 41.9178 +cpp_rational 128 + 8.33358 +cpp_rational 128 - 8.3543 +cpp_rational 128 * 15.3196 +cpp_rational 128 / 31.794 +cpp_rational 128 str 0.00980984 +cpp_rational 128 +(int)1.14042 +cpp_rational 128 -(int)1.13947 +cpp_rational 128 *(int)1.3425 +cpp_rational 128 /(int)1.35276 +cpp_rational 256 + 24.5753 +cpp_rational 256 - 24.3831 +cpp_rational 256 * 45.9283 +cpp_rational 256 / 80.7871 +cpp_rational 256 str 0.0288878 +cpp_rational 256 +(int)1.54697 +cpp_rational 256 -(int)1.55711 +cpp_rational 256 *(int)2.05921 +cpp_rational 256 /(int)2.12933 +cpp_rational 512 + 58.1983 +cpp_rational 512 - 58.3044 +cpp_rational 512 * 111.528 +cpp_rational 512 / 184.73 +cpp_rational 512 str 0.067039 +cpp_rational 512 +(int)1.83113 +cpp_rational 512 -(int)1.82889 +cpp_rational 512 *(int)2.75206 +cpp_rational 512 /(int)2.75885 +cpp_rational 1024 + 139.884 +cpp_rational 1024 - 139.665 +cpp_rational 1024 * 270.253 +cpp_rational 1024 / 436.471 +cpp_rational 1024 str 0.165057 +cpp_rational 1024 +(int)2.65768 +cpp_rational 1024 -(int)2.68279 +cpp_rational 1024 *(int)4.26866 +cpp_rational 1024 /(int)4.27228 +mpq_rational 128 + 0.518878 +mpq_rational 128 - 0.520249 +mpq_rational 128 * 0.940549 +mpq_rational 128 / 2.63335 +mpq_rational 128 str 0.000732008 +mpq_rational 128 +(int)0.145745 +mpq_rational 128 -(int)0.142505 +mpq_rational 128 *(int)0.173305 +mpq_rational 128 /(int)0.178914 +mpq_rational 256 + 2.2747 +mpq_rational 256 - 2.27886 +mpq_rational 256 * 4.27402 +mpq_rational 256 / 8.07149 +mpq_rational 256 str 0.00123256 +mpq_rational 256 +(int)0.164417 +mpq_rational 256 -(int)0.161741 +mpq_rational 256 *(int)0.193095 +mpq_rational 256 /(int)0.202255 +mpq_rational 512 + 5.09463 +mpq_rational 512 - 5.09757 +mpq_rational 512 * 9.6481 +mpq_rational 512 / 16.9064 +mpq_rational 512 str 0.00244388 +mpq_rational 512 +(int)0.202901 +mpq_rational 512 -(int)0.200644 +mpq_rational 512 *(int)0.248942 +mpq_rational 512 /(int)0.251928 +mpq_rational 1024 + 11.2492 +mpq_rational 1024 - 11.2528 +mpq_rational 1024 * 21.0227 +mpq_rational 1024 / 35.7647 +mpq_rational 1024 str 0.00559869 +mpq_rational 1024 +(int)0.287349 +mpq_rational 1024 -(int)0.28136 +mpq_rational 1024 *(int)0.337805 +mpq_rational 1024 /(int)0.351164 +tommath_int 128 + 0.0169999 +tommath_int 128 - 0.025088 +tommath_int 128 * 0.0608098 +tommath_int 128 / 1.14807 +tommath_int 128 str 0.00864677 +tommath_int 128 +(int)0.170239 +tommath_int 128 -(int)0.169805 +tommath_int 128 *(int)0.18998 +tommath_int 128 /(int)0.936106 +tommath_int 128 % 1.10993 +tommath_int 128 | 0.0742258 +tommath_int 128 & 0.0747022 +tommath_int 128 ^ 0.0734074 +tommath_int 128 << 0.0316344 +tommath_int 128 >> 0.139155 +tommath_int 128 %(int)0.871093 +tommath_int 128 |(int)0.249135 +tommath_int 128 &(int)0.224394 +tommath_int 128 ^(int)0.248407 +tommath_int 128 gcd 7.6073 +tommath_int 256 + 0.0191462 +tommath_int 256 - 0.0267191 +tommath_int 256 * 0.0843842 +tommath_int 256 / 1.34052 +tommath_int 256 str 0.0212684 +tommath_int 256 +(int)0.173633 +tommath_int 256 -(int)0.173084 +tommath_int 256 *(int)0.20074 +tommath_int 256 /(int)1.17192 +tommath_int 256 % 1.33781 +tommath_int 256 | 0.0740269 +tommath_int 256 & 0.0747001 +tommath_int 256 ^ 0.0741847 +tommath_int 256 << 0.0379471 +tommath_int 256 >> 0.14164 +tommath_int 256 %(int)1.52193 +tommath_int 256 |(int)0.251418 +tommath_int 256 &(int)0.230435 +tommath_int 256 ^(int)0.249516 +tommath_int 256 gcd 15.8851 +tommath_int 512 + 0.0241933 +tommath_int 512 - 0.032154 +tommath_int 512 * 0.195855 +tommath_int 512 / 2.061 +tommath_int 512 str 0.0827649 +tommath_int 512 +(int)0.25223 +tommath_int 512 -(int)0.25482 +tommath_int 512 *(int)0.305608 +tommath_int 512 /(int)1.76155 +tommath_int 512 % 1.97453 +tommath_int 512 | 0.0795209 +tommath_int 512 & 0.0815029 +tommath_int 512 ^ 0.0793004 +tommath_int 512 << 0.0449753 +tommath_int 512 >> 0.149597 +tommath_int 512 %(int)1.74258 +tommath_int 512 |(int)0.253519 +tommath_int 512 &(int)0.235246 +tommath_int 512 ^(int)0.261762 +tommath_int 512 gcd 33.8904 +tommath_int 1024 + 0.0356467 +tommath_int 1024 - 0.0426379 +tommath_int 1024 * 0.563154 +tommath_int 1024 / 3.3106 +tommath_int 1024 str 0.200351 +tommath_int 1024 +(int)0.183982 +tommath_int 1024 -(int)0.182348 +tommath_int 1024 *(int)0.265242 +tommath_int 1024 /(int)2.99248 +tommath_int 1024 % 3.36442 +tommath_int 1024 | 0.0935681 +tommath_int 1024 & 0.0990244 +tommath_int 1024 ^ 0.0948247 +tommath_int 1024 << 0.0671463 +tommath_int 1024 >> 0.167341 +tommath_int 1024 %(int)2.8911 +tommath_int 1024 |(int)0.26358 +tommath_int 1024 &(int)0.244976 +tommath_int 1024 ^(int)0.261357 +tommath_int 1024 gcd 67.1657 +cpp_dec_float 50 + 0.0139248 +cpp_dec_float 50 - 0.0142418 +cpp_dec_float 50 * 0.118247 +cpp_dec_float 50 / 1.82747 +cpp_dec_float 50 str 0.00932849 +cpp_dec_float 50 +(int)0.0253923 +cpp_dec_float 50 -(int)0.0248418 +cpp_dec_float 50 *(int)0.0371704 +cpp_dec_float 50 /(int)0.199883 +cpp_dec_float 100 + 0.0171021 +cpp_dec_float 100 - 0.0176287 +cpp_dec_float 100 * 0.237033 +cpp_dec_float 100 / 3.63766 +cpp_dec_float 100 str 0.0201057 +cpp_dec_float 100 +(int)0.0330663 +cpp_dec_float 100 -(int)0.0332922 +cpp_dec_float 100 *(int)0.0606472 +cpp_dec_float 100 /(int)0.343778 +cpp_dec_float 500 + 0.043194 +cpp_dec_float 500 - 0.0443422 +cpp_dec_float 500 * 2.12299 +cpp_dec_float 500 / 25.7245 +cpp_dec_float 500 str 0.0655127 +cpp_dec_float 500 +(int)0.0706977 +cpp_dec_float 500 -(int)0.0727089 +cpp_dec_float 500 *(int)0.239796 +cpp_dec_float 500 /(int)1.39609 +mpfr_float 50 + 0.019179 +mpfr_float 50 - 0.0225632 +mpfr_float 50 * 0.0588765 +mpfr_float 50 / 0.317276 +mpfr_float 50 str 0.00725414 +mpfr_float 50 +(int)0.0286079 +mpfr_float 50 -(int)0.0465151 +mpfr_float 50 *(int)0.0362579 +mpfr_float 50 /(int)0.0888645 +mpfr_float 100 + 0.0210236 +mpfr_float 100 - 0.0250703 +mpfr_float 100 * 0.0946262 +mpfr_float 100 / 0.456375 +mpfr_float 100 str 0.00900848 +mpfr_float 100 +(int)0.0320443 +mpfr_float 100 -(int)0.0487733 +mpfr_float 100 *(int)0.0437034 +mpfr_float 100 /(int)0.154203 +mpfr_float 500 + 0.033691 +mpfr_float 500 - 0.0371954 +mpfr_float 500 * 0.851721 +mpfr_float 500 / 2.7946 +mpfr_float 500 str 0.0342011 +mpfr_float 500 +(int)0.0414774 +mpfr_float 500 -(int)0.0616173 +mpfr_float 500 *(int)0.0826485 +mpfr_float 500 /(int)0.254227 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.08334 (0.118247s)][2.50494 (0.237033s)][2.49259 (2.12299s)]] +[[gmp_float][[*1] (0.0567584s)][1.0272 (0.0972s)][1.10221 (0.938779s)]] +[[mpfr_float][1.03732 (0.0588765s)][[*1] (0.0946262s)][[*1] (0.851721s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.88436 (0.0371704s)][2.41392 (0.0606472s)][5.11303 (0.239796s)]] +[[gmp_float][[*1] (0.0197258s)][[*1] (0.0251239s)][[*1] (0.046899s)]] +[[mpfr_float][1.8381 (0.0362579s)][1.73951 (0.0437034s)][1.76227 (0.0826485s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0139248s)][[*1] (0.0171021s)][1.28206 (0.043194s)]] +[[gmp_float][1.29901 (0.0180885s)][1.15177 (0.0196977s)][1.01312 (0.034133s)]] +[[mpfr_float][1.37732 (0.019179s)][1.2293 (0.0210236s)][[*1] (0.033691s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.96327 (0.0253923s)][2.13604 (0.0330663s)][3.20133 (0.0706977s)]] +[[gmp_float][[*1] (0.0129337s)][[*1] (0.0154802s)][[*1] (0.0220839s)]] +[[mpfr_float][2.21189 (0.0286079s)][2.07002 (0.0320443s)][1.87818 (0.0414774s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0142418s)][[*1] (0.0176287s)][1.19214 (0.0443422s)]] +[[gmp_float][1.5989 (0.0227712s)][1.40368 (0.024745s)][1.10618 (0.0411447s)]] +[[mpfr_float][1.5843 (0.0225632s)][1.42213 (0.0250703s)][[*1] (0.0371954s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0248418s)][1.37357 (0.0332922s)][2.33904 (0.0727089s)]] +[[gmp_float][1.03159 (0.0256267s)][[*1] (0.0242376s)][[*1] (0.0310849s)]] +[[mpfr_float][1.87245 (0.0465151s)][2.0123 (0.0487733s)][1.98223 (0.0616173s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][6.32206 (1.82747s)][9.23752 (3.63766s)][16.1049 (25.7245s)]] +[[gmp_float][[*1] (0.289062s)][[*1] (0.393792s)][[*1] (1.5973s)]] +[[mpfr_float][1.09761 (0.317276s)][1.15892 (0.456375s)][1.74957 (2.7946s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.27696 (0.199883s)][3.41769 (0.343778s)][5.8047 (1.39609s)]] +[[gmp_float][[*1] (0.087785s)][[*1] (0.100588s)][[*1] (0.240511s)]] +[[mpfr_float][1.0123 (0.0888645s)][1.53302 (0.154203s)][1.05703 (0.254227s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.62876 (0.00932849s)][3.80613 (0.0201057s)][1.91552 (0.0655127s)]] +[[gmp_float][[*1] (0.00354863s)][[*1] (0.00528245s)][1.18878 (0.0406575s)]] +[[mpfr_float][2.04421 (0.00725414s)][1.70536 (0.00900848s)][[*1] (0.0342011s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.35064 (0.226534s)][2.1428 (0.435207s)][3.03946 (0.719958s)][4.22281 (1.27181s)]] +[[cpp_int(fixed)][1.21726 (0.204164s)][1.58068 (0.321039s)][2.61838 (0.620217s)][3.6486 (1.09888s)]] +[[gmp_int][[*1] (0.167724s)][[*1] (0.203102s)][[*1] (0.23687s)][[*1] (0.301177s)]] +[[tommath_int][6.61759 (1.10993s)][6.58689 (1.33781s)][8.33593 (1.97453s)][11.1709 (3.36442s)]] +] +[table Operator %(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][4.43928 (0.181554s)][5.31056 (0.279274s)][8.141 (0.53345s)][12.5735 (0.962651s)]] +[[cpp_int(fixed)][2.82619 (0.115583s)][4.54202 (0.238857s)][7.49924 (0.491398s)][12.2974 (0.941513s)]] +[[gmp_int][[*1] (0.0408971s)][[*1] (0.0525884s)][[*1] (0.0655264s)][[*1] (0.0765616s)]] +[[tommath_int][21.2996 (0.871093s)][28.9405 (1.52193s)][26.5936 (1.74258s)][37.7618 (2.8911s)]] +] +[table Operator & +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.88968 (0.0244482s)][1.79292 (0.028049s)][1.77526 (0.0342017s)][1.93398 (0.0456006s)]] +[[cpp_int(fixed)][1.11185 (0.0143848s)][[*1] (0.0156443s)][[*1] (0.0192657s)][1.68783 (0.0397966s)]] +[[gmp_int][[*1] (0.0129377s)][1.09124 (0.0170717s)][1.08747 (0.0209509s)][[*1] (0.0235786s)]] +[[tommath_int][5.77397 (0.0747022s)][4.7749 (0.0747001s)][4.23046 (0.0815029s)][4.19976 (0.0990244s)]] +] +[table Operator &(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.51385 (0.0426893s)][1.56497 (0.0338674s)][1.52989 (0.0424884s)][1.15907 (0.0577198s)]] +[[cpp_int(fixed)][[*1] (0.0169816s)][[*1] (0.021641s)][[*1] (0.0277722s)][[*1] (0.0497983s)]] +[[gmp_int][2.9563 (0.0502028s)][2.3492 (0.0508389s)][1.91894 (0.0532932s)][1.03011 (0.0512979s)]] +[[tommath_int][13.2139 (0.224394s)][10.6481 (0.230435s)][8.47057 (0.235246s)][4.91936 (0.244976s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.21032 (0.0363846s)][2.59769 (0.100083s)][3.28466 (0.343683s)][3.88666 (1.28548s)]] +[[cpp_int(fixed)][1.22547 (0.0201727s)][[*1] (0.0385279s)][1.14595 (0.119904s)][1.12192 (0.371065s)]] +[[gmp_int][[*1] (0.0164612s)][1.28554 (0.0495293s)][[*1] (0.104633s)][[*1] (0.330741s)]] +[[tommath_int][3.69412 (0.0608098s)][2.19021 (0.0843842s)][1.87184 (0.195855s)][1.70271 (0.563154s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.8402 (0.0257193s)][1.92542 (0.0294836s)][2.06094 (0.039305s)][1.6562 (0.0540818s)]] +[[cpp_int(fixed)][1.3108 (0.0183201s)][1.40725 (0.021549s)][1.48723 (0.0283635s)][1.51354 (0.0494233s)]] +[[gmp_int][[*1] (0.0139764s)][[*1] (0.0153128s)][[*1] (0.0190714s)][[*1] (0.0326542s)]] +[[tommath_int][13.593 (0.18998s)][13.1093 (0.20074s)][16.0244 (0.305608s)][8.12274 (0.265242s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.33096 (0.0226262s)][1.43935 (0.0275581s)][1.39258 (0.033691s)][1.28136 (0.0456764s)]] +[[cpp_int(fixed)][1.08205 (0.0183948s)][1.13659 (0.0217614s)][1.17718 (0.0284799s)][1.1125 (0.0396571s)]] +[[gmp_int][1.39192 (0.0236625s)][1.34375 (0.0257277s)][1.17204 (0.0283556s)][1.17063 (0.0417292s)]] +[[tommath_int][[*1] (0.0169999s)][[*1] (0.0191462s)][[*1] (0.0241933s)][[*1] (0.0356467s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.73044 (0.0156956s)][1.66346 (0.017033s)][1.60196 (0.0196755s)][[*1] (0.0241476s)]] +[[cpp_int(fixed)][1.06691 (0.00967714s)][[*1] (0.0102395s)][[*1] (0.0122821s)][1.05229 (0.0254102s)]] +[[gmp_int][[*1] (0.00907029s)][1.26028 (0.0129046s)][1.27777 (0.0156938s)][1.07144 (0.0258726s)]] +[[tommath_int][18.7688 (0.170239s)][16.9572 (0.173633s)][20.5363 (0.25223s)][7.61905 (0.183982s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.40057 (0.0256171s)][1.46382 (0.0305114s)][1.49343 (0.0422701s)][1.39142 (0.0574919s)]] +[[cpp_int(fixed)][[*1] (0.0182905s)][[*1] (0.0208437s)][[*1] (0.028304s)][[*1] (0.0413187s)]] +[[gmp_int][1.39653 (0.0255431s)][1.50686 (0.0314085s)][1.40796 (0.0398509s)][1.22212 (0.0504965s)]] +[[tommath_int][1.37164 (0.025088s)][1.28188 (0.0267191s)][1.13602 (0.032154s)][1.03193 (0.0426379s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.50784 (0.0122229s)][1.54914 (0.0143035s)][1.55501 (0.0171212s)][1.0172 (0.0212992s)]] +[[cpp_int(fixed)][[*1] (0.00810627s)][[*1] (0.00923316s)][[*1] (0.0110103s)][[*1] (0.020939s)]] +[[gmp_int][1.49189 (0.0120936s)][1.76716 (0.0163165s)][1.86002 (0.0204795s)][1.12695 (0.0235972s)]] +[[tommath_int][20.9474 (0.169805s)][18.7459 (0.173084s)][23.1437 (0.25482s)][8.70855 (0.182348s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.12441 (0.227187s)][1.92471 (0.467116s)][2.5683 (0.755608s)][3.45487 (1.30086s)]] +[[cpp_int(fixed)][1.02377 (0.206852s)][1.32377 (0.321272s)][2.09615 (0.616699s)][2.89679 (1.09072s)]] +[[gmp_int][[*1] (0.20205s)][[*1] (0.242695s)][[*1] (0.294206s)][[*1] (0.376529s)]] +[[tommath_int][5.68214 (1.14807s)][5.52349 (1.34052s)][7.00529 (2.061s)][8.79242 (3.3106s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.11845 (0.129609s)][4.15783 (0.303922s)][5.55849 (0.535727s)][6.76415 (1.00179s)]] +[[cpp_int(fixed)][1.81934 (0.111309s)][2.99804 (0.219146s)][4.68327 (0.451373s)][5.87635 (0.870306s)]] +[[gmp_int][[*1] (0.061181s)][[*1] (0.0730963s)][[*1] (0.09638s)][[*1] (0.148103s)]] +[[tommath_int][15.3006 (0.936106s)][16.0325 (1.17192s)][18.2771 (1.76155s)][20.2054 (2.99248s)]] +] +[table Operator << +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.66271 (0.0182175s)][1.44338 (0.0210768s)][1.50386 (0.0269161s)][1.91115 (0.0394128s)]] +[[cpp_int(fixed)][1.19703 (0.0131154s)][1.16109 (0.0169546s)][1.05186 (0.0188263s)][1.90315 (0.0392477s)]] +[[gmp_int][[*1] (0.0109566s)][[*1] (0.0146023s)][[*1] (0.0178981s)][[*1] (0.0206225s)]] +[[tommath_int][2.88726 (0.0316344s)][2.5987 (0.0379471s)][2.51285 (0.0449753s)][3.25597 (0.0671463s)]] +] +[table Operator >> +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.36287 (0.0215535s)][1.70778 (0.0175781s)][1.77078 (0.0216914s)][2.29189 (0.0294462s)]] +[[cpp_int(fixed)][[*1] (0.00912176s)][1.10889 (0.0114138s)][1.2417 (0.0152103s)][1.6714 (0.0214742s)]] +[[gmp_int][1.17612 (0.0107283s)][[*1] (0.010293s)][[*1] (0.0122496s)][[*1] (0.012848s)]] +[[tommath_int][15.2553 (0.139155s)][13.7608 (0.14164s)][12.2124 (0.149597s)][13.0247 (0.167341s)]] +] +[table Operator ^ +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.78798 (0.0243197s)][1.8085 (0.0280192s)][1.78828 (0.033929s)][1.79594 (0.0456494s)]] +[[cpp_int(fixed)][1.0129 (0.0137773s)][[*1] (0.015493s)][[*1] (0.018973s)][1.5504 (0.0394082s)]] +[[gmp_int][[*1] (0.0136018s)][1.03786 (0.0160796s)][1.40572 (0.0266707s)][[*1] (0.0254182s)]] +[[tommath_int][5.39689 (0.0734074s)][4.78827 (0.0741847s)][4.17964 (0.0793004s)][3.73059 (0.0948247s)]] +] +[table Operator ^(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.76928 (0.0404509s)][1.83515 (0.0299941s)][1.77409 (0.0323887s)][1.11493 (0.0372218s)]] +[[cpp_int(fixed)][[*1] (0.014607s)][[*1] (0.0163443s)][[*1] (0.0182565s)][[*1] (0.0333848s)]] +[[gmp_int][3.25823 (0.047593s)][3.05166 (0.0498771s)][2.96144 (0.0540655s)][1.47308 (0.0491785s)]] +[[tommath_int][17.006 (0.248407s)][15.2663 (0.249516s)][14.338 (0.261762s)][7.82864 (0.261357s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.20736 (4.16823s)][3.91955 (8.51244s)][4.00539 (19.489s)][4.64192 (47.7651s)]] +[[cpp_int(fixed)][6.34685 (2.87326s)][3.07855 (6.68597s)][3.32507 (16.1788s)][4.07366 (41.9178s)]] +[[gmp_int][[*1] (0.452707s)][[*1] (2.17179s)][[*1] (4.86569s)][[*1] (10.2899s)]] +[[tommath_int][16.804 (7.6073s)][7.31428 (15.8851s)][6.96518 (33.8904s)][6.52732 (67.1657s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.76995 (0.000703371s)][2.94246 (0.00181769s)][3.45149 (0.00434022s)][4.14052 (0.0122363s)]] +[[cpp_int(fixed)][1.58559 (0.000630107s)][2.42804 (0.00149991s)][3.30542 (0.00415653s)][3.90693 (0.011546s)]] +[[gmp_int][[*1] (0.000397397s)][[*1] (0.000617745s)][[*1] (0.00125749s)][[*1] (0.00295526s)]] +[[tommath_int][21.7585 (0.00864677s)][34.4291 (0.0212684s)][65.8175 (0.0827649s)][67.7946 (0.200351s)]] +] +[table Operator | +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.91883 (0.0242976s)][1.88265 (0.0281237s)][1.78879 (0.0339623s)][1.74117 (0.0457886s)]] +[[cpp_int(fixed)][1.08025 (0.0136789s)][1.03489 (0.0154596s)][[*1] (0.0189862s)][1.49756 (0.0393824s)]] +[[gmp_int][[*1] (0.0126627s)][[*1] (0.0149383s)][1.28585 (0.0244134s)][[*1] (0.0262977s)]] +[[tommath_int][5.86177 (0.0742258s)][4.9555 (0.0740269s)][4.18835 (0.0795209s)][3.55804 (0.0935681s)]] +] +[table Operator |(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.76183 (0.0454215s)][2.05967 (0.0323883s)][1.78143 (0.0324562s)][1.22147 (0.0372077s)]] +[[cpp_int(fixed)][[*1] (0.0164462s)][[*1] (0.015725s)][[*1] (0.0182191s)][[*1] (0.0304613s)]] +[[gmp_int][2.81912 (0.0463637s)][3.18611 (0.0501017s)][2.94469 (0.0536497s)][1.62702 (0.0495613s)]] +[[tommath_int][15.1485 (0.249135s)][15.9884 (0.251418s)][13.915 (0.253519s)][8.65293 (0.26358s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.2879 (15.3196s)][10.7459 (45.9283s)][11.5596 (111.528s)][12.8553 (270.253s)]] +[[mpq_rational][[*1] (0.940549s)][[*1] (4.27402s)][[*1] (9.6481s)][[*1] (21.0227s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.7465 (1.3425s)][10.6643 (2.05921s)][11.055 (2.75206s)][12.6365 (4.26866s)]] +[[mpq_rational][[*1] (0.173305s)][[*1] (0.193095s)][[*1] (0.248942s)][[*1] (0.337805s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.0608 (8.33358s)][10.8037 (24.5753s)][11.4235 (58.1983s)][12.435 (139.884s)]] +[[mpq_rational][[*1] (0.518878s)][[*1] (2.2747s)][[*1] (5.09463s)][[*1] (11.2492s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.82472 (1.14042s)][9.40883 (1.54697s)][9.02478 (1.83113s)][9.24894 (2.65768s)]] +[[mpq_rational][[*1] (0.145745s)][[*1] (0.164417s)][[*1] (0.202901s)][[*1] (0.287349s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][16.0583 (8.3543s)][10.6997 (24.3831s)][11.4377 (58.3044s)][12.4116 (139.665s)]] +[[mpq_rational][[*1] (0.520249s)][[*1] (2.27886s)][[*1] (5.09757s)][[*1] (11.2528s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.99602 (1.13947s)][9.62717 (1.55711s)][9.1151 (1.82889s)][9.53508 (2.68279s)]] +[[mpq_rational][[*1] (0.142505s)][[*1] (0.161741s)][[*1] (0.200644s)][[*1] (0.28136s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][12.0736 (31.794s)][10.0089 (80.7871s)][10.9267 (184.73s)][12.204 (436.471s)]] +[[mpq_rational][[*1] (2.63335s)][[*1] (8.07149s)][[*1] (16.9064s)][[*1] (35.7647s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][7.56092 (1.35276s)][10.5279 (2.12933s)][10.9509 (2.75885s)][12.166 (4.27228s)]] +[[mpq_rational][[*1] (0.178914s)][[*1] (0.202255s)][[*1] (0.251928s)][[*1] (0.351164s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][13.4013 (0.00980984s)][23.4372 (0.0288878s)][27.4314 (0.067039s)][29.4814 (0.165057s)]] +[[mpq_rational][[*1] (0.000732008s)][[*1] (0.00123256s)][[*1] (0.00244388s)][[*1] (0.00559869s)]] +] +[endsect] diff --git a/libs/multiprecision/performance/performance_test-intel-linux.log b/libs/multiprecision/performance/performance_test-intel-linux.log new file mode 100644 index 0000000000..e721729eb6 --- /dev/null +++ b/libs/multiprecision/performance/performance_test-intel-linux.log @@ -0,0 +1,422 @@ +gmp_int 64 + 0.016582 +gmp_int 64 - 0.0174517 +gmp_int 64 * 0.0112253 +gmp_int 64 / 0.170951 +gmp_int 64 str 0.000343689 +gmp_int 64 +(int)0.00688382 +gmp_int 64 -(int)0.00734613 +gmp_int 64 *(int)0.00881438 +gmp_int 64 /(int)0.0465651 +gmp_int 64 % 0.164576 +gmp_int 64 | 0.0101555 +gmp_int 64 & 0.00955666 +gmp_int 64 ^ 0.00987346 +gmp_int 64 << 0.0106043 +gmp_int 64 >> 0.0093887 +gmp_int 64 %(int)0.0297463 +gmp_int 64 |(int)0.0403338 +gmp_int 64 &(int)0.0417288 +gmp_int 64 ^(int)0.0405779 +gmp_int 64 gcd 0.173816 +gmp_int 128 + 0.0183088 +gmp_int 128 - 0.0189266 +gmp_int 128 * 0.0161084 +gmp_int 128 / 0.191775 +gmp_int 128 str 0.000374699 +gmp_int 128 +(int)0.00866339 +gmp_int 128 -(int)0.0089443 +gmp_int 128 *(int)0.0114143 +gmp_int 128 /(int)0.0534638 +gmp_int 128 % 0.161212 +gmp_int 128 | 0.0107201 +gmp_int 128 & 0.0113559 +gmp_int 128 ^ 0.0112116 +gmp_int 128 << 0.0103295 +gmp_int 128 >> 0.00813413 +gmp_int 128 %(int)0.03692 +gmp_int 128 |(int)0.0412168 +gmp_int 128 &(int)0.0428359 +gmp_int 128 ^(int)0.0418522 +gmp_int 128 gcd 0.43131 +gmp_int 256 + 0.0224834 +gmp_int 256 - 0.025062 +gmp_int 256 * 0.0417471 +gmp_int 256 / 0.233656 +gmp_int 256 str 0.00059903 +gmp_int 256 +(int)0.0112071 +gmp_int 256 -(int)0.0116302 +gmp_int 256 *(int)0.0137181 +gmp_int 256 /(int)0.0667669 +gmp_int 256 % 0.191884 +gmp_int 256 | 0.0129489 +gmp_int 256 & 0.012778 +gmp_int 256 ^ 0.0134548 +gmp_int 256 << 0.0121471 +gmp_int 256 >> 0.00832878 +gmp_int 256 %(int)0.0474363 +gmp_int 256 |(int)0.0425591 +gmp_int 256 &(int)0.0436742 +gmp_int 256 ^(int)0.0425636 +gmp_int 256 gcd 2.06855 +gmp_int 512 + 0.0277439 +gmp_int 512 - 0.0318874 +gmp_int 512 * 0.0991032 +gmp_int 512 / 0.274993 +gmp_int 512 str 0.00129458 +gmp_int 512 +(int)0.014283 +gmp_int 512 -(int)0.0149874 +gmp_int 512 *(int)0.0180512 +gmp_int 512 /(int)0.0906691 +gmp_int 512 % 0.222477 +gmp_int 512 | 0.0217103 +gmp_int 512 & 0.0165285 +gmp_int 512 ^ 0.0208848 +gmp_int 512 << 0.014839 +gmp_int 512 >> 0.00988994 +gmp_int 512 %(int)0.0605682 +gmp_int 512 |(int)0.0462909 +gmp_int 512 &(int)0.046599 +gmp_int 512 ^(int)0.0456608 +gmp_int 512 gcd 4.68499 +gmp_int 1024 + 0.0397479 +gmp_int 1024 - 0.042232 +gmp_int 1024 * 0.31703 +gmp_int 1024 / 0.345984 +gmp_int 1024 str 0.00271592 +gmp_int 1024 +(int)0.0189969 +gmp_int 1024 -(int)0.0195046 +gmp_int 1024 *(int)0.0260306 +gmp_int 1024 /(int)0.140151 +gmp_int 1024 % 0.286399 +gmp_int 1024 | 0.0261953 +gmp_int 1024 & 0.023083 +gmp_int 1024 ^ 0.0248084 +gmp_int 1024 << 0.0202635 +gmp_int 1024 >> 0.0127909 +gmp_int 1024 %(int)0.0761102 +gmp_int 1024 |(int)0.049175 +gmp_int 1024 &(int)0.0499195 +gmp_int 1024 ^(int)0.0487102 +gmp_int 1024 gcd 10.1127 +cpp_int 64 + 0.0152915 +cpp_int 64 - 0.0191821 +cpp_int 64 * 0.0326218 +cpp_int 64 / 0.0951094 +cpp_int 64 str 0.000428547 +cpp_int 64 +(int)0.0132027 +cpp_int 64 -(int)0.0126144 +cpp_int 64 *(int)0.0151037 +cpp_int 64 /(int)0.0491116 +cpp_int 64 % 0.0951581 +cpp_int 64 | 0.0199629 +cpp_int 64 & 0.0196969 +cpp_int 64 ^ 0.0208608 +cpp_int 64 << 0.0179372 +cpp_int 64 >> 0.0146206 +cpp_int 64 %(int)0.0229261 +cpp_int 64 |(int)0.0185797 +cpp_int 64 &(int)0.0225055 +cpp_int 64 ^(int)0.0191337 +cpp_int 64 gcd 1.50205 +cpp_int 128 + 0.0170788 +cpp_int 128 - 0.0228373 +cpp_int 128 * 0.0375831 +cpp_int 128 / 0.163958 +cpp_int 128 str 0.000744647 +cpp_int 128 +(int)0.0144833 +cpp_int 128 -(int)0.013922 +cpp_int 128 *(int)0.0176402 +cpp_int 128 /(int)0.0972057 +cpp_int 128 % 0.169015 +cpp_int 128 | 0.0229631 +cpp_int 128 & 0.023126 +cpp_int 128 ^ 0.0229278 +cpp_int 128 << 0.0215749 +cpp_int 128 >> 0.0149198 +cpp_int 128 %(int)0.0476063 +cpp_int 128 |(int)0.0194697 +cpp_int 128 &(int)0.0270183 +cpp_int 128 ^(int)0.0194481 +cpp_int 128 gcd 3.36986 +cpp_int 256 + 0.0231877 +cpp_int 256 - 0.0293424 +cpp_int 256 * 0.113247 +cpp_int 256 / 0.336287 +cpp_int 256 str 0.00190436 +cpp_int 256 +(int)0.0161733 +cpp_int 256 -(int)0.0173225 +cpp_int 256 *(int)0.0199426 +cpp_int 256 /(int)0.229286 +cpp_int 256 % 0.306542 +cpp_int 256 | 0.0257191 +cpp_int 256 & 0.0254172 +cpp_int 256 ^ 0.0259082 +cpp_int 256 << 0.0253994 +cpp_int 256 >> 0.0172635 +cpp_int 256 %(int)0.116093 +cpp_int 256 |(int)0.0233559 +cpp_int 256 &(int)0.0367792 +cpp_int 256 ^(int)0.0232914 +cpp_int 256 gcd 7.88882 +cpp_int 512 + 0.0291058 +cpp_int 512 - 0.0380025 +cpp_int 512 * 0.337161 +cpp_int 512 / 0.487075 +cpp_int 512 str 0.00494162 +cpp_int 512 +(int)0.0201989 +cpp_int 512 -(int)0.0200688 +cpp_int 512 *(int)0.0311497 +cpp_int 512 /(int)0.375279 +cpp_int 512 % 0.459737 +cpp_int 512 | 0.0297101 +cpp_int 512 & 0.0297235 +cpp_int 512 ^ 0.0296913 +cpp_int 512 << 0.0328422 +cpp_int 512 >> 0.0234706 +cpp_int 512 %(int)0.194709 +cpp_int 512 |(int)0.0258992 +cpp_int 512 &(int)0.0529542 +cpp_int 512 ^(int)0.0258749 +cpp_int 512 gcd 19.7141 +cpp_int 1024 + 0.0410101 +cpp_int 1024 - 0.0576733 +cpp_int 1024 * 1.19319 +cpp_int 1024 / 0.850798 +cpp_int 1024 str 0.0149378 +cpp_int 1024 +(int)0.0222435 +cpp_int 1024 -(int)0.0219408 +cpp_int 1024 *(int)0.0435058 +cpp_int 1024 /(int)0.6795 +cpp_int 1024 % 0.800961 +cpp_int 1024 | 0.0369613 +cpp_int 1024 & 0.0368423 +cpp_int 1024 ^ 0.0371252 +cpp_int 1024 << 0.0474759 +cpp_int 1024 >> 0.0297527 +cpp_int 1024 %(int)0.360619 +cpp_int 1024 |(int)0.0326194 +cpp_int 1024 &(int)0.0801744 +cpp_int 1024 ^(int)0.0319848 +cpp_int 1024 gcd 53.3224 +fixed_int 64 + 0.00207275 +fixed_int 64 - 0.00214524 +fixed_int 64 * 0.00391097 +fixed_int 64 / 0.0608466 +fixed_int 64 str 0.000292286 +fixed_int 64 +(int)0.00357336 +fixed_int 64 -(int)0.00352796 +fixed_int 64 *(int)0.00292725 +fixed_int 64 /(int)0.0243018 +fixed_int 64 % 0.0603067 +fixed_int 64 | 0.00258063 +fixed_int 64 & 0.00257379 +fixed_int 64 ^ 0.00258525 +fixed_int 64 << 0.00134947 +fixed_int 64 >> 0.00560378 +fixed_int 64 %(int)0.0241499 +fixed_int 64 |(int)0.00201939 +fixed_int 64 &(int)0.00206716 +fixed_int 64 ^(int)0.00201848 +fixed_int 64 gcd 0.82127 +fixed_int 128 + 0.00325349 +fixed_int 128 - 0.00366953 +fixed_int 128 * 0.010445 +fixed_int 128 / 0.113697 +fixed_int 128 str 0.000564877 +fixed_int 128 +(int)0.00377625 +fixed_int 128 -(int)0.00360179 +fixed_int 128 *(int)0.00418426 +fixed_int 128 /(int)0.091141 +fixed_int 128 % 0.113804 +fixed_int 128 | 0.00360961 +fixed_int 128 & 0.00359913 +fixed_int 128 ^ 0.00361317 +fixed_int 128 << 0.0065905 +fixed_int 128 >> 0.00654308 +fixed_int 128 %(int)0.0809135 +fixed_int 128 |(int)0.00237125 +fixed_int 128 &(int)0.00231056 +fixed_int 128 ^(int)0.00190464 +fixed_int 128 gcd 2.05126 +fixed_int 256 + 0.00785776 +fixed_int 256 - 0.00635884 +fixed_int 256 * 0.0323875 +fixed_int 256 / 0.203194 +fixed_int 256 str 0.0013816 +fixed_int 256 +(int)0.00413397 +fixed_int 256 -(int)0.00379699 +fixed_int 256 *(int)0.00852456 +fixed_int 256 /(int)0.183053 +fixed_int 256 % 0.200368 +fixed_int 256 | 0.0105747 +fixed_int 256 & 0.0105856 +fixed_int 256 ^ 0.0105755 +fixed_int 256 << 0.00874545 +fixed_int 256 >> 0.00906624 +fixed_int 256 %(int)0.152826 +fixed_int 256 |(int)0.00261619 +fixed_int 256 &(int)0.00424202 +fixed_int 256 ^(int)0.00263274 +fixed_int 256 gcd 5.42715 +fixed_int 512 + 0.0131311 +fixed_int 512 - 0.0122513 +fixed_int 512 * 0.205979 +fixed_int 512 / 0.383601 +fixed_int 512 str 0.0043558 +fixed_int 512 +(int)0.00639746 +fixed_int 512 -(int)0.00641876 +fixed_int 512 *(int)0.0152369 +fixed_int 512 /(int)0.363289 +fixed_int 512 % 0.38201 +fixed_int 512 | 0.0131075 +fixed_int 512 & 0.0131292 +fixed_int 512 ^ 0.01314 +fixed_int 512 << 0.0130248 +fixed_int 512 >> 0.0131451 +fixed_int 512 %(int)0.304714 +fixed_int 512 |(int)0.00574368 +fixed_int 512 &(int)0.00810836 +fixed_int 512 ^(int)0.00576694 +fixed_int 512 gcd 16.6269 +fixed_int 1024 + 0.0322386 +fixed_int 1024 - 0.0312142 +fixed_int 1024 * 0.716002 +fixed_int 1024 / 0.728338 +fixed_int 1024 str 0.0135445 +fixed_int 1024 +(int)0.011986 +fixed_int 1024 -(int)0.0119838 +fixed_int 1024 *(int)0.0349878 +fixed_int 1024 /(int)0.708856 +fixed_int 1024 % 0.723622 +fixed_int 1024 | 0.0181468 +fixed_int 1024 & 0.0182648 +fixed_int 1024 ^ 0.018185 +fixed_int 1024 << 0.0252997 +fixed_int 1024 >> 0.0257832 +fixed_int 1024 %(int)0.597535 +fixed_int 1024 |(int)0.0116417 +fixed_int 1024 &(int)0.0172111 +fixed_int 1024 ^(int)0.011526 +fixed_int 1024 gcd 70.6396 +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.5779 (0.0951581s)][1.48514 (0.169015s)][1.59753 (0.306542s)][2.06645 (0.459737s)][2.79666 (0.800961s)]] +[[fixed_int][[*1] (0.0603067s)][[*1] (0.113804s)][1.04421 (0.200368s)][1.71708 (0.38201s)][2.52662 (0.723622s)]] +[[gmp_int][2.72898 (0.164576s)][1.41658 (0.161212s)][[*1] (0.191884s)][[*1] (0.222477s)][[*1] (0.286399s)]] +] +[table Operator %(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][[*1] (0.0229261s)][1.28944 (0.0476063s)][2.44735 (0.116093s)][3.21471 (0.194709s)][4.73812 (0.360619s)]] +[[fixed_int][1.05338 (0.0241499s)][2.19159 (0.0809135s)][3.22171 (0.152826s)][5.03092 (0.304714s)][7.85093 (0.597535s)]] +[[gmp_int][1.29749 (0.0297463s)][[*1] (0.03692s)][[*1] (0.0474363s)][[*1] (0.0605682s)][[*1] (0.0761102s)]] +] +[table Operator & +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][7.65289 (0.0196969s)][6.42545 (0.023126s)][2.4011 (0.0254172s)][2.26393 (0.0297235s)][2.01712 (0.0368423s)]] +[[fixed_int][[*1] (0.00257379s)][[*1] (0.00359913s)][[*1] (0.0105856s)][[*1] (0.0131292s)][[*1] (0.0182648s)]] +[[gmp_int][3.71307 (0.00955666s)][3.15518 (0.0113559s)][1.2071 (0.012778s)][1.25891 (0.0165285s)][1.2638 (0.023083s)]] +] +[table Operator &(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][10.8871 (0.0225055s)][11.6934 (0.0270183s)][8.67021 (0.0367792s)][6.53082 (0.0529542s)][4.65829 (0.0801744s)]] +[[fixed_int][[*1] (0.00206716s)][[*1] (0.00231056s)][[*1] (0.00424202s)][[*1] (0.00810836s)][[*1] (0.0172111s)]] +[[gmp_int][20.1865 (0.0417288s)][18.5392 (0.0428359s)][10.2956 (0.0436742s)][5.74703 (0.046599s)][2.90042 (0.0499195s)]] +] +[table Operator * +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.34111 (0.0326218s)][3.59818 (0.0375831s)][3.49662 (0.113247s)][3.40211 (0.337161s)][3.76364 (1.19319s)]] +[[fixed_int][[*1] (0.00391097s)][[*1] (0.010445s)][[*1] (0.0323875s)][2.07843 (0.205979s)][2.25847 (0.716002s)]] +[[gmp_int][2.87022 (0.0112253s)][1.54221 (0.0161084s)][1.28899 (0.0417471s)][[*1] (0.0991032s)][[*1] (0.31703s)]] +] +[table Operator *(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][5.15967 (0.0151037s)][4.21584 (0.0176402s)][2.33943 (0.0199426s)][2.04436 (0.0311497s)][1.67133 (0.0435058s)]] +[[fixed_int][[*1] (0.00292725s)][[*1] (0.00418426s)][[*1] (0.00852456s)][[*1] (0.0152369s)][1.3441 (0.0349878s)]] +[[gmp_int][3.01114 (0.00881438s)][2.72791 (0.0114143s)][1.60924 (0.0137181s)][1.1847 (0.0180512s)][[*1] (0.0260306s)]] +] +[table Operator + +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][7.37741 (0.0152915s)][5.2494 (0.0170788s)][2.95092 (0.0231877s)][2.21655 (0.0291058s)][1.27208 (0.0410101s)]] +[[fixed_int][[*1] (0.00207275s)][[*1] (0.00325349s)][[*1] (0.00785776s)][[*1] (0.0131311s)][[*1] (0.0322386s)]] +[[gmp_int][7.99998 (0.016582s)][5.62745 (0.0183088s)][2.86129 (0.0224834s)][2.11283 (0.0277439s)][1.23293 (0.0397479s)]] +] +[table Operator +(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][3.69474 (0.0132027s)][3.83536 (0.0144833s)][3.91229 (0.0161733s)][3.15733 (0.0201989s)][1.85579 (0.0222435s)]] +[[fixed_int][[*1] (0.00357336s)][[*1] (0.00377625s)][[*1] (0.00413397s)][[*1] (0.00639746s)][[*1] (0.011986s)]] +[[gmp_int][1.92643 (0.00688382s)][2.29418 (0.00866339s)][2.71097 (0.0112071s)][2.23261 (0.014283s)][1.58492 (0.0189969s)]] +] +[table Operator - +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.94166 (0.0191821s)][6.22351 (0.0228373s)][4.61443 (0.0293424s)][3.10192 (0.0380025s)][1.84766 (0.0576733s)]] +[[fixed_int][[*1] (0.00214524s)][[*1] (0.00366953s)][[*1] (0.00635884s)][[*1] (0.0122513s)][[*1] (0.0312142s)]] +[[gmp_int][8.13505 (0.0174517s)][5.15777 (0.0189266s)][3.94128 (0.025062s)][2.60278 (0.0318874s)][1.35297 (0.042232s)]] +] +[table Operator -(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][3.57555 (0.0126144s)][3.86529 (0.013922s)][4.56215 (0.0173225s)][3.12658 (0.0200688s)][1.83087 (0.0219408s)]] +[[fixed_int][[*1] (0.00352796s)][[*1] (0.00360179s)][[*1] (0.00379699s)][[*1] (0.00641876s)][[*1] (0.0119838s)]] +[[gmp_int][2.08226 (0.00734613s)][2.4833 (0.0089443s)][3.063 (0.0116302s)][2.33493 (0.0149874s)][1.62759 (0.0195046s)]] +] +[table Operator / +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.5631 (0.0951094s)][1.44205 (0.163958s)][1.655 (0.336287s)][1.77123 (0.487075s)][2.45907 (0.850798s)]] +[[fixed_int][[*1] (0.0608466s)][[*1] (0.113697s)][[*1] (0.203194s)][1.39495 (0.383601s)][2.10512 (0.728338s)]] +[[gmp_int][2.80954 (0.170951s)][1.68671 (0.191775s)][1.14992 (0.233656s)][[*1] (0.274993s)][[*1] (0.345984s)]] +] +[table Operator /(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.0209 (0.0491116s)][1.81816 (0.0972057s)][3.43412 (0.229286s)][4.13899 (0.375279s)][4.84836 (0.6795s)]] +[[fixed_int][[*1] (0.0243018s)][1.70472 (0.091141s)][2.74167 (0.183053s)][4.00675 (0.363289s)][5.05782 (0.708856s)]] +[[gmp_int][1.91611 (0.0465651s)][[*1] (0.0534638s)][[*1] (0.0667669s)][[*1] (0.0906691s)][[*1] (0.140151s)]] +] +[table Operator << +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][13.292 (0.0179372s)][3.27363 (0.0215749s)][2.9043 (0.0253994s)][2.52151 (0.0328422s)][2.34293 (0.0474759s)]] +[[fixed_int][[*1] (0.00134947s)][[*1] (0.0065905s)][[*1] (0.00874545s)][[*1] (0.0130248s)][1.24854 (0.0252997s)]] +[[gmp_int][7.85814 (0.0106043s)][1.56732 (0.0103295s)][1.38897 (0.0121471s)][1.13928 (0.014839s)][[*1] (0.0202635s)]] +] +[table Operator >> +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.60907 (0.0146206s)][2.28025 (0.0149198s)][2.07275 (0.0172635s)][2.37318 (0.0234706s)][2.32609 (0.0297527s)]] +[[fixed_int][[*1] (0.00560378s)][[*1] (0.00654308s)][1.08854 (0.00906624s)][1.32914 (0.0131451s)][2.01575 (0.0257832s)]] +[[gmp_int][1.67542 (0.0093887s)][1.24317 (0.00813413s)][[*1] (0.00832878s)][[*1] (0.00988994s)][[*1] (0.0127909s)]] +] +[table Operator ^ +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.06918 (0.0208608s)][6.34562 (0.0229278s)][2.44983 (0.0259082s)][2.25961 (0.0296913s)][2.04153 (0.0371252s)]] +[[fixed_int][[*1] (0.00258525s)][[*1] (0.00361317s)][[*1] (0.0105755s)][[*1] (0.01314s)][[*1] (0.018185s)]] +[[gmp_int][3.81916 (0.00987346s)][3.10299 (0.0112116s)][1.27226 (0.0134548s)][1.5894 (0.0208848s)][1.36422 (0.0248084s)]] +] +[table Operator ^(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.47925 (0.0191337s)][10.2109 (0.0194481s)][8.84686 (0.0232914s)][4.48677 (0.0258749s)][2.775 (0.0319848s)]] +[[fixed_int][[*1] (0.00201848s)][[*1] (0.00190464s)][[*1] (0.00263274s)][[*1] (0.00576694s)][[*1] (0.011526s)]] +[[gmp_int][20.1032 (0.0405779s)][21.9738 (0.0418522s)][16.1671 (0.0425636s)][7.91768 (0.0456608s)][4.2261 (0.0487102s)]] +] +[table Operator gcd +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.64165 (1.50205s)][7.81307 (3.36986s)][3.81369 (7.88882s)][4.20792 (19.7141s)][5.27284 (53.3224s)]] +[[fixed_int][4.72495 (0.82127s)][4.75589 (2.05126s)][2.62364 (5.42715s)][3.54898 (16.6269s)][6.98527 (70.6396s)]] +[[gmp_int][[*1] (0.173816s)][[*1] (0.43131s)][[*1] (2.06855s)][[*1] (4.68499s)][[*1] (10.1127s)]] +] +[table Operator str +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.46619 (0.000428547s)][1.98732 (0.000744647s)][3.17907 (0.00190436s)][3.81717 (0.00494162s)][5.50009 (0.0149378s)]] +[[fixed_int][[*1] (0.000292286s)][1.50755 (0.000564877s)][2.30639 (0.0013816s)][3.36465 (0.0043558s)][4.98706 (0.0135445s)]] +[[gmp_int][1.17587 (0.000343689s)][[*1] (0.000374699s)][[*1] (0.00059903s)][[*1] (0.00129458s)][[*1] (0.00271592s)]] +] +[table Operator | +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][7.73565 (0.0199629s)][6.36166 (0.0229631s)][2.43214 (0.0257191s)][2.26665 (0.0297101s)][2.0368 (0.0369613s)]] +[[fixed_int][[*1] (0.00258063s)][[*1] (0.00360961s)][[*1] (0.0105747s)][[*1] (0.0131075s)][[*1] (0.0181468s)]] +[[gmp_int][3.9353 (0.0101555s)][2.96987 (0.0107201s)][1.22452 (0.0129489s)][1.65632 (0.0217103s)][1.44352 (0.0261953s)]] +] +[table Operator |(int) +[[Backend][64 Bits][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.20066 (0.0185797s)][8.21071 (0.0194697s)][8.92746 (0.0233559s)][4.50916 (0.0258992s)][2.80194 (0.0326194s)]] +[[fixed_int][[*1] (0.00201939s)][[*1] (0.00237125s)][[*1] (0.00261619s)][[*1] (0.00574368s)][[*1] (0.0116417s)]] +[[gmp_int][19.9733 (0.0403338s)][17.3819 (0.0412168s)][16.2676 (0.0425591s)][8.05945 (0.0462909s)][4.22404 (0.049175s)]] +] +[endsect] diff --git a/libs/multiprecision/performance/performance_test-msvc-10.log b/libs/multiprecision/performance/performance_test-msvc-10.log new file mode 100644 index 0000000000..3e271ff954 --- /dev/null +++ b/libs/multiprecision/performance/performance_test-msvc-10.log @@ -0,0 +1,1220 @@ +gmp_float 50 + 0.110988 +gmp_float 50 - 0.119898 +gmp_float 50 * 0.275044 +gmp_float 50 / 1.27708 +gmp_float 50 str 0.013276 +gmp_float 50 +(int)0.0330888 +gmp_float 50 -(int)0.134451 +gmp_float 50 *(int)0.0422135 +gmp_float 50 /(int)0.180393 +gmp_float 50 construct0.19737 +gmp_float 50 construct(unsigned)0.208078 +gmp_float 50 construct(unsigned long long)0.520025 +gmp_float 50 + 0.498089 +gmp_float 50 - 0.502235 +gmp_float 50 * 0.564768 +gmp_float 50 / 0.90324 +gmp_float 50 + 0.477999 +gmp_float 50 - 0.499682 +gmp_float 50 * 0.551747 +gmp_float 50 / 0.893752 +gmp_float 100 + 0.111217 +gmp_float 100 - 0.120498 +gmp_float 100 * 0.416175 +gmp_float 100 / 1.69515 +gmp_float 100 str 0.0202949 +gmp_float 100 +(int)0.0386882 +gmp_float 100 -(int)0.1351 +gmp_float 100 *(int)0.0493716 +gmp_float 100 /(int)0.23378 +gmp_float 100 construct0.196599 +gmp_float 100 construct(unsigned)0.207062 +gmp_float 100 construct(unsigned long long)0.51936 +gmp_float 100 + 0.517172 +gmp_float 100 - 0.509588 +gmp_float 100 * 0.575954 +gmp_float 100 / 1.04262 +gmp_float 100 + 0.476701 +gmp_float 100 - 0.503546 +gmp_float 100 * 0.564962 +gmp_float 100 / 1.03328 +gmp_float 500 + 0.15445 +gmp_float 500 - 0.164099 +gmp_float 500 * 3.32799 +gmp_float 500 / 8.12655 +gmp_float 500 str 0.141162 +gmp_float 500 +(int)0.0646201 +gmp_float 500 -(int)0.176876 +gmp_float 500 *(int)0.0857876 +gmp_float 500 /(int)0.710204 +gmp_float 500 construct0.206063 +gmp_float 500 construct(unsigned)0.217019 +gmp_float 500 construct(unsigned long long)0.538021 +gmp_float 500 + 0.552532 +gmp_float 500 - 0.555754 +gmp_float 500 * 0.717186 +gmp_float 500 / 2.24686 +gmp_float 500 + 0.490614 +gmp_float 500 - 0.547751 +gmp_float 500 * 0.700957 +gmp_float 500 / 2.24146 +gmp_int 128 + 0.0421662 +gmp_int 128 - 0.0411848 +gmp_int 128 * 0.0708996 +gmp_int 128 / 0.868916 +gmp_int 128 str 0.00185638 +gmp_int 128 +(int)0.0311237 +gmp_int 128 -(int)0.030585 +gmp_int 128 *(int)0.022756 +gmp_int 128 /(int)0.0560401 +gmp_int 128 construct0.196182 +gmp_int 128 construct(unsigned)0.206113 +gmp_int 128 construct(unsigned long long)0.719741 +gmp_int 128 % 0.64148 +gmp_int 128 | 0.0474678 +gmp_int 128 & 0.0538128 +gmp_int 128 ^ 0.0497194 +gmp_int 128 << 0.0273994 +gmp_int 128 >> 0.0288237 +gmp_int 128 %(int)0.0572117 +gmp_int 128 |(int)0.141119 +gmp_int 128 &(int)0.141306 +gmp_int 128 ^(int)0.143934 +gmp_int 128 gcd 2.45095 +gmp_int 128 + 0.71217 +gmp_int 128 - 0.687129 +gmp_int 128 * 0.716479 +gmp_int 128 / 1.04926 +gmp_int 128 + 0.68136 +gmp_int 128 - 0.681187 +gmp_int 128 * 3.1627 +gmp_int 128 / 0.685487 +gmp_int 256 + 0.0449584 +gmp_int 256 - 0.0461316 +gmp_int 256 * 0.134302 +gmp_int 256 / 0.951505 +gmp_int 256 str 0.00344576 +gmp_int 256 +(int)0.0428011 +gmp_int 256 -(int)0.0400434 +gmp_int 256 *(int)0.0282672 +gmp_int 256 /(int)0.0982823 +gmp_int 256 construct0.201199 +gmp_int 256 construct(unsigned)0.211295 +gmp_int 256 construct(unsigned long long)0.729487 +gmp_int 256 % 0.703592 +gmp_int 256 | 0.0618281 +gmp_int 256 & 0.0652169 +gmp_int 256 ^ 0.0630174 +gmp_int 256 << 0.031973 +gmp_int 256 >> 0.0310184 +gmp_int 256 %(int)0.10258 +gmp_int 256 |(int)0.142987 +gmp_int 256 &(int)0.139398 +gmp_int 256 ^(int)0.144825 +gmp_int 256 gcd 5.89505 +gmp_int 256 + 0.728978 +gmp_int 256 - 0.707806 +gmp_int 256 * 0.731454 +gmp_int 256 / 1.17203 +gmp_int 256 + 0.68929 +gmp_int 256 - 0.683532 +gmp_int 256 * 3.15114 +gmp_int 256 / 0.689516 +gmp_int 512 + 0.0522202 +gmp_int 512 - 0.0567637 +gmp_int 512 * 0.532277 +gmp_int 512 / 1.06442 +gmp_int 512 str 0.00618403 +gmp_int 512 +(int)0.0665539 +gmp_int 512 -(int)0.0578194 +gmp_int 512 *(int)0.0361075 +gmp_int 512 /(int)0.183564 +gmp_int 512 construct0.19783 +gmp_int 512 construct(unsigned)0.206944 +gmp_int 512 construct(unsigned long long)0.724649 +gmp_int 512 % 0.819828 +gmp_int 512 | 0.0856626 +gmp_int 512 & 0.092104 +gmp_int 512 ^ 0.0869819 +gmp_int 512 << 0.0471709 +gmp_int 512 >> 0.0337511 +gmp_int 512 %(int)0.188529 +gmp_int 512 |(int)0.155656 +gmp_int 512 &(int)0.142498 +gmp_int 512 ^(int)0.152773 +gmp_int 512 gcd 13.6993 +gmp_int 512 + 0.759532 +gmp_int 512 - 0.732529 +gmp_int 512 * 0.779921 +gmp_int 512 / 1.39149 +gmp_int 512 + 0.694235 +gmp_int 512 - 0.69246 +gmp_int 512 * 3.17094 +gmp_int 512 / 0.688995 +gmp_int 1024 + 0.0699873 +gmp_int 1024 - 0.0731244 +gmp_int 1024 * 1.57852 +gmp_int 1024 / 1.30215 +gmp_int 1024 str 0.0144523 +gmp_int 1024 +(int)0.108272 +gmp_int 1024 -(int)0.100541 +gmp_int 1024 *(int)0.0518882 +gmp_int 1024 /(int)0.352238 +gmp_int 1024 construct0.19744 +gmp_int 1024 construct(unsigned)0.216229 +gmp_int 1024 construct(unsigned long long)0.722262 +gmp_int 1024 % 1.01959 +gmp_int 1024 | 0.136082 +gmp_int 1024 & 0.144412 +gmp_int 1024 ^ 0.139109 +gmp_int 1024 << 0.0721984 +gmp_int 1024 >> 0.0388038 +gmp_int 1024 %(int)0.355222 +gmp_int 1024 |(int)0.163236 +gmp_int 1024 &(int)0.141249 +gmp_int 1024 ^(int)0.161662 +gmp_int 1024 gcd 33.2232 +gmp_int 1024 + 0.83035 +gmp_int 1024 - 0.78115 +gmp_int 1024 * 0.815503 +gmp_int 1024 / 1.84054 +gmp_int 1024 + 0.690013 +gmp_int 1024 - 0.690838 +gmp_int 1024 * 3.20893 +gmp_int 1024 / 0.707578 +cpp_int(unsigned, fixed)64 + 0.00232166 +cpp_int(unsigned, fixed)64 - 0.00234506 +cpp_int(unsigned, fixed)64 * 0.00470304 +cpp_int(unsigned, fixed)64 / 0.0714786 +cpp_int(unsigned, fixed)64 str 0.00256457 +cpp_int(unsigned, fixed)64 +(int)0.00162053 +cpp_int(unsigned, fixed)64 -(int)0.00163617 +cpp_int(unsigned, fixed)64 *(int)0.00236511 +cpp_int(unsigned, fixed)64 /(int)0.0299559 +cpp_int(unsigned, fixed)64 construct0.00111299 +cpp_int(unsigned, fixed)64 construct(unsigned)0.00110489 +cpp_int(unsigned, fixed)64 construct(unsigned long long)0.00240876 +cpp_int(unsigned, fixed)64 % 0.0702826 +cpp_int(unsigned, fixed)64 | 0.00265921 +cpp_int(unsigned, fixed)64 & 0.00261653 +cpp_int(unsigned, fixed)64 ^ 0.0040003 +cpp_int(unsigned, fixed)64 << 0.00161592 +cpp_int(unsigned, fixed)64 >> 0.00161599 +cpp_int(unsigned, fixed)64 %(int)0.0298064 +cpp_int(unsigned, fixed)64 |(int)0.00165538 +cpp_int(unsigned, fixed)64 &(int)0.00161431 +cpp_int(unsigned, fixed)64 ^(int)0.00184507 +cpp_int(unsigned, fixed)64 gcd 0.602722 +cpp_int(unsigned, fixed)64 + 0.00253726 +cpp_int(unsigned, fixed)64 - 0.00301519 +cpp_int(unsigned, fixed)64 * 0.00474872 +cpp_int(unsigned, fixed)64 / 0.0450108 +cpp_int(unsigned, fixed)64 + 0.0020173 +cpp_int(unsigned, fixed)64 - 0.00191079 +cpp_int(unsigned, fixed)64 * 0.00445077 +cpp_int(unsigned, fixed)64 / 0.0294528 +cpp_int(fixed) 64 + 0.00573474 +cpp_int(fixed) 64 - 0.0096272 +cpp_int(fixed) 64 * 0.00897607 +cpp_int(fixed) 64 / 0.0783882 +cpp_int(fixed) 64 str 0.00251659 +cpp_int(fixed) 64 +(int)0.00636247 +cpp_int(fixed) 64 -(int)0.00668367 +cpp_int(fixed) 64 *(int)0.00548722 +cpp_int(fixed) 64 /(int)0.0362985 +cpp_int(fixed) 64 construct0.00161745 +cpp_int(fixed) 64 construct(unsigned)0.00209147 +cpp_int(fixed) 64 construct(unsigned long long)0.00204998 +cpp_int(fixed) 64 % 0.0777437 +cpp_int(fixed) 64 | 0.0108982 +cpp_int(fixed) 64 & 0.0124165 +cpp_int(fixed) 64 ^ 0.0110313 +cpp_int(fixed) 64 << 0.00516511 +cpp_int(fixed) 64 >> 0.00399499 +cpp_int(fixed) 64 %(int)0.0341425 +cpp_int(fixed) 64 |(int)0.0111002 +cpp_int(fixed) 64 &(int)0.0104782 +cpp_int(fixed) 64 ^(int)0.0107199 +cpp_int(fixed) 64 gcd 0.604291 +cpp_int(fixed) 64 + 0.00605482 +cpp_int(fixed) 64 - 0.00714372 +cpp_int(fixed) 64 * 0.00873093 +cpp_int(fixed) 64 / 0.0510195 +cpp_int(fixed) 64 + 0.00430062 +cpp_int(fixed) 64 - 0.00387577 +cpp_int(fixed) 64 * 0.00567824 +cpp_int(fixed) 64 / 0.0320162 +cpp_int(fixed) 128 + 0.0358493 +cpp_int(fixed) 128 - 0.0397574 +cpp_int(fixed) 128 * 0.0672363 +cpp_int(fixed) 128 / 0.222933 +cpp_int(fixed) 128 str 0.0015613 +cpp_int(fixed) 128 +(int)0.0268311 +cpp_int(fixed) 128 -(int)0.0241848 +cpp_int(fixed) 128 *(int)0.0328109 +cpp_int(fixed) 128 /(int)0.137619 +cpp_int(fixed) 128 construct0.00164665 +cpp_int(fixed) 128 construct(unsigned)0.0015986 +cpp_int(fixed) 128 construct(unsigned long long)0.00312994 +cpp_int(fixed) 128 % 0.1971 +cpp_int(fixed) 128 | 0.0380136 +cpp_int(fixed) 128 & 0.0341411 +cpp_int(fixed) 128 ^ 0.0351059 +cpp_int(fixed) 128 << 0.0320915 +cpp_int(fixed) 128 >> 0.0293055 +cpp_int(fixed) 128 %(int)0.103684 +cpp_int(fixed) 128 |(int)0.0317854 +cpp_int(fixed) 128 &(int)0.0417383 +cpp_int(fixed) 128 ^(int)0.0312355 +cpp_int(fixed) 128 gcd 4.18006 +cpp_int(fixed) 128 + 0.0341301 +cpp_int(fixed) 128 - 0.0346952 +cpp_int(fixed) 128 * 0.0675308 +cpp_int(fixed) 128 / 0.466907 +cpp_int(fixed) 128 + 0.0168342 +cpp_int(fixed) 128 - 0.0169449 +cpp_int(fixed) 128 * 0.0673436 +cpp_int(fixed) 128 / 0.0327432 +cpp_int(fixed) 256 + 0.0552275 +cpp_int(fixed) 256 - 0.0560103 +cpp_int(fixed) 256 * 0.166666 +cpp_int(fixed) 256 / 0.349956 +cpp_int(fixed) 256 str 0.00297279 +cpp_int(fixed) 256 +(int)0.0410749 +cpp_int(fixed) 256 -(int)0.0368306 +cpp_int(fixed) 256 *(int)0.049867 +cpp_int(fixed) 256 /(int)0.253796 +cpp_int(fixed) 256 construct0.00363363 +cpp_int(fixed) 256 construct(unsigned)0.00370466 +cpp_int(fixed) 256 construct(unsigned long long)0.00388115 +cpp_int(fixed) 256 % 0.334027 +cpp_int(fixed) 256 | 0.0529581 +cpp_int(fixed) 256 & 0.0501131 +cpp_int(fixed) 256 ^ 0.0530521 +cpp_int(fixed) 256 << 0.0507053 +cpp_int(fixed) 256 >> 0.039006 +cpp_int(fixed) 256 %(int)0.200647 +cpp_int(fixed) 256 |(int)0.0466958 +cpp_int(fixed) 256 &(int)0.0539427 +cpp_int(fixed) 256 ^(int)0.0476923 +cpp_int(fixed) 256 gcd 10.2671 +cpp_int(fixed) 256 + 0.0452762 +cpp_int(fixed) 256 - 0.0444216 +cpp_int(fixed) 256 * 0.112885 +cpp_int(fixed) 256 / 1.36886 +cpp_int(fixed) 256 + 0.0170491 +cpp_int(fixed) 256 - 0.0176783 +cpp_int(fixed) 256 * 0.107306 +cpp_int(fixed) 256 / 0.0340708 +cpp_int(fixed) 512 + 0.0760722 +cpp_int(fixed) 512 - 0.0756027 +cpp_int(fixed) 512 * 0.500399 +cpp_int(fixed) 512 / 0.560837 +cpp_int(fixed) 512 str 0.00708386 +cpp_int(fixed) 512 +(int)0.0524416 +cpp_int(fixed) 512 -(int)0.0503396 +cpp_int(fixed) 512 *(int)0.0658566 +cpp_int(fixed) 512 /(int)0.446782 +cpp_int(fixed) 512 construct0.00576526 +cpp_int(fixed) 512 construct(unsigned)0.0058189 +cpp_int(fixed) 512 construct(unsigned long long)0.00556537 +cpp_int(fixed) 512 % 0.539708 +cpp_int(fixed) 512 | 0.0676884 +cpp_int(fixed) 512 & 0.0588367 +cpp_int(fixed) 512 ^ 0.0695132 +cpp_int(fixed) 512 << 0.0597514 +cpp_int(fixed) 512 >> 0.0515714 +cpp_int(fixed) 512 %(int)0.377704 +cpp_int(fixed) 512 |(int)0.0536974 +cpp_int(fixed) 512 &(int)0.070425 +cpp_int(fixed) 512 ^(int)0.0540962 +cpp_int(fixed) 512 gcd 26.2762 +cpp_int(fixed) 512 + 0.0571069 +cpp_int(fixed) 512 - 0.0563175 +cpp_int(fixed) 512 * 0.177444 +cpp_int(fixed) 512 / 3.1662 +cpp_int(fixed) 512 + 0.0172628 +cpp_int(fixed) 512 - 0.0180756 +cpp_int(fixed) 512 * 0.171821 +cpp_int(fixed) 512 / 0.0444905 +cpp_int(fixed) 1024 + 0.121124 +cpp_int(fixed) 1024 - 0.114246 +cpp_int(fixed) 1024 * 1.54633 +cpp_int(fixed) 1024 / 0.975643 +cpp_int(fixed) 1024 str 0.0172514 +cpp_int(fixed) 1024 +(int)0.0728817 +cpp_int(fixed) 1024 -(int)0.0621059 +cpp_int(fixed) 1024 *(int)0.0948565 +cpp_int(fixed) 1024 /(int)0.84764 +cpp_int(fixed) 1024 construct0.00535599 +cpp_int(fixed) 1024 construct(unsigned)0.00836042 +cpp_int(fixed) 1024 construct(unsigned long long)0.00577713 +cpp_int(fixed) 1024 % 0.94847 +cpp_int(fixed) 1024 | 0.100936 +cpp_int(fixed) 1024 & 0.0774574 +cpp_int(fixed) 1024 ^ 0.09783 +cpp_int(fixed) 1024 << 0.0677088 +cpp_int(fixed) 1024 >> 0.0626121 +cpp_int(fixed) 1024 %(int)0.743202 +cpp_int(fixed) 1024 |(int)0.0819107 +cpp_int(fixed) 1024 &(int)0.112823 +cpp_int(fixed) 1024 ^(int)0.0806317 +cpp_int(fixed) 1024 gcd 76.2849 +cpp_int(fixed) 1024 + 0.0636724 +cpp_int(fixed) 1024 - 0.06467 +cpp_int(fixed) 1024 * 0.303514 +cpp_int(fixed) 1024 / 8.04418 +cpp_int(fixed) 1024 + 0.0181245 +cpp_int(fixed) 1024 - 0.0190581 +cpp_int(fixed) 1024 * 0.299236 +cpp_int(fixed) 1024 / 0.106788 +cpp_int 128 + 0.0273725 +cpp_int 128 - 0.0303219 +cpp_int 128 * 0.0774619 +cpp_int 128 / 0.589941 +cpp_int 128 str 0.00189808 +cpp_int 128 +(int)0.0159069 +cpp_int 128 -(int)0.0151244 +cpp_int 128 *(int)0.0235876 +cpp_int 128 /(int)0.235955 +cpp_int 128 construct0.00293927 +cpp_int 128 construct(unsigned)0.00270684 +cpp_int 128 construct(unsigned long long)0.00719854 +cpp_int 128 % 0.37333 +cpp_int 128 | 0.030991 +cpp_int 128 & 0.031605 +cpp_int 128 ^ 0.0318172 +cpp_int 128 << 0.0256107 +cpp_int 128 >> 0.0237523 +cpp_int 128 %(int)0.104856 +cpp_int 128 |(int)0.0280516 +cpp_int 128 &(int)0.0377678 +cpp_int 128 ^(int)0.0283305 +cpp_int 128 gcd 4.98644 +cpp_int 128 + 0.0283071 +cpp_int 128 - 0.027289 +cpp_int 128 * 0.0584001 +cpp_int 128 / 0.733741 +cpp_int 128 + 0.0196594 +cpp_int 128 - 0.0210968 +cpp_int 128 * 7.6372 +cpp_int 128 / 0.0578293 +cpp_int 256 + 0.0384835 +cpp_int 256 - 0.0402028 +cpp_int 256 * 0.211395 +cpp_int 256 / 0.708882 +cpp_int 256 str 0.00391656 +cpp_int 256 +(int)0.0218386 +cpp_int 256 -(int)0.017199 +cpp_int 256 *(int)0.0318939 +cpp_int 256 /(int)0.35212 +cpp_int 256 construct0.00277479 +cpp_int 256 construct(unsigned)0.0030529 +cpp_int 256 construct(unsigned long long)0.00725455 +cpp_int 256 % 0.673748 +cpp_int 256 | 0.0429658 +cpp_int 256 & 0.0455929 +cpp_int 256 ^ 0.0425243 +cpp_int 256 << 0.0401135 +cpp_int 256 >> 0.0302534 +cpp_int 256 %(int)0.203012 +cpp_int 256 |(int)0.0363929 +cpp_int 256 &(int)0.0471524 +cpp_int 256 ^(int)0.0353555 +cpp_int 256 gcd 11.1816 +cpp_int 256 + 0.030223 +cpp_int 256 - 0.0319489 +cpp_int 256 * 0.0885733 +cpp_int 256 / 1.62706 +cpp_int 256 + 0.0215291 +cpp_int 256 - 0.0213343 +cpp_int 256 * 7.7121 +cpp_int 256 / 0.0615507 +cpp_int 512 + 0.0561351 +cpp_int 512 - 0.0543342 +cpp_int 512 * 0.703234 +cpp_int 512 / 0.924042 +cpp_int 512 str 0.00832019 +cpp_int 512 +(int)0.0316584 +cpp_int 512 -(int)0.0248084 +cpp_int 512 *(int)0.0427792 +cpp_int 512 /(int)0.568032 +cpp_int 512 construct0.0028102 +cpp_int 512 construct(unsigned)0.00288857 +cpp_int 512 construct(unsigned long long)0.00723891 +cpp_int 512 % 0.701584 +cpp_int 512 | 0.0537846 +cpp_int 512 & 0.0546439 +cpp_int 512 ^ 0.0542436 +cpp_int 512 << 0.0436188 +cpp_int 512 >> 0.0355247 +cpp_int 512 %(int)0.391566 +cpp_int 512 |(int)0.0418143 +cpp_int 512 &(int)0.0647085 +cpp_int 512 ^(int)0.041758 +cpp_int 512 gcd 27.2257 +cpp_int 512 + 0.0382495 +cpp_int 512 - 0.0386744 +cpp_int 512 * 0.14417 +cpp_int 512 / 3.61202 +cpp_int 512 + 0.0228565 +cpp_int 512 - 0.0222868 +cpp_int 512 * 7.72815 +cpp_int 512 / 0.0732298 +cpp_int 1024 + 0.0928746 +cpp_int 1024 - 0.0853837 +cpp_int 1024 * 2.6591 +cpp_int 1024 / 1.38142 +cpp_int 1024 str 0.0221599 +cpp_int 1024 +(int)0.0430289 +cpp_int 1024 -(int)0.0331224 +cpp_int 1024 *(int)0.0668616 +cpp_int 1024 /(int)0.989885 +cpp_int 1024 construct0.00277298 +cpp_int 1024 construct(unsigned)0.00265201 +cpp_int 1024 construct(unsigned long long)0.00732796 +cpp_int 1024 % 1.14369 +cpp_int 1024 | 0.0827684 +cpp_int 1024 & 0.0843863 +cpp_int 1024 ^ 0.08333 +cpp_int 1024 << 0.0628544 +cpp_int 1024 >> 0.044717 +cpp_int 1024 %(int)0.768511 +cpp_int 1024 |(int)0.0527075 +cpp_int 1024 &(int)0.10089 +cpp_int 1024 ^(int)0.0538323 +cpp_int 1024 gcd 73.3735 +cpp_int 1024 + 0.0463315 +cpp_int 1024 - 0.0468398 +cpp_int 1024 * 0.255279 +cpp_int 1024 / 8.42528 +cpp_int 1024 + 0.0227402 +cpp_int 1024 - 0.0234526 +cpp_int 1024 * 7.86395 +cpp_int 1024 / 0.123568 +cpp_rational 128 + 18.0021 +cpp_rational 128 - 18.0006 +cpp_rational 128 * 31.5924 +cpp_rational 128 / 65.714 +cpp_rational 128 str 0.020339 +cpp_rational 128 +(int)2.47739 +cpp_rational 128 -(int)2.47959 +cpp_rational 128 *(int)2.4377 +cpp_rational 128 /(int)2.50843 +cpp_rational 128 construct0.0102665 +cpp_rational 128 construct(unsigned)0.0624887 +cpp_rational 128 construct(unsigned long long)0.0658436 +cpp_rational 128 + 2.58812 +cpp_rational 128 - 2.60864 +cpp_rational 128 * 5.53837 +cpp_rational 128 / 5.63033 +cpp_rational 128 + 2.68363 +cpp_rational 128 - 2.72926 +cpp_rational 128 * 57.9393 +cpp_rational 128 / 58.0332 +cpp_rational 256 + 46.3981 +cpp_rational 256 - 46.4818 +cpp_rational 256 * 86.0189 +cpp_rational 256 / 172.8 +cpp_rational 256 str 0.0517328 +cpp_rational 256 +(int)2.92179 +cpp_rational 256 -(int)2.90579 +cpp_rational 256 *(int)2.91325 +cpp_rational 256 /(int)3.00689 +cpp_rational 256 construct0.0101737 +cpp_rational 256 construct(unsigned)0.0609531 +cpp_rational 256 construct(unsigned long long)0.0665504 +cpp_rational 256 + 3.0953 +cpp_rational 256 - 3.08277 +cpp_rational 256 * 6.78796 +cpp_rational 256 / 6.90941 +cpp_rational 256 + 3.15142 +cpp_rational 256 - 3.19882 +cpp_rational 256 * 59.3172 +cpp_rational 256 / 59.5431 +cpp_rational 512 + 108.57 +cpp_rational 512 - 108.81 +cpp_rational 512 * 202.007 +cpp_rational 512 / 348.46 +cpp_rational 512 str 0.119248 +cpp_rational 512 +(int)3.80252 +cpp_rational 512 -(int)3.80714 +cpp_rational 512 *(int)3.94768 +cpp_rational 512 /(int)4.00588 +cpp_rational 512 construct0.0101965 +cpp_rational 512 construct(unsigned)0.0613968 +cpp_rational 512 construct(unsigned long long)0.0659082 +cpp_rational 512 + 4.00751 +cpp_rational 512 - 4.0117 +cpp_rational 512 * 9.43852 +cpp_rational 512 / 9.39508 +cpp_rational 512 + 4.05684 +cpp_rational 512 - 4.08474 +cpp_rational 512 * 61.8998 +cpp_rational 512 / 61.9712 +cpp_rational 1024 + 252.723 +cpp_rational 1024 - 253.81 +cpp_rational 1024 * 484.128 +cpp_rational 1024 / 834.057 +cpp_rational 1024 str 0.286067 +cpp_rational 1024 +(int)5.51612 +cpp_rational 1024 -(int)5.51949 +cpp_rational 1024 *(int)5.87507 +cpp_rational 1024 /(int)5.92837 +cpp_rational 1024 construct0.0102909 +cpp_rational 1024 construct(unsigned)0.062674 +cpp_rational 1024 construct(unsigned long long)0.0659089 +cpp_rational 1024 + 5.7444 +cpp_rational 1024 - 5.73296 +cpp_rational 1024 * 15.1475 +cpp_rational 1024 / 14.9497 +cpp_rational 1024 + 5.80438 +cpp_rational 1024 - 5.86 +cpp_rational 1024 * 67.4139 +cpp_rational 1024 / 67.4254 +mpq_rational 128 + 3.16879 +mpq_rational 128 - 3.18835 +mpq_rational 128 * 5.96709 +mpq_rational 128 / 15.0571 +mpq_rational 128 str 0.0037011 +mpq_rational 128 +(int)0.669634 +mpq_rational 128 -(int)0.666993 +mpq_rational 128 *(int)1.18047 +mpq_rational 128 /(int)1.43177 +mpq_rational 128 construct0.383107 +mpq_rational 128 construct(unsigned)0.394551 +mpq_rational 128 construct(unsigned long long)2.13183 +mpq_rational 128 + 2.33701 +mpq_rational 128 - 2.33227 +mpq_rational 128 * 4.15268 +mpq_rational 128 / 4.26818 +mpq_rational 128 + 2.33097 +mpq_rational 128 - 2.31793 +mpq_rational 128 * 9.34086 +mpq_rational 128 / 9.74135 +mpq_rational 256 + 6.93507 +mpq_rational 256 - 6.90939 +mpq_rational 256 * 12.9674 +mpq_rational 256 / 27.1144 +mpq_rational 256 str 0.00573278 +mpq_rational 256 +(int)0.707818 +mpq_rational 256 -(int)0.719174 +mpq_rational 256 *(int)1.22229 +mpq_rational 256 /(int)1.46082 +mpq_rational 256 construct0.381537 +mpq_rational 256 construct(unsigned)0.390987 +mpq_rational 256 construct(unsigned long long)2.12727 +mpq_rational 256 + 2.4159 +mpq_rational 256 - 2.41594 +mpq_rational 256 * 4.3447 +mpq_rational 256 / 4.43342 +mpq_rational 256 + 2.40187 +mpq_rational 256 - 2.39792 +mpq_rational 256 * 9.51195 +mpq_rational 256 / 9.65697 +mpq_rational 512 + 16.0886 +mpq_rational 512 - 16.1169 +mpq_rational 512 * 29.597 +mpq_rational 512 / 54.8579 +mpq_rational 512 str 0.012222 +mpq_rational 512 +(int)0.812783 +mpq_rational 512 -(int)0.810939 +mpq_rational 512 *(int)1.37678 +mpq_rational 512 /(int)1.6328 +mpq_rational 512 construct0.381355 +mpq_rational 512 construct(unsigned)0.392309 +mpq_rational 512 construct(unsigned long long)2.1179 +mpq_rational 512 + 2.55999 +mpq_rational 512 - 2.52842 +mpq_rational 512 * 4.82251 +mpq_rational 512 / 4.88079 +mpq_rational 512 + 2.5091 +mpq_rational 512 - 2.50572 +mpq_rational 512 * 9.90285 +mpq_rational 512 / 10.0077 +mpq_rational 1024 + 38.8883 +mpq_rational 1024 - 38.9096 +mpq_rational 1024 * 71.0635 +mpq_rational 1024 / 123.985 +mpq_rational 1024 str 0.0291802 +mpq_rational 1024 +(int)0.906471 +mpq_rational 1024 -(int)0.908293 +mpq_rational 1024 *(int)1.52386 +mpq_rational 1024 /(int)1.78575 +mpq_rational 1024 construct0.383461 +mpq_rational 1024 construct(unsigned)0.393504 +mpq_rational 1024 construct(unsigned long long)2.12279 +mpq_rational 1024 + 2.67794 +mpq_rational 1024 - 2.65991 +mpq_rational 1024 * 5.4209 +mpq_rational 1024 / 5.47417 +mpq_rational 1024 + 2.66144 +mpq_rational 1024 - 2.64168 +mpq_rational 1024 * 10.4664 +mpq_rational 1024 / 10.6781 +tommath_int 128 + 0.0222815 +tommath_int 128 - 0.027712 +tommath_int 128 * 0.113094 +tommath_int 128 / 3.09636 +tommath_int 128 str 0.0175165 +tommath_int 128 +(int)0.205506 +tommath_int 128 -(int)0.203148 +tommath_int 128 *(int)0.245897 +tommath_int 128 /(int)2.08045 +tommath_int 128 construct0.207455 +tommath_int 128 construct(unsigned)0.477971 +tommath_int 128 construct(unsigned long long)0.709516 +tommath_int 128 % 3.15171 +tommath_int 128 | 0.153434 +tommath_int 128 & 0.153508 +tommath_int 128 ^ 0.153931 +tommath_int 128 << 0.0408165 +tommath_int 128 >> 0.324163 +tommath_int 128 %(int)2.11648 +tommath_int 128 |(int)0.376671 +tommath_int 128 &(int)0.389144 +tommath_int 128 ^(int)0.374303 +tommath_int 128 gcd 12.5322 +tommath_int 128 + 0.514965 +tommath_int 128 - 0.517555 +tommath_int 128 * 0.607102 +tommath_int 128 / 2.36098 +tommath_int 128 + 0.510608 +tommath_int 128 - 0.520979 +tommath_int 128 * 18.5642 +tommath_int 128 / 1.13357 +tommath_int 256 + 0.0322049 +tommath_int 256 - 0.0407704 +tommath_int 256 * 0.346903 +tommath_int 256 / 4.01311 +tommath_int 256 str 0.0409078 +tommath_int 256 +(int)0.211847 +tommath_int 256 -(int)0.206481 +tommath_int 256 *(int)0.26894 +tommath_int 256 /(int)2.7099 +tommath_int 256 construct0.208012 +tommath_int 256 construct(unsigned)0.470752 +tommath_int 256 construct(unsigned long long)0.709045 +tommath_int 256 % 4.08522 +tommath_int 256 | 0.170093 +tommath_int 256 & 0.176384 +tommath_int 256 ^ 0.172198 +tommath_int 256 << 0.0698155 +tommath_int 256 >> 0.383757 +tommath_int 256 %(int)2.74052 +tommath_int 256 |(int)0.375206 +tommath_int 256 &(int)0.389768 +tommath_int 256 ^(int)0.379255 +tommath_int 256 gcd 26.1755 +tommath_int 256 + 0.530504 +tommath_int 256 - 0.527832 +tommath_int 256 * 0.648438 +tommath_int 256 / 3.16803 +tommath_int 256 + 0.526199 +tommath_int 256 - 0.527479 +tommath_int 256 * 18.624 +tommath_int 256 / 1.1208 +tommath_int 512 + 0.0455267 +tommath_int 512 - 0.0515883 +tommath_int 512 * 0.999026 +tommath_int 512 / 5.95775 +tommath_int 512 str 0.111392 +tommath_int 512 +(int)0.227429 +tommath_int 512 -(int)0.219998 +tommath_int 512 *(int)0.31746 +tommath_int 512 /(int)4.1339 +tommath_int 512 construct0.205622 +tommath_int 512 construct(unsigned)0.473807 +tommath_int 512 construct(unsigned long long)0.703879 +tommath_int 512 % 5.70483 +tommath_int 512 | 0.179084 +tommath_int 512 & 0.182373 +tommath_int 512 ^ 0.183434 +tommath_int 512 << 0.0973643 +tommath_int 512 >> 0.398354 +tommath_int 512 %(int)3.96918 +tommath_int 512 |(int)0.381428 +tommath_int 512 &(int)0.40432 +tommath_int 512 ^(int)0.390434 +tommath_int 512 gcd 56.7747 +tommath_int 512 + 0.546222 +tommath_int 512 - 0.53408 +tommath_int 512 * 0.718764 +tommath_int 512 / 5.07545 +tommath_int 512 + 0.543084 +tommath_int 512 - 0.535411 +tommath_int 512 * 18.745 +tommath_int 512 / 1.15084 +tommath_int 1024 + 0.074223 +tommath_int 1024 - 0.0786205 +tommath_int 1024 * 3.20269 +tommath_int 1024 / 12.7383 +tommath_int 1024 str 0.345861 +tommath_int 1024 +(int)0.250477 +tommath_int 1024 -(int)0.2372 +tommath_int 1024 *(int)0.408933 +tommath_int 1024 /(int)9.04346 +tommath_int 1024 construct0.207377 +tommath_int 1024 construct(unsigned)0.475755 +tommath_int 1024 construct(unsigned long long)0.712949 +tommath_int 1024 % 12.6845 +tommath_int 1024 | 0.436588 +tommath_int 1024 & 0.429721 +tommath_int 1024 ^ 0.429478 +tommath_int 1024 << 0.167289 +tommath_int 1024 >> 0.570323 +tommath_int 1024 %(int)9.09202 +tommath_int 1024 |(int)0.622404 +tommath_int 1024 &(int)0.653128 +tommath_int 1024 ^(int)0.62285 +tommath_int 1024 gcd 132.299 +tommath_int 1024 + 0.578521 +tommath_int 1024 - 0.552649 +tommath_int 1024 * 0.871648 +tommath_int 1024 / 12.2672 +tommath_int 1024 + 0.568301 +tommath_int 1024 - 0.54931 +tommath_int 1024 * 19.0954 +tommath_int 1024 / 1.21165 +cpp_dec_float 50 + 0.0250949 +cpp_dec_float 50 - 0.0264782 +cpp_dec_float 50 * 0.163403 +cpp_dec_float 50 / 3.9502 +cpp_dec_float 50 str 0.0207318 +cpp_dec_float 50 +(int)0.0441266 +cpp_dec_float 50 -(int)0.0442578 +cpp_dec_float 50 *(int)0.234992 +cpp_dec_float 50 /(int)1.81469 +cpp_dec_float 50 construct0.00925753 +cpp_dec_float 50 construct(unsigned)0.0588752 +cpp_dec_float 50 construct(unsigned long long)0.0587691 +cpp_dec_float 50 + 0.0770875 +cpp_dec_float 50 - 0.0741921 +cpp_dec_float 50 * 0.329282 +cpp_dec_float 50 / 1.9701 +cpp_dec_float 50 + 0.0640148 +cpp_dec_float 50 - 0.0643402 +cpp_dec_float 50 * 0.321363 +cpp_dec_float 50 / 1.97464 +cpp_dec_float 100 + 0.0291508 +cpp_dec_float 100 - 0.0307447 +cpp_dec_float 100 * 0.284182 +cpp_dec_float 100 / 7.68823 +cpp_dec_float 100 str 0.0328218 +cpp_dec_float 100 +(int)0.0558389 +cpp_dec_float 100 -(int)0.0563278 +cpp_dec_float 100 *(int)0.460635 +cpp_dec_float 100 /(int)3.62471 +cpp_dec_float 100 construct0.0263234 +cpp_dec_float 100 construct(unsigned)0.0747853 +cpp_dec_float 100 construct(unsigned long long)0.076338 +cpp_dec_float 100 + 0.0845054 +cpp_dec_float 100 - 0.0844193 +cpp_dec_float 100 * 0.582119 +cpp_dec_float 100 / 3.8773 +cpp_dec_float 100 + 0.0708668 +cpp_dec_float 100 - 0.0730765 +cpp_dec_float 100 * 0.574512 +cpp_dec_float 100 / 3.83437 +cpp_dec_float 500 + 0.0630915 +cpp_dec_float 500 - 0.0651113 +cpp_dec_float 500 * 2.22501 +cpp_dec_float 500 / 50.6121 +cpp_dec_float 500 str 0.131293 +cpp_dec_float 500 +(int)0.0935946 +cpp_dec_float 500 -(int)0.0950432 +cpp_dec_float 500 *(int)4.36195 +cpp_dec_float 500 /(int)24.4855 +cpp_dec_float 500 construct0.0306104 +cpp_dec_float 500 construct(unsigned)0.114772 +cpp_dec_float 500 construct(unsigned long long)0.117075 +cpp_dec_float 500 + 0.12407 +cpp_dec_float 500 - 0.122646 +cpp_dec_float 500 * 4.75508 +cpp_dec_float 500 / 25.1602 +cpp_dec_float 500 + 0.0865073 +cpp_dec_float 500 - 0.0929075 +cpp_dec_float 500 * 4.74128 +cpp_dec_float 500 / 25.1175 +mpfr_float 50 + 0.0624318 +mpfr_float 50 - 0.0764497 +mpfr_float 50 * 0.342248 +mpfr_float 50 / 1.69721 +mpfr_float 50 str 0.0289013 +mpfr_float 50 +(int)0.121683 +mpfr_float 50 -(int)0.149605 +mpfr_float 50 *(int)0.1548 +mpfr_float 50 /(int)0.213367 +mpfr_float 50 construct0.214552 +mpfr_float 50 construct(unsigned)0.293892 +mpfr_float 50 construct(unsigned long long)0.638307 +mpfr_float 50 + 0.553442 +mpfr_float 50 - 0.565687 +mpfr_float 50 * 0.841214 +mpfr_float 50 / 1.26072 +mpfr_float 50 + 0.537349 +mpfr_float 50 - 0.561924 +mpfr_float 50 * 0.833423 +mpfr_float 50 / 1.25318 +mpfr_float 100 + 0.0669494 +mpfr_float 100 - 0.0820912 +mpfr_float 100 * 0.478422 +mpfr_float 100 / 2.33995 +mpfr_float 100 str 0.0390764 +mpfr_float 100 +(int)0.117387 +mpfr_float 100 -(int)0.150557 +mpfr_float 100 *(int)0.166496 +mpfr_float 100 /(int)0.267439 +mpfr_float 100 construct0.222594 +mpfr_float 100 construct(unsigned)0.297568 +mpfr_float 100 construct(unsigned long long)0.643108 +mpfr_float 100 + 0.573918 +mpfr_float 100 - 0.592139 +mpfr_float 100 * 0.978674 +mpfr_float 100 / 1.5879 +mpfr_float 100 + 0.561143 +mpfr_float 100 - 0.580528 +mpfr_float 100 * 0.97887 +mpfr_float 100 / 1.58378 +mpfr_float 500 + 0.0817812 +mpfr_float 500 - 0.0975533 +mpfr_float 500 * 3.8308 +mpfr_float 500 / 13.8283 +mpfr_float 500 str 0.156188 +mpfr_float 500 +(int)0.129266 +mpfr_float 500 -(int)0.16446 +mpfr_float 500 *(int)0.273431 +mpfr_float 500 /(int)0.731526 +mpfr_float 500 construct0.222587 +mpfr_float 500 construct(unsigned)0.311108 +mpfr_float 500 construct(unsigned long long)0.653074 +mpfr_float 500 + 0.667956 +mpfr_float 500 - 0.684152 +mpfr_float 500 * 1.2661 +mpfr_float 500 / 7.46167 +mpfr_float 500 + 0.642822 +mpfr_float 500 - 0.65164 +mpfr_float 500 * 1.25714 +mpfr_float 500 / 7.46171 +[section:float_performance Float Type Perfomance] +[table Operator * +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.321363s)][1.0169 (0.574512s)][6.76401 (4.74128s)]] +[[gmp_float][1.7169 (0.551747s)][[*1] (0.564962s)][[*1] (0.700957s)]] +[[mpfr_float][2.5934 (0.833423s)][1.73263 (0.97887s)][1.79346 (1.25714s)]] +] +[table Operator *(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][5.56675 (0.234992s)][9.32996 (0.460635s)][50.8459 (4.36195s)]] +[[gmp_float][[*1] (0.0422135s)][[*1] (0.0493716s)][[*1] (0.0857876s)]] +[[mpfr_float][3.66707 (0.1548s)][3.37231 (0.166496s)][3.1873 (0.273431s)]] +] +[table Operator + +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0640148s)][[*1] (0.0708668s)][[*1] (0.0865073s)]] +[[gmp_float][7.467 (0.477999s)][6.72671 (0.476701s)][5.67136 (0.490614s)]] +[[mpfr_float][8.39413 (0.537349s)][7.91828 (0.561143s)][7.43085 (0.642822s)]] +] +[table Operator +(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.33358 (0.0441266s)][1.4433 (0.0558389s)][1.44838 (0.0935946s)]] +[[gmp_float][[*1] (0.0330888s)][[*1] (0.0386882s)][[*1] (0.0646201s)]] +[[mpfr_float][3.67747 (0.121683s)][3.03419 (0.117387s)][2.00041 (0.129266s)]] +] +[table Operator - +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0643402s)][[*1] (0.0730765s)][[*1] (0.0929075s)]] +[[gmp_float][7.76625 (0.499682s)][6.89067 (0.503546s)][5.89566 (0.547751s)]] +[[mpfr_float][8.73364 (0.561924s)][7.94411 (0.580528s)][7.01385 (0.65164s)]] +] +[table Operator -(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0442578s)][[*1] (0.0563278s)][[*1] (0.0950432s)]] +[[gmp_float][3.0379 (0.134451s)][2.39847 (0.1351s)][1.86101 (0.176876s)]] +[[mpfr_float][3.38031 (0.149605s)][2.67288 (0.150557s)][1.73037 (0.16446s)]] +] +[table Operator / +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][2.20938 (1.97464s)][3.71086 (3.83437s)][11.2059 (25.1175s)]] +[[gmp_float][[*1] (0.893752s)][[*1] (1.03328s)][[*1] (2.24146s)]] +[[mpfr_float][1.40216 (1.25318s)][1.53276 (1.58378s)][3.32895 (7.46171s)]] +] +[table Operator /(int) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][10.0596 (1.81469s)][15.5048 (3.62471s)][34.4767 (24.4855s)]] +[[gmp_float][[*1] (0.180393s)][[*1] (0.23378s)][[*1] (0.710204s)]] +[[mpfr_float][1.18279 (0.213367s)][1.14398 (0.267439s)][1.03002 (0.731526s)]] +] +[table Operator construct +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.00925753s)][[*1] (0.0263234s)][[*1] (0.0306104s)]] +[[gmp_float][21.32 (0.19737s)][7.4686 (0.196599s)][6.73181 (0.206063s)]] +[[mpfr_float][23.176 (0.214552s)][8.45613 (0.222594s)][7.27162 (0.222587s)]] +] +[table Operator construct(unsigned long long) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0587691s)][[*1] (0.076338s)][[*1] (0.117075s)]] +[[gmp_float][8.84863 (0.520025s)][6.80343 (0.51936s)][4.59554 (0.538021s)]] +[[mpfr_float][10.8613 (0.638307s)][8.42448 (0.643108s)][5.57826 (0.653074s)]] +] +[table Operator construct(unsigned) +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][[*1] (0.0588752s)][[*1] (0.0747853s)][[*1] (0.114772s)]] +[[gmp_float][3.53421 (0.208078s)][2.76875 (0.207062s)][1.89088 (0.217019s)]] +[[mpfr_float][4.99178 (0.293892s)][3.97896 (0.297568s)][2.71067 (0.311108s)]] +] +[table Operator str +[[Backend][50 Bits][100 Bits][500 Bits]] +[[cpp_dec_float][1.5616 (0.0207318s)][1.61725 (0.0328218s)][[*1] (0.131293s)]] +[[gmp_float][[*1] (0.013276s)][[*1] (0.0202949s)][1.07517 (0.141162s)]] +[[mpfr_float][2.17696 (0.0289013s)][1.92543 (0.0390764s)][1.18962 (0.156188s)]] +] +[endsect] +[section:integer_performance Integer Type Perfomance] +[table Operator % +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][5.31184 (0.37333s)][1.99944e+236 (0.673748s)][2.08204e+236 (0.701584s)][3.39405e+236 (1.14369s)]] +[[cpp_int(fixed)][1.10616 (0.0777437s)][5.8492e+235 (0.1971s)][9.91271e+235 (0.334027s)][1.60165e+236 (0.539708s)][-1.#INF (0.94847s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0702826s)]] +[[gmp_int][9.12715 (0.64148s)][2.088e+236 (0.703592s)][2.43295e+236 (0.819828s)][3.02578e+236 (1.01959s)]] +[[tommath_int][44.8434 (3.15171s)][1.21234e+237 (4.08522s)][1.69298e+237 (5.70483s)][3.7643e+237 (12.6845s)]] +] +[table Operator %(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][3.51789 (0.104856s)][-1.#INF (0.203012s)][-1.#INF (0.391566s)][-1.#INF (0.768511s)]] +[[cpp_int(fixed)][1.14548 (0.0341425s)][-1.#INF (0.103684s)][-1.#INF (0.200647s)][-1.#INF (0.377704s)][-1.#INF (0.743202s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0298064s)]] +[[gmp_int][1.91945 (0.0572117s)][-1.#INF (0.10258s)][-1.#INF (0.188529s)][-1.#INF (0.355222s)]] +[[tommath_int][71.0078 (2.11648s)][-1.#INF (2.74052s)][-1.#INF (3.96918s)][-1.#INF (9.09202s)]] +] +[table Operator & +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][12.079 (0.031605s)][-1.11772e+007 (0.0455929s)][-1.33961e+007 (0.0546439s)][-2.06875e+007 (0.0843863s)]] +[[cpp_int(fixed)][4.74538 (0.0124165s)][-8.36978e+006 (0.0341411s)][-1.22854e+007 (0.0501131s)][-1.4424e+007 (0.0588367s)][-1.#INF (0.0774574s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00261653s)]] +[[gmp_int][20.5664 (0.0538128s)][-1.59881e+007 (0.0652169s)][-2.25796e+007 (0.092104s)][-3.5403e+007 (0.144412s)]] +[[tommath_int][58.6685 (0.153508s)][-4.3241e+007 (0.176384s)][-4.47093e+007 (0.182373s)][-1.05347e+008 (0.429721s)]] +] +[table Operator &(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][23.3956 (0.0377678s)][-7.85844e+307 (0.0471524s)][-1.07843e+308 (0.0647085s)][-1.68143e+308 (0.10089s)]] +[[cpp_int(fixed)][6.49083 (0.0104782s)][-6.95612e+307 (0.0417383s)][-8.99012e+307 (0.0539427s)][-1.17371e+308 (0.070425s)][-1.#INF (0.112823s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00161431s)]] +[[gmp_int][87.5331 (0.141306s)][-1.#INF (0.139398s)][-1.#INF (0.142498s)][-1.#INF (0.141249s)]] +[[tommath_int][241.059 (0.389144s)][-1.#INF (0.389768s)][-1.#INF (0.40432s)][-1.#INF (0.653128s)]] +] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1715.93 (7.6372s)][-4.15607e+276 (7.7121s)][-4.16472e+276 (7.72815s)][-4.23791e+276 (7.86395s)]] +[[cpp_int(fixed)][1.27579 (0.00567824s)][-3.62916e+274 (0.0673436s)][-5.78275e+274 (0.107306s)][-9.2595e+274 (0.171821s)][-1.#INF (0.299236s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00445077s)]] +[[gmp_int][710.595 (3.1627s)][-1.69816e+276 (3.15114s)][-1.70883e+276 (3.17094s)][-1.7293e+276 (3.20893s)]] +[[tommath_int][4171.01 (18.5642s)][-1.00365e+277 (18.624s)][-1.01017e+277 (18.745s)][-1.02906e+277 (19.0954s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.97316 (0.0235876s)][1.#INF (0.0318939s)][1.#INF (0.0427792s)][1.#INF (0.0668616s)]] +[[cpp_int(fixed)][2.32007 (0.00548722s)][1.#INF (0.0328109s)][1.#INF (0.049867s)][1.#INF (0.0658566s)][-1.#INF (0.0948565s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00236511s)]] +[[gmp_int][9.62157 (0.022756s)][1.#INF (0.0282672s)][1.#INF (0.0361075s)][1.#INF (0.0518882s)]] +[[tommath_int][103.969 (0.245897s)][1.#INF (0.26894s)][1.#INF (0.31746s)][1.#INF (0.408933s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.74543 (0.0196594s)][3.98952e+276 (0.0215291s)][4.2355e+276 (0.0228565s)][4.21393e+276 (0.0227402s)]] +[[cpp_int(fixed)][2.13187 (0.00430062s)][3.11951e+276 (0.0168342s)][3.15933e+276 (0.0170491s)][3.19893e+276 (0.0172628s)][-1.#INF (0.0181245s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0020173s)]] +[[gmp_int][337.759 (0.68136s)][1.27731e+278 (0.68929s)][1.28647e+278 (0.694235s)][1.27865e+278 (0.690013s)]] +[[tommath_int][253.115 (0.510608s)][9.75089e+277 (0.526199s)][1.00638e+278 (0.543084s)][1.05311e+278 (0.568301s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.81588 (0.0159069s)][-5.71737e+244 (0.0218386s)][-8.2882e+244 (0.0316584s)][-1.1265e+245 (0.0430289s)]] +[[cpp_int(fixed)][3.92617 (0.00636247s)][-7.02443e+244 (0.0268311s)][-1.07535e+245 (0.0410749s)][-1.37293e+245 (0.0524416s)][-1.#INF (0.0728817s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00162053s)]] +[[gmp_int][19.2059 (0.0311237s)][-1.12054e+245 (0.0428011s)][-1.74239e+245 (0.0665539s)][-2.83458e+245 (0.108272s)]] +[[tommath_int][126.815 (0.205506s)][-5.54618e+245 (0.211847s)][-5.95413e+245 (0.227429s)][-6.55751e+245 (0.250477s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][11.0409 (0.0210968s)][3.86227e+276 (0.0213343s)][4.03471e+276 (0.0222868s)][4.24576e+276 (0.0234526s)]] +[[cpp_int(fixed)][2.02836 (0.00387577s)][3.06763e+276 (0.0169449s)][3.2004e+276 (0.0176783s)][3.27232e+276 (0.0180756s)][-1.#INF (0.0190581s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00191079s)]] +[[gmp_int][356.496 (0.681187s)][1.23744e+278 (0.683532s)][1.2536e+278 (0.69246s)][1.25066e+278 (0.690838s)]] +[[tommath_int][272.651 (0.520979s)][9.54925e+277 (0.527479s)][9.69283e+277 (0.535411s)][9.94446e+277 (0.54931s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][9.24378 (0.0151244s)][-1.01975e-199 (0.017199s)][-1.47092e-199 (0.0248084s)][-1.96387e-199 (0.0331224s)]] +[[cpp_int(fixed)][4.08494 (0.00668367s)][-1.43394e-199 (0.0241848s)][-2.18373e-199 (0.0368306s)][-2.98469e-199 (0.0503396s)][-1.#INF (0.0621059s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00163617s)]] +[[gmp_int][18.693 (0.030585s)][-2.37422e-199 (0.0400434s)][-3.42818e-199 (0.0578194s)][-5.96116e-199 (0.100541s)]] +[[tommath_int][124.161 (0.203148s)][-1.22425e-198 (0.206481s)][-1.30439e-198 (0.219998s)][-1.40639e-198 (0.2372s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.96346 (0.0578293s)][-1.51814e+061 (0.0615507s)][-1.8062e+061 (0.0732298s)][-3.04778e+061 (0.123568s)]] +[[cpp_int(fixed)][1.08704 (0.0320162s)][-8.07606e+060 (0.0327432s)][-8.40351e+060 (0.0340708s)][-1.09735e+061 (0.0444905s)][-1.#INF (0.106788s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0294528s)]] +[[gmp_int][23.2741 (0.685487s)][-1.70068e+062 (0.689516s)][-1.6994e+062 (0.688995s)][-1.74523e+062 (0.707578s)]] +[[tommath_int][38.4876 (1.13357s)][-2.76443e+062 (1.1208s)][-2.83854e+062 (1.15084s)][-2.98853e+062 (1.21165s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][7.87676 (0.235955s)][1.#INF (0.35212s)][1.#INF (0.568032s)][1.#INF (0.989885s)]] +[[cpp_int(fixed)][1.21173 (0.0362985s)][1.#INF (0.137619s)][1.#INF (0.253796s)][1.#INF (0.446782s)][-1.#INF (0.84764s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0299559s)]] +[[gmp_int][1.87075 (0.0560401s)][1.#INF (0.0982823s)][1.#INF (0.183564s)][1.#INF (0.352238s)]] +[[tommath_int][69.4504 (2.08045s)][1.#INF (2.7099s)][1.#INF (4.1339s)][1.#INF (9.04346s)]] +] +[table Operator << +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][15.849 (0.0256107s)][-5.85461e+126 (0.0401135s)][-6.36621e+126 (0.0436188s)][-9.17366e+126 (0.0628544s)]] +[[cpp_int(fixed)][3.19639 (0.00516511s)][-4.68379e+126 (0.0320915s)][-7.40049e+126 (0.0507053s)][-8.72078e+126 (0.0597514s)][-1.#INF (0.0677088s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00161592s)]] +[[gmp_int][16.956 (0.0273994s)][-4.66649e+126 (0.031973s)][-6.88464e+126 (0.0471709s)][-1.05374e+127 (0.0721984s)]] +[[tommath_int][25.259 (0.0408165s)][-1.01897e+127 (0.0698155s)][-1.42104e+127 (0.0973643s)][-2.4416e+127 (0.167289s)]] +] +[table Operator >> +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][14.6983 (0.0237523s)][-2.28921e+307 (0.0302534s)][-2.68808e+307 (0.0355247s)][-3.38364e+307 (0.044717s)]] +[[cpp_int(fixed)][2.47217 (0.00399499s)][-2.21749e+307 (0.0293055s)][-2.9515e+307 (0.039006s)][-3.9023e+307 (0.0515714s)][-1.#INF (0.0626121s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00161599s)]] +[[gmp_int][17.8366 (0.0288237s)][-2.3471e+307 (0.0310184s)][-2.55387e+307 (0.0337511s)][-2.9362e+307 (0.0388038s)]] +[[tommath_int][200.597 (0.324163s)][-1.#INF (0.383757s)][-1.#INF (0.398354s)][-1.#INF (0.570323s)]] +] +[table Operator ^ +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][7.95372 (0.0318172s)][1.21131 (0.0425243s)][1.02246 (0.0542436s)][1.19877 (0.08333s)]] +[[cpp_int(fixed)][2.75762 (0.0110313s)][[*1] (0.0351059s)][[*1] (0.0530521s)][[*1] (0.0695132s)][-1.#INF (0.09783s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.0040003s)]] +[[gmp_int][12.4289 (0.0497194s)][1.79507 (0.0630174s)][1.63955 (0.0869819s)][2.0012 (0.139109s)]] +[[tommath_int][38.4798 (0.153931s)][4.9051 (0.172198s)][3.45761 (0.183434s)][6.17837 (0.429478s)]] +] +[table Operator ^(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][15.3547 (0.0283305s)][-8.92021e+307 (0.0353555s)][-1.05356e+308 (0.041758s)][-1.35819e+308 (0.0538323s)]] +[[cpp_int(fixed)][5.81005 (0.0107199s)][-7.88073e+307 (0.0312355s)][-1.20328e+308 (0.0476923s)][-1.36485e+308 (0.0540962s)][-1.#INF (0.0806317s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00184507s)]] +[[gmp_int][78.0102 (0.143934s)][-1.#INF (0.144825s)][-1.#INF (0.152773s)][-1.#INF (0.161662s)]] +[[tommath_int][202.867 (0.374303s)][-1.#INF (0.379255s)][-1.#INF (0.390434s)][-1.#INF (0.62285s)]] +] +[table Operator construct +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.64088 (0.00293927s)][1.47161e+238 (0.00277479s)][1.49039e+238 (0.0028102s)][1.47064e+238 (0.00277298s)]] +[[cpp_int(fixed)][1.45325 (0.00161745s)][8.73297e+237 (0.00164665s)][1.92709e+238 (0.00363363s)][3.0576e+238 (0.00576526s)][-1.#INF (0.00535599s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00111299s)]] +[[gmp_int][176.266 (0.196182s)][1.06706e+240 (0.201199s)][1.04919e+240 (0.19783s)][1.04712e+240 (0.19744s)]] +[[tommath_int][186.394 (0.207455s)][1.10319e+240 (0.208012s)][1.09052e+240 (0.205622s)][1.09982e+240 (0.207377s)]] +] +[table Operator construct(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][3.51152 (0.00719854s)][-2.80497e-148 (0.00725455s)][-2.79893e-148 (0.00723891s)][-2.83336e-148 (0.00732796s)]] +[[cpp_int(fixed)][[*1] (0.00204998s)][-1.21019e-148 (0.00312994s)][-1.50065e-148 (0.00388115s)][-2.15185e-148 (0.00556537s)][-1.#INF (0.00577713s)]] +[[cpp_int(unsigned, fixed)][1.17501 (0.00240876s)]] +[[gmp_int][351.097 (0.719741s)][-2.82056e-146 (0.729487s)][-2.80186e-146 (0.724649s)][-2.79263e-146 (0.722262s)]] +[[tommath_int][346.109 (0.709516s)][-2.74152e-146 (0.709045s)][-2.72155e-146 (0.703879s)][-2.75662e-146 (0.712949s)]] +] +[table Operator construct(unsigned) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][2.44987 (0.00270684s)][1.90974 (0.0030529s)][[*1] (0.00288857s)][[*1] (0.00265201s)]] +[[cpp_int(fixed)][1.89292 (0.00209147s)][[*1] (0.0015986s)][1.28253 (0.00370466s)][2.19414 (0.0058189s)][-1.#INF (0.00836042s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00110489s)]] +[[gmp_int][186.546 (0.206113s)][132.175 (0.211295s)][71.6424 (0.206944s)][81.5339 (0.216229s)]] +[[tommath_int][432.596 (0.477971s)][294.478 (0.470752s)][164.029 (0.473807s)][179.394 (0.475755s)]] +] +[table Operator gcd +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][8.27321 (4.98644s)][-1.#INF (11.1816s)][-1.#INF (27.2257s)][-1.#INF (73.3735s)]] +[[cpp_int(fixed)][1.0026 (0.604291s)][-1.#INF (4.18006s)][-1.#INF (10.2671s)][-1.#INF (26.2762s)][-1.#INF (76.2849s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.602722s)]] +[[gmp_int][4.06647 (2.45095s)][-1.#INF (5.89505s)][-1.#INF (13.6993s)][-1.#INF (33.2232s)]] +[[tommath_int][20.7927 (12.5322s)][-1.#INF (26.1755s)][-1.#INF (56.7747s)][-1.#INF (132.299s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][1.02246 (0.00189808s)][-3.42215e+178 (0.00391656s)][-7.26989e+178 (0.00832019s)][-1.93625e+179 (0.0221599s)]] +[[cpp_int(fixed)][1.35564 (0.00251659s)][-1.36421e+178 (0.0015613s)][-2.59752e+178 (0.00297279s)][-6.18963e+178 (0.00708386s)][-1.#INF (0.0172514s)]] +[[cpp_int(unsigned, fixed)][1.38149 (0.00256457s)]] +[[gmp_int][[*1] (0.00185638s)][-3.01078e+178 (0.00344576s)][-5.40339e+178 (0.00618403s)][-1.26279e+179 (0.0144523s)]] +[[tommath_int][9.43586 (0.0175165s)][-3.57438e+179 (0.0409078s)][-9.73304e+179 (0.111392s)][-3.02201e+180 (0.345861s)]] +] +[table Operator | +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][11.6542 (0.030991s)][-6.48076e+046 (0.0429658s)][-8.11261e+046 (0.0537846s)][-1.24844e+047 (0.0827684s)]] +[[cpp_int(fixed)][4.09831 (0.0108982s)][-5.73378e+046 (0.0380136s)][-7.98794e+046 (0.0529581s)][-1.02098e+047 (0.0676884s)][-1.#INF (0.100936s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00265921s)]] +[[gmp_int][17.8503 (0.0474678s)][-9.32586e+046 (0.0618281s)][-1.29209e+047 (0.0856626s)][-2.0526e+047 (0.136082s)]] +[[tommath_int][57.6991 (0.153434s)][-2.5656e+047 (0.170093s)][-2.70121e+047 (0.179084s)][-6.58529e+047 (0.436588s)]] +] +[table Operator |(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_int][16.9457 (0.0280516s)][-4.17523e+307 (0.0363929s)][-4.79721e+307 (0.0418143s)][-6.04694e+307 (0.0527075s)]] +[[cpp_int(fixed)][6.70551 (0.0111002s)][-3.64663e+307 (0.0317854s)][-5.35725e+307 (0.0466958s)][-6.16052e+307 (0.0536974s)][-1.#INF (0.0819107s)]] +[[cpp_int(unsigned, fixed)][[*1] (0.00165538s)]] +[[gmp_int][85.2488 (0.141119s)][-1.64044e+308 (0.142987s)][-1.78579e+308 (0.155656s)][-1.#INF (0.163236s)]] +[[tommath_int][227.544 (0.376671s)][-1.#INF (0.375206s)][-1.#INF (0.381428s)][-1.#INF (0.622404s)]] +] +[endsect] +[section:rational_performance Rational Type Perfomance] +[table Operator * +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][6.20279 (57.9393s)][6.23608 (59.3172s)][6.25071 (61.8998s)][6.44097 (67.4139s)]] +[[mpq_rational][[*1] (9.34086s)][[*1] (9.51195s)][[*1] (9.90285s)][[*1] (10.4664s)]] +] +[table Operator *(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][2.06502 (2.4377s)][2.38344 (2.91325s)][2.86734 (3.94768s)][3.8554 (5.87507s)]] +[[mpq_rational][[*1] (1.18047s)][[*1] (1.22229s)][[*1] (1.37678s)][[*1] (1.52386s)]] +] +[table Operator + +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.1513 (2.68363s)][1.31207 (3.15142s)][1.61685 (4.05684s)][2.18092 (5.80438s)]] +[[mpq_rational][[*1] (2.33097s)][[*1] (2.40187s)][[*1] (2.5091s)][[*1] (2.66144s)]] +] +[table Operator +(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.69962 (2.47739s)][4.12788 (2.92179s)][4.67839 (3.80252s)][6.08526 (5.51612s)]] +[[mpq_rational][[*1] (0.669634s)][[*1] (0.707818s)][[*1] (0.812783s)][[*1] (0.906471s)]] +] +[table Operator - +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.17746 (2.72926s)][1.334 (3.19882s)][1.63017 (4.08474s)][2.21829 (5.86s)]] +[[mpq_rational][[*1] (2.31793s)][[*1] (2.39792s)][[*1] (2.50572s)][[*1] (2.64168s)]] +] +[table Operator -(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][3.71756 (2.47959s)][4.04045 (2.90579s)][4.69474 (3.80714s)][6.07677 (5.51949s)]] +[[mpq_rational][[*1] (0.666993s)][[*1] (0.719174s)][[*1] (0.810939s)][[*1] (0.908293s)]] +] +[table Operator / +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.95741 (58.0332s)][6.16582 (59.5431s)][6.19235 (61.9712s)][6.31439 (67.4254s)]] +[[mpq_rational][[*1] (9.74135s)][[*1] (9.65697s)][[*1] (10.0077s)][[*1] (10.6781s)]] +] +[table Operator /(int) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][1.75198 (2.50843s)][2.05836 (3.00689s)][2.45339 (4.00588s)][3.31983 (5.92837s)]] +[[mpq_rational][[*1] (1.43177s)][[*1] (1.46082s)][[*1] (1.6328s)][[*1] (1.78575s)]] +] +[table Operator construct +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.0102665s)][[*1] (0.0101737s)][[*1] (0.0101965s)][[*1] (0.0102909s)]] +[[mpq_rational][37.3164 (0.383107s)][37.5023 (0.381537s)][37.4005 (0.381355s)][37.2621 (0.383461s)]] +] +[table Operator construct(unsigned long long) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.0658436s)][[*1] (0.0665504s)][[*1] (0.0659082s)][[*1] (0.0659089s)]] +[[mpq_rational][32.3771 (2.13183s)][31.9648 (2.12727s)][32.1342 (2.1179s)][32.2079 (2.12279s)]] +] +[table Operator construct(unsigned) +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][[*1] (0.0624887s)][[*1] (0.0609531s)][[*1] (0.0613968s)][[*1] (0.062674s)]] +[[mpq_rational][6.31396 (0.394551s)][6.41455 (0.390987s)][6.38973 (0.392309s)][6.27858 (0.393504s)]] +] +[table Operator str +[[Backend][128 Bits][256 Bits][512 Bits][1024 Bits]] +[[cpp_rational][5.4954 (0.020339s)][9.02403 (0.0517328s)][9.75685 (0.119248s)][9.80346 (0.286067s)]] +[[mpq_rational][[*1] (0.0037011s)][[*1] (0.00573278s)][[*1] (0.012222s)][[*1] (0.0291802s)]] +] +[endsect] diff --git a/libs/multiprecision/performance/performance_test.cpp b/libs/multiprecision/performance/performance_test.cpp new file mode 100644 index 0000000000..be3daeee4d --- /dev/null +++ b/libs/multiprecision/performance/performance_test.cpp @@ -0,0 +1,852 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_CHRONO_HEADER_ONLY + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPF) && !defined(TEST_MPZ) && \ + !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \ + && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ + && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF +# define TEST_MPZ +# define TEST_MPQ +# define TEST_MPFR +# define TEST_CPP_DEC_FLOAT +# define TEST_MPQ +# define TEST_TOMMATH +# define TEST_CPP_INT +# define TEST_CPP_INT_RATIONAL +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) || defined(TEST_MPZ_BOOST_RATIONAL) +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/rational_adaptor.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_TOMMATH) || defined(TEST_TOMMATH_BOOST_RATIONAL) +#include <boost/multiprecision/tommath.hpp> +#include <boost/multiprecision/rational_adaptor.hpp> +#endif +#if defined(TEST_CPP_INT) || defined(TEST_CPP_INT_RATIONAL) +#include <boost/multiprecision/cpp_int.hpp> +#endif + +#include <boost/chrono.hpp> +#include <vector> +#include <map> +#include <string> +#include <cstring> +#include <cctype> +#include <iostream> +#include <iomanip> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +unsigned bits_wanted; // for integer types + +template <class T, int Type> +struct tester +{ + tester() + { + a.assign(500, 0); + for(int i = 0; i < 500; ++i) + { + b.push_back(generate_random()); + c.push_back(generate_random()); + small.push_back(gen()); + } + } + double test_add() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_subtract() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_add_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_subtract_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - 1; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_multiply() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned k = 0; k < b.size(); ++k) + a[k] = b[k] * c[k]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_multiply_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] * 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_divide() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / c[i] + b[i] / small[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_divide_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / 3; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_str(const boost::mpl::false_&) + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < b.size(); ++i) + a[i] = boost::lexical_cast<T>(boost::lexical_cast<std::string>(b[i])); + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_str(const boost::mpl::true_&) + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < b.size(); ++i) + a[i].assign(b[i].str()); + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_str() + { + return test_str(boost::is_class<T>()); + } + // + // The following tests only work for integer types: + // + double test_mod() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] % c[i] + b[i] % small[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_mod_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] % 254; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_or() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] | c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_or_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] | 234; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_and() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] & c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_and_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] & 234; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_xor() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] ^ c[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_xor_int() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] ^ 234; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_complement() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = ~b[i]; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_left_shift() + { + int shift = std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits : bits_wanted; + shift /= 2; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] << shift; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_right_shift() + { + int shift = std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits : bits_wanted; + shift /= 2; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] >> shift; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_gcd() + { + using boost::math::gcd; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = gcd(b[i], c[i]); + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_powm() + { + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 25; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = powm(b[i], b[i] / 2, c[i]); + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + double test_construct() + { + std::allocator<T> a; + T* pt = a.allocate(1000); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < 1000; ++i) + new(pt+i) T(); + for(unsigned i = 0; i < 1000; ++i) + a.destroy(pt+i); + } + double result = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } + double test_construct_unsigned() + { + std::allocator<T> a; + T* pt = a.allocate(1000); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < 1000; ++i) + new(pt+i) T(i); + for(unsigned i = 0; i < 1000; ++i) + a.destroy(pt+i); + } + double result = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } + double test_construct_unsigned_ll() + { + std::allocator<T> a; + T* pt = a.allocate(1000); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned long long j = 0; j < 1000; ++j) + new(pt+j) T(j); + for(unsigned j = 0; j < 1000; ++j) + a.destroy(pt+j); + } + double result = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + a.deallocate(pt, 1000); + return result; + } + + // + // Hetero operations: + // + template <class U> + static U get_hetero_test_value(boost::mpl::false_ const&) + { + return U(2) / 3; + } + template <class U> + static U get_hetero_test_value(boost::mpl::true_ const&) + { + return (std::numeric_limits<U>::max)() >> 4; + } + template <class U> + static U get_hetero_test_value() + { + return get_hetero_test_value<U>(boost::is_integral<U>()); + } + template <class U> + double test_multiply_hetero() + { + static const U val = get_hetero_test_value<U>(); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] * val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_inplace_multiply_hetero() + { + static const U val = get_hetero_test_value<U>(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] *= val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_add_hetero() + { + static const U val = get_hetero_test_value<U>(); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] + val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_inplace_add_hetero() + { + static const U val = get_hetero_test_value<U>(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] += val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_subtract_hetero() + { + static const U val = get_hetero_test_value<U>(); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] - val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_inplace_subtract_hetero() + { + static const U val = get_hetero_test_value<U>(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] -= val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_divide_hetero() + { + static const U val = get_hetero_test_value<U>(); + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i] / val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } + template <class U> + double test_inplace_divide_hetero() + { + static const U val = get_hetero_test_value<U>(); + for(unsigned i = 0; i < b.size(); ++i) + a[i] = b[i]; + stopwatch<boost::chrono::high_resolution_clock> w; + for(unsigned i = 0; i < 1000; ++i) + { + for(unsigned i = 0; i < b.size(); ++i) + a[i] /= val; + } + return boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + } +private: + T generate_random() + { + return generate_random(boost::mpl::int_<Type>()); + } + T generate_random(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&) + { + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + int e; + val = frexp(val, &e); + + typedef typename T::backend_type::exponent_type e_type; + static boost::random::uniform_int_distribution<e_type> ui(-30, 30); + return ldexp(val, static_cast<int>(ui(gen))); + } + T generate_random(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&) + { + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; + } + T generate_random(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&) + { + typedef boost::random::mt19937::result_type random_type; + typedef typename boost::multiprecision::component_type<T>::type IntType; + + IntType max_val; + unsigned digits; + if(std::numeric_limits<IntType>::is_bounded) + { + max_val = (std::numeric_limits<IntType>::max)(); + digits = std::numeric_limits<IntType>::digits; + } + else + { + max_val = IntType(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + IntType val = 0; + IntType denom = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + for(unsigned i = 0; i < terms_needed; ++i) + { + denom *= (gen.max)(); + denom += gen(); + } + if(denom == 0) + denom = 1; + val %= max_val; + denom %= max_val; + return T(val, denom); + } + std::vector<T> a, b, c, small; + static boost::random::mt19937 gen; +}; + +template <class N, int V> +boost::random::mt19937 tester<N, V>::gen; + +const char* category_name(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&) +{ + return "integer"; +} +const char* category_name(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&) +{ + return "float"; +} +const char* category_name(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&) +{ + return "rational"; +} + +// +// Keys in order are: +// Category +// Operator +// Type +// Precision +// Time +// +std::map<std::string, std::map<std::string, std::map<std::string, std::map<int, double> > > > result_table; + +void report_result(const char* cat, const char* type, const char* op, unsigned precision, double time) +{ + std::cout << std::left << std::setw(15) << type << std::setw(10) << precision << std::setw(35) << op << time << std::endl; + result_table[cat][op][type][precision] = time; +} + +template <class Number, int N> +void test_int_ops(tester<Number, N>& t, const char* type, unsigned precision, const boost::mpl::int_<boost::multiprecision::number_kind_integer>&) +{ + const char* cat = "integer"; + report_result(cat, type, "%", precision, t.test_mod()); + report_result(cat, type, "|", precision, t.test_or()); + report_result(cat, type, "&", precision, t.test_and()); + report_result(cat, type, "^", precision, t.test_xor()); + //report_result(cat, type, "~", precision, t.test_complement()); + report_result(cat, type, "<<", precision, t.test_left_shift()); + report_result(cat, type, ">>", precision, t.test_right_shift()); + // integer ops: + report_result(cat, type, "%(int)", precision, t.test_mod_int()); + report_result(cat, type, "|(int)", precision, t.test_or_int()); + report_result(cat, type, "&(int)", precision, t.test_and_int()); + report_result(cat, type, "^(int)", precision, t.test_xor_int()); + report_result(cat, type, "gcd", precision, t.test_gcd()); + report_result(cat, type, "powm", precision, t.test_powm()); +} +template <class Number, int N, class U> +void test_int_ops(tester<Number, N>& t, const char* type, unsigned precision, const U&) +{ +} + +template <class Number> +void test(const char* type, unsigned precision) +{ + bits_wanted = precision; + tester<Number, boost::multiprecision::number_category<Number>::value> t; + const char* cat = category_name(typename boost::multiprecision::number_category<Number>::type()); + // + // call t.test_multiply() first so that the destination operands are + // forced to perform whatever memory allocation may be needed. That way + // we measure only algorithm performance, and not memory allocation effects. + // + t.test_multiply(); + // + // Now the actual tests: + // + report_result(cat, type, "+", precision, t.test_add()); + report_result(cat, type, "-", precision, t.test_subtract()); + report_result(cat, type, "*", precision, t.test_multiply()); + report_result(cat, type, "/", precision, t.test_divide()); + report_result(cat, type, "str", precision, t.test_str()); + // integer ops: + report_result(cat, type, "+(int)", precision, t.test_add_int()); + report_result(cat, type, "-(int)", precision, t.test_subtract_int()); + report_result(cat, type, "*(int)", precision, t.test_multiply_int()); + report_result(cat, type, "/(int)", precision, t.test_divide_int()); + // construction and destruction: + report_result(cat, type, "construct", precision, t.test_construct()); + report_result(cat, type, "construct(unsigned)", precision, t.test_construct_unsigned()); + report_result(cat, type, "construct(unsigned long long)", precision, t.test_construct_unsigned_ll()); + test_int_ops(t, type, precision, typename boost::multiprecision::number_category<Number>::type()); + // Hetero ops: + report_result(cat, type, "+(unsigned long long)", precision, t.template test_add_hetero<unsigned long long>()); + report_result(cat, type, "-(unsigned long long)", precision, t.template test_subtract_hetero<unsigned long long>()); + report_result(cat, type, "*(unsigned long long)", precision, t.template test_multiply_hetero<unsigned long long>()); + report_result(cat, type, "/(unsigned long long)", precision, t.template test_divide_hetero<unsigned long long>()); + report_result(cat, type, "+=(unsigned long long)", precision, t.template test_inplace_add_hetero<unsigned long long>()); + report_result(cat, type, "-=(unsigned long long)", precision, t.template test_inplace_subtract_hetero<unsigned long long>()); + report_result(cat, type, "*=(unsigned long long)", precision, t.template test_inplace_multiply_hetero<unsigned long long>()); + report_result(cat, type, "/=(unsigned long long)", precision, t.template test_inplace_divide_hetero<unsigned long long>()); +} + +void quickbook_results() +{ + // + // Keys in order are: + // Category + // Operator + // Type + // Precision + // Time + // + typedef std::map<std::string, std::map<std::string, std::map<std::string, std::map<int, double> > > >::const_iterator category_iterator; + typedef std::map<std::string, std::map<std::string, std::map<int, double> > >::const_iterator operator_iterator; + typedef std::map<std::string, std::map<int, double> >::const_iterator type_iterator; + typedef std::map<int, double>::const_iterator precision_iterator; + + for(category_iterator i = result_table.begin(); i != result_table.end(); ++i) + { + std::string cat = i->first; + cat[0] = std::toupper(cat[0]); + std::cout << "[section:" << i->first << "_performance " << cat << " Type Perfomance]" << std::endl; + + for(operator_iterator j = i->second.begin(); j != i->second.end(); ++j) + { + std::string op = j->first; + std::cout << "[table Operator " << op << std::endl; + std::cout << "[[Backend]"; + + for(precision_iterator k = j->second.begin()->second.begin(); k != j->second.begin()->second.end(); ++k) + { + std::cout << "[" << k->first << " Bits]"; + } + std::cout << "]\n"; + + std::vector<double> best_times(j->second.begin()->second.size(), (std::numeric_limits<double>::max)()); + for(unsigned m = 0; m < j->second.begin()->second.size(); ++m) + { + for(type_iterator k = j->second.begin(); k != j->second.end(); ++k) + { + precision_iterator l = k->second.begin(); + std::advance(l, m); + if(best_times[m] > l->second) + best_times[m] = l->second ? l->second : best_times[m]; + } + } + + for(type_iterator k = j->second.begin(); k != j->second.end(); ++k) + { + std::cout << "[[" << k->first << "]"; + + unsigned m = 0; + for(precision_iterator l = k->second.begin(); l != k->second.end(); ++l) + { + double rel_time = l->second / best_times[m]; + if(rel_time == 1) + std::cout << "[[*" << rel_time << "]"; + else + std::cout << "[" << rel_time; + std::cout << " (" << l->second << "s)]"; + ++m; + } + + std::cout << "]\n"; + } + + std::cout << "]\n"; + } + + std::cout << "[endsect]" << std::endl; + } +} + + +int main() +{ +#ifdef TEST_INT64 + test<boost::uint64_t>("boost::uint64_t", 64); +#endif +#ifdef TEST_MPF + test<boost::multiprecision::mpf_float_50>("gmp_float", 50); + test<boost::multiprecision::mpf_float_100>("gmp_float", 100); + test<boost::multiprecision::mpf_float_500>("gmp_float", 500); +#endif +#ifdef TEST_MPZ + test<boost::multiprecision::mpz_int>("gmp_int", 128); + test<boost::multiprecision::mpz_int>("gmp_int", 256); + test<boost::multiprecision::mpz_int>("gmp_int", 512); + test<boost::multiprecision::mpz_int>("gmp_int", 1024); +#endif +#ifdef TEST_CPP_INT + //test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(unsigned, fixed)", 64); + //test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(fixed)", 64); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<128, 128, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(fixed)", 128); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<256, 256, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(fixed)", 256); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<512, 512, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(fixed)", 512); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<1024, 1024, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void>, boost::multiprecision::et_off> >("cpp_int(fixed)", 1024); + + test<boost::multiprecision::cpp_int>("cpp_int", 128); + test<boost::multiprecision::cpp_int>("cpp_int", 256); + test<boost::multiprecision::cpp_int>("cpp_int", 512); + test<boost::multiprecision::cpp_int>("cpp_int", 1024); +#endif +#ifdef TEST_CPP_INT_RATIONAL + test<boost::multiprecision::cpp_rational>("cpp_rational", 128); + test<boost::multiprecision::cpp_rational>("cpp_rational", 256); + test<boost::multiprecision::cpp_rational>("cpp_rational", 512); + test<boost::multiprecision::cpp_rational>("cpp_rational", 1024); +#endif +#ifdef TEST_MPQ + test<boost::multiprecision::mpq_rational>("mpq_rational", 128); + test<boost::multiprecision::mpq_rational>("mpq_rational", 256); + test<boost::multiprecision::mpq_rational>("mpq_rational", 512); + test<boost::multiprecision::mpq_rational>("mpq_rational", 1024); +#endif +#ifdef TEST_TOMMATH + test<boost::multiprecision::tom_int>("tommath_int", 128); + test<boost::multiprecision::tom_int>("tommath_int", 256); + test<boost::multiprecision::tom_int>("tommath_int", 512); + test<boost::multiprecision::tom_int>("tommath_int", 1024); + /* + // + // These are actually too slow to test!!! + // + test<boost::multiprecision::tom_rational>("tom_rational", 128); + test<boost::multiprecision::tom_rational>("tom_rational", 256); + test<boost::multiprecision::tom_rational>("tom_rational", 512); + test<boost::multiprecision::tom_rational>("tom_rational", 1024); + */ +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>("cpp_dec_float", 50); + test<boost::multiprecision::cpp_dec_float_100>("cpp_dec_float", 100); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<500> > >("cpp_dec_float", 500); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>("cpp_bin_float", 50); + test<boost::multiprecision::cpp_bin_float_100>("cpp_bin_float", 100); + test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<500> > >("cpp_bin_float", 500); +#endif +#ifdef TEST_MPFR + test<boost::multiprecision::mpfr_float_50>("mpfr_float", 50); + test<boost::multiprecision::mpfr_float_100>("mpfr_float", 100); + test<boost::multiprecision::mpfr_float_500>("mpfr_float", 500); +#endif + quickbook_results(); + return 0; +} + diff --git a/libs/multiprecision/performance/sf_performance-msvc-10.log b/libs/multiprecision/performance/sf_performance-msvc-10.log new file mode 100644 index 0000000000..9dc8de7b18 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance-msvc-10.log @@ -0,0 +1,69 @@ +0 +11 +24 +3 +13 +27 +Testing Bessel Functions..... +Time for mpfr_float_50 = 6.47208 seconds +Total allocations for mpfr_float_50 = 2684348 +Time for mpf_float_50 = 11.6627 seconds +Total allocations for mpf_float_50 = 2601366 +Time for cpp_float_50 = 20.2855 seconds +Total allocations for cpp_float_50 = 0 +Time for mpfr_class (50 digits) = 6.48063 seconds +Total allocations for mpfr_class (50 digits) = 3946031 +Time for mpreal (50 digits) = 9.98151 seconds +Total allocations for mpreal (50 digits) = 13223017 +Time for mpfr_float_100 = 10.154 seconds +Total allocations for mpfr_float_50 = 3671485 +Time for mpf_float_100 = 8.51179 seconds +Total allocations for mpf_float_100 = 3593669 +Time for cpp_float_100 = 21.0198 seconds +Total allocations for cpp_float_100 = 0 +Time for mpfr_class (100 digits) = 9.80571 seconds +Total allocations for mpfr_class (100 digits) = 5447348 +Time for mpreal (100 digits) = 13.7021 seconds +Total allocations for mpreal (100 digits) = 16671065 +Testing Polynomial Evaluation..... +Time for mpfr_float_50 = 0.00823841 seconds +Total allocations for mpfr_float_50 = 2996 +Time for mpf_float_50 = 0.00401608 seconds +Total allocations for mpf_float_50 = 2996 +Time for cpp_float_50 = 0.00492116 seconds +Total allocations for cpp_float_50 = 0 +Time for mpfr_class (50 digits) = 0.00935629 seconds +Total allocations for mpfr_class (50 digits) = 12976 +Time for mpreal (50 digits) = 0.0148374 seconds +Total allocations for mpreal (50 digits = 27947 +Time for mpfr_float_100 = 0.00948452 seconds +Total allocations for mpfr_float_100 = 2996 +Time for mpf_float_100 = 0.00390071 seconds +Total allocations for mpf_float_100 = 2996 +Time for cpp_float_100 = 0.00893563 seconds +Total allocations for cpp_float_100 = 0 +Time for mpfr_class (100 digits) = 0.0106166 seconds +Total allocations for mpfr_class (100 digits) = 12976 +Time for mpreal (100 digits) = 0.0162364 seconds +Total allocations for mpreal (100 digits) = 27947 +Testing Non-Central T..... +Time for mpfr_float_50 = 258.087 seconds +Total allocations for mpfr_float_50 = 139149049 +Time for mpf_float_50 = 197.303 seconds +Total allocations for mpf_float_50 = 134600354 +Time for cpp_float_50 = 334.503 seconds +Total allocations for cpp_float_50 = 0 +Time for mpfr_class (50 digits) = 266.389 seconds +Total allocations for mpfr_class (50 digits) = 252401115 +Time for mpreal (50 digits) = 346.641 seconds +Total allocations for mpreal (50 digits) = 447009420 +Time for mpfr_float_100 = 516.741 seconds +Total allocations for mpfr_float_100 = 220400854 +Time for mpf_float_100 = 397.302 seconds +Total allocations for mpf_float_100 = 212307349 +Time for cpp_float_100 = 1064.53 seconds +Total allocations for cpp_float_100 = 0 +Time for mpfr_class (100 digits) = 525.74 seconds +Total allocations for mpfr_class (100 digits) = 407154781 +Time for mpreal (100 digits) = 649.941 seconds +Total allocations for mpreal (100 digits) = 724581024 diff --git a/libs/multiprecision/performance/sf_performance.cpp b/libs/multiprecision/performance/sf_performance.cpp new file mode 100644 index 0000000000..95c08d1820 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance.cpp @@ -0,0 +1,45 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +int main() +{ + using namespace boost::multiprecision; + +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) || defined(TEST_MPREAL) || defined(TEST_MPF) + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); +#endif + + basic_tests(); + bessel_tests(); + poly_tests(); + nct_tests(); +} + diff --git a/libs/multiprecision/performance/sf_performance.hpp b/libs/multiprecision/performance/sf_performance.hpp new file mode 100644 index 0000000000..4b056e1e25 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance.hpp @@ -0,0 +1,214 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#define BOOST_MATH_MAX_ROOT_ITERATION_POLICY 750 +#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false + +#if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPFR +# define TEST_MPF +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_BIN_FLOAT +//# define TEST_MPFR_CLASS +//# define TEST_MPREAL +# define TEST_FLOAT +#endif + +#ifdef TEST_FLOAT +#include "arithmetic_backend.hpp" +#endif +#ifdef TEST_MPFR_CLASS +#include <boost/math/bindings/mpfr.hpp> +#endif +#ifdef TEST_MPFR +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_MPREAL +#include <boost/math/bindings/mpreal.hpp> +#endif +#ifdef TEST_MPF +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#include <boost/multiprecision/mpfr.hpp> +#endif +#include <boost/math/special_functions/bessel.hpp> +#include <boost/math/tools/rational.hpp> +#include <boost/math/distributions/non_central_t.hpp> +#include <libs/math/test/table_type.hpp> +#include <boost/chrono.hpp> +#include <boost/array.hpp> +#include <boost/thread.hpp> + +template <class Real> +Real test_bessel(); + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +template <class Real> +Real test_bessel() +{ + try{ +# define T double +# define SC_(x) x +# include "libs/math/test/bessel_i_int_data.ipp" +# include "libs/math/test/bessel_i_data.ipp" + + Real r; + + for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_int_data[i][0]), Real(bessel_i_int_data[i][1])); + } + for(unsigned i = 0; i < bessel_i_data.size(); ++i) + { + r += boost::math::cyl_bessel_i(Real(bessel_i_data[i][0]), Real(bessel_i_data[i][1])); + } + +#include "libs/math/test/bessel_j_int_data.ipp" + for(unsigned i = 0; i < bessel_j_int_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_int_data[i][0]), Real(bessel_j_int_data[i][1])); + } + +#include "libs/math/test/bessel_j_data.ipp" + for(unsigned i = 0; i < bessel_j_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_data[i][0]), Real(bessel_j_data[i][1])); + } + +#include "libs/math/test/bessel_j_large_data.ipp" + for(unsigned i = 0; i < bessel_j_large_data.size(); ++i) + { + r += boost::math::cyl_bessel_j(Real(bessel_j_large_data[i][0]), Real(bessel_j_large_data[i][1])); + } + +#include "libs/math/test/sph_bessel_data.ipp" + for(unsigned i = 0; i < sph_bessel_data.size(); ++i) + { + r += boost::math::sph_bessel(static_cast<unsigned>(sph_bessel_data[i][0]), Real(sph_bessel_data[i][1])); + } + + return r; + } + catch(const std::exception& e) + { + std::cout << e.what() << std::endl; + } + return 0; +} + +template <class Real> +Real test_polynomial() +{ + static const unsigned t[] = { + 2, 3, 4, 5, 6, 7, 8 }; + Real result = 0; + for(Real k = 2; k < 1000; ++k) + result += boost::math::tools::evaluate_polynomial(t, k); + + return result; +} + +template <class Real> +Real test_nct() +{ +#define T double +#include "libs/math/test/nct.ipp" + + Real result = 0; + for(unsigned i = 0; i < nct.size(); ++i) + { + try{ + result += quantile(boost::math::non_central_t_distribution<Real>(nct[i][0], nct[i][1]), nct[i][3]); + result += cdf(boost::math::non_central_t_distribution<Real>(nct[i][0], nct[i][1]), nct[i][2]); + } + catch(const std::exception&) + {} + } + return result; +} + +extern unsigned allocation_count; + +template <class Real> +void basic_allocation_test(const char* name, Real x) +{ + static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; + allocation_count = 0; + Real result = (((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]; + std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; +} + +template <class Real> +void poly_allocation_test(const char* name, Real x) +{ + static const unsigned a[] = { 2, 3, 4, 5, 6, 7, 8 }; + allocation_count = 0; + Real result = boost::math::tools::evaluate_polynomial(a, x); + std::cout << "Allocation count for type " << name << " = " << allocation_count << std::endl; +} + +template <class Real> +void time_proc(const char* name, Real (*proc)(), unsigned threads = 1) +{ + try{ + static Real total = 0; + allocation_count = 0; + boost::chrono::duration<double> time; + stopwatch<boost::chrono::high_resolution_clock> c; + total += proc(); + time = c.elapsed(); + std::cout << "Time for " << name << " = " << time << std::endl; + std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; + + for(unsigned thread_count = 1; thread_count < threads; ++thread_count) + { + c.reset(); + boost::thread_group g; + for(unsigned i = 0; i <= thread_count; ++i) + g.create_thread(proc); + g.join_all(); + time = c.elapsed(); + std::cout << "Time for " << name << " (" << (thread_count + 1) << " threads) = " << time << std::endl; + std::cout << "Total allocations for " << name << " = " << allocation_count << std::endl; + } + } + catch(const std::exception& e) + { + std::cout << e.what() << std::endl; + } +} + +using namespace boost::multiprecision; + +void basic_tests(); +void bessel_tests(); +void poly_tests(); +void nct_tests(); diff --git a/libs/multiprecision/performance/sf_performance_basic.cpp b/libs/multiprecision/performance/sf_performance_basic.cpp new file mode 100644 index 0000000000..a433288fdb --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_basic.cpp @@ -0,0 +1,49 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void basic_tests() +{ + + std::cout << "Allocation Counts for Horner Evaluation:\n"; +#ifdef TEST_MPFR + basic_allocation_test("mpfr_float_50", mpfr_float_50(2)); + basic_allocation_test("mpfr_float_50 - no expression templates", number<mpfr_float_backend<50>, et_off>(2)); +#endif +#ifdef TEST_MPFR_CLASS + basic_allocation_test("mpfr_class", mpfr_class(2)); +#endif +#ifdef TEST_MPREAL + basic_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); +#endif + + std::cout << "Allocation Counts for boost::math::tools::evaluate_polynomial:\n"; +#ifdef TEST_MPFR + poly_allocation_test("mpfr_float_50", mpfr_float_50(2)); + poly_allocation_test("mpfr_float_50 - no expression templates", number<mpfr_float_backend<50>, et_off>(2)); +#endif +#ifdef TEST_MPFR_CLASS + poly_allocation_test("mpfr_class", mpfr_class(2)); +#endif +#ifdef TEST_MPREAL + poly_allocation_test("mpfr::mpreal", mpfr::mpreal(2)); +#endif + + // + // Comparison for builtin floats: + // +#ifdef TEST_FLOAT + time_proc("Bessel Functions - double", test_bessel<double>); + time_proc("Bessel Functions - real_concept", test_bessel<boost::math::concepts::real_concept>); + time_proc("Bessel Functions - arithmetic_backend<double>", test_bessel<number<arithmetic_backend<double>, et_on> >); + time_proc("Bessel Functions - arithmetic_backend<double> - no expression templates", test_bessel<number<arithmetic_backend<double>, et_off> >); + + time_proc("Non-central T - double", test_nct<double>); + time_proc("Non-central T - real_concept", test_nct<boost::math::concepts::real_concept>); + time_proc("Non-central T - arithmetic_backend<double>", test_nct<number<arithmetic_backend<double>, et_on> >); + time_proc("Non-central T - arithmetic_backend<double> - no expression templates", test_nct<number<arithmetic_backend<double>, et_off> >); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel.cpp b/libs/multiprecision/performance/sf_performance_bessel.cpp new file mode 100644 index 0000000000..817f5a56ab --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_1(); +void bessel_tests_2(); +void bessel_tests_3(); +void bessel_tests_4(); +void bessel_tests_5(); +void bessel_tests_6(); + +void bessel_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Bessel Functions at 50 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif + + bessel_tests_1(); + bessel_tests_2(); + bessel_tests_3(); + + // + // Then 100 digits: + // + std::cout << "Testing Bessel Functions at 100 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(100 * 1000L / 301L); +#endif + bessel_tests_4(); + bessel_tests_5(); + bessel_tests_6(); +} diff --git a/libs/multiprecision/performance/sf_performance_bessel1.cpp b/libs/multiprecision/performance/sf_performance_bessel1.cpp new file mode 100644 index 0000000000..6c13315f2d --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel1.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_1() +{ +#ifdef TEST_MPFR +#if MPFR_VERSION<MPFR_VERSION_NUM(3,0,0) + time_proc("mpfr_float_50", test_bessel<boost::multiprecision::mpfr_float_50>, 1); + time_proc("mpfr_float_50 (no expression templates)", test_bessel<number<mpfr_float_backend<50>, et_off> >, 1); + time_proc("static_mpfr_float_50", test_bessel<number<mpfr_float_backend<50, allocate_stack>, et_on> >, 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel<number<mpfr_float_backend<50, allocate_stack>, et_off> >, 1); +#else + time_proc("mpfr_float_50", test_bessel<boost::multiprecision::mpfr_float_50>, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("mpfr_float_50 (no expression templates", test_bessel<number<mpfr_float_backend<50>, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50", test_bessel<number<mpfr_float_backend<50, allocate_stack>, et_on> >, mpfr_buildopt_tls_p() ? 3 : 1); + time_proc("static_mpfr_float_50 (no expression templates)", test_bessel<number<mpfr_float_backend<50, allocate_stack>, et_off> >, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel2.cpp b/libs/multiprecision/performance/sf_performance_bessel2.cpp new file mode 100644 index 0000000000..13b0f597d9 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel2.cpp @@ -0,0 +1,20 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_2() +{ +#ifdef TEST_MPF + time_proc("mpf_float_50", test_bessel<mpf_float_50>, 3); + time_proc("mpf_float_50 (no expression templates", test_bessel<number<gmp_float<50>, et_off> >, 3); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_bessel<cpp_dec_float_50>, 3); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_bessel<cpp_bin_float_50>, 3); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel3.cpp b/libs/multiprecision/performance/sf_performance_bessel3.cpp new file mode 100644 index 0000000000..67ee0fba63 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel3.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_3() +{ +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_bessel<mpfr_class>, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_bessel<mpfr::mpreal>, mpfr_buildopt_tls_p() ? 3 : 1); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel4.cpp b/libs/multiprecision/performance/sf_performance_bessel4.cpp new file mode 100644 index 0000000000..108d62e130 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel4.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_4() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_bessel<mpfr_float_100>); + time_proc("mpfr_float_100 (no expression templates", test_bessel<number<mpfr_float_backend<100>, et_off> >); + time_proc("static_mpfr_float_100", test_bessel<static_mpfr_float_100>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel5.cpp b/libs/multiprecision/performance/sf_performance_bessel5.cpp new file mode 100644 index 0000000000..f1154b5929 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel5.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_5() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_100", test_bessel<mpf_float_100>); + time_proc("mpf_float_100 (no expression templates", test_bessel<number<gmp_float<100>, et_off> >); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_bessel6.cpp b/libs/multiprecision/performance/sf_performance_bessel6.cpp new file mode 100644 index 0000000000..342c10930f --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_bessel6.cpp @@ -0,0 +1,22 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void bessel_tests_6() +{ +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_bessel<cpp_dec_float_100>); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_bessel<cpp_bin_float_100>); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_bessel<mpfr_class>); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_bessel<mpfr::mpreal>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct.cpp b/libs/multiprecision/performance/sf_performance_nct.cpp new file mode 100644 index 0000000000..c0a713bad2 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct.cpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_1(); +void nct_tests_2(); +void nct_tests_3(); +void nct_tests_4(); +void nct_tests_5(); +void nct_tests_6(); + +void nct_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Non-Central T at 50 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(50 * 1000L / 301L); +#endif + + nct_tests_1(); + nct_tests_2(); + nct_tests_3(); + + // + // Then 100 digits: + // + std::cout << "Testing Non-Central T at 100 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(100 * 1000L / 301L); +#endif + nct_tests_4(); + nct_tests_5(); + nct_tests_6(); +} diff --git a/libs/multiprecision/performance/sf_performance_nct1.cpp b/libs/multiprecision/performance/sf_performance_nct1.cpp new file mode 100644 index 0000000000..cde285c922 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct1.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_1() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_50", test_nct<mpfr_float_50>); + time_proc("mpfr_float_50 (no expression templates", test_nct<number<mpfr_float_backend<50>, et_off> >); + time_proc("static_mpfr_float_50", test_nct<static_mpfr_float_50>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct2.cpp b/libs/multiprecision/performance/sf_performance_nct2.cpp new file mode 100644 index 0000000000..76142bea49 --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct2.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_2() +{ +#ifdef TEST_MPF + time_proc("mpf_float_50", test_nct<mpf_float_50>); + time_proc("mpf_float_50 (no expression templates", test_nct<number<gmp_float<50>, et_off> >); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct3.cpp b/libs/multiprecision/performance/sf_performance_nct3.cpp new file mode 100644 index 0000000000..a229669aea --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct3.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_3() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_nct<cpp_dec_float_50>); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_nct<cpp_bin_float_50>, 3); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_nct<mpfr_class>); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_nct<mpfr::mpreal>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct4.cpp b/libs/multiprecision/performance/sf_performance_nct4.cpp new file mode 100644 index 0000000000..1ad302711a --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct4.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_4() +{ +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_nct<mpfr_float_100>); + time_proc("mpfr_float_100 (no expression templates", test_nct<number<mpfr_float_backend<100>, et_off> >); + time_proc("static_mpfr_float_100", test_nct<static_mpfr_float_100>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct5.cpp b/libs/multiprecision/performance/sf_performance_nct5.cpp new file mode 100644 index 0000000000..c098ab201c --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct5.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_5() +{ +#ifdef TEST_MPF + time_proc("mpf_float_100", test_nct<mpf_float_100>); + time_proc("mpf_float_100 (no expression templates", test_nct<number<gmp_float<100>, et_off> >); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_nct6.cpp b/libs/multiprecision/performance/sf_performance_nct6.cpp new file mode 100644 index 0000000000..571ff56efa --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_nct6.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void nct_tests_6() +{ +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_nct<cpp_dec_float_100>); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_nct<cpp_bin_float_100>); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_nct<mpfr_class>); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_nct<mpfr::mpreal>); +#endif +} diff --git a/libs/multiprecision/performance/sf_performance_poly.cpp b/libs/multiprecision/performance/sf_performance_poly.cpp new file mode 100644 index 0000000000..563ac6684b --- /dev/null +++ b/libs/multiprecision/performance/sf_performance_poly.cpp @@ -0,0 +1,72 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "sf_performance.hpp" + +void poly_tests() +{ + // + // 50 digits first: + // + std::cout << "Testing Polynomial Evaluation at 50 digits....." << std::endl; +#if defined(TEST_MPFR) || defined(TEST_MPFR_CLASS) + mpfr_set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(50 * 1000L / 301L); +#endif +#ifdef TEST_MPFR + time_proc("mpfr_float_50", test_polynomial<mpfr_float_50>); + time_proc("mpfr_float_50 (no expression templates", test_polynomial<number<mpfr_float_backend<50>, et_off> >); + time_proc("static_mpfr_float_50", test_polynomial<static_mpfr_float_50>); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_50", test_polynomial<mpf_float_50>); + time_proc("mpf_float_50 (no expression templates", test_polynomial<number<gmp_float<50>, et_off> >); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_50", test_polynomial<cpp_dec_float_50>); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_polynomial<cpp_bin_float_50>); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_polynomial<mpfr_class>); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_polynomial<mpfr::mpreal>); +#endif + // + // Then 100 digits: + // + std::cout << "Testing Polynomial Evaluation at 100 digits....." << std::endl; +#ifdef TEST_MPFR_CLASS + mpfr_set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPREAL + mpfr::mpreal::set_default_prec(100 * 1000L / 301L); +#endif +#ifdef TEST_MPFR + time_proc("mpfr_float_100", test_polynomial<mpfr_float_100>); + time_proc("mpfr_float_100 (no expression templates", test_polynomial<number<mpfr_float_backend<100>, et_off> >); + time_proc("static_mpfr_float_100", test_polynomial<static_mpfr_float_100>); +#endif +#ifdef TEST_MPF + time_proc("mpf_float_100", test_polynomial<mpf_float_100>); + time_proc("mpf_float_100 (no expression templates", test_polynomial<number<gmp_float<100>, et_off> >); +#endif +#ifdef TEST_CPP_DEC_FLOAT + time_proc("cpp_dec_float_100", test_polynomial<cpp_dec_float_100>); +#endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_polynomial<cpp_bin_float_100>); +#endif +#ifdef TEST_MPFR_CLASS + time_proc("mpfr_class", test_polynomial<mpfr_class>); +#endif +#ifdef TEST_MPREAL + time_proc("mpfr::mpreal", test_polynomial<mpfr::mpreal>); +#endif +} diff --git a/libs/multiprecision/performance/voronoi_performance.cpp b/libs/multiprecision/performance/voronoi_performance.cpp new file mode 100644 index 0000000000..a976578039 --- /dev/null +++ b/libs/multiprecision/performance/voronoi_performance.cpp @@ -0,0 +1,229 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +#pragma warning(disable:4244) +#endif + +#include <boost/polygon/detail/voronoi_predicates.hpp> +#include <boost/polygon/detail/voronoi_structures.hpp> +#include <boost/polygon/detail/skeleton_predicates.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int_distribution.hpp> +#include <vector> +#include <map> +#include <boost/chrono.hpp> +#include <boost/multiprecision/cpp_int.hpp> + +#ifdef TEST_GMP +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_TOMMATH +#include <boost/multiprecision/tommath.hpp> +#endif + +#include "arithmetic_backend.hpp" + +typedef boost::polygon::detail::point_2d<boost::int32_t> i_point; + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +std::vector<i_point> points; +boost::random::mt19937 gen; + +template <class Big> +struct cpp_int_voronoi_traits +{ + typedef boost::int32_t int_type; + typedef boost::int64_t int_x2_type; + typedef boost::uint64_t uint_x2_type; + typedef Big big_int_type; + typedef double fpt_type; + typedef boost::polygon::detail::extended_exponent_fpt<fpt_type> efpt_type; + typedef boost::polygon::detail::ulp_comparison<fpt_type> ulp_cmp_type; + struct to_fpt_converter_type + { + template <class B, boost::multiprecision::expression_template_option ET> + double operator ()(const boost::multiprecision::number<B, ET>& val) + { + return val.template convert_to<double>(); + } + double operator ()(double val) + { + return val; + } + double operator()(const efpt_type& that) const + { + return that.d(); + } + template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> + double operator()(const boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) + { + typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type r_t; + r_t r(e); + return r.template convert_to<double>(); + } + }; + struct to_efpt_converter_type + { + template <class B, boost::multiprecision::expression_template_option ET> + efpt_type operator ()(const boost::multiprecision::number<B, ET>& val) + { + return efpt_type(val.template convert_to<double>(), 0); + } + efpt_type operator ()(double val) + { + return efpt_type(val, 0); + } + template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> + double operator()(const boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) + { + typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type r_t; + r_t r(e); + return efpt_type(r.template convert_to<double>(), 0); + } + }; +}; + +template <class Big> +struct native_int_voronoi_traits +{ + typedef boost::int32_t int_type; + typedef boost::int64_t int_x2_type; + typedef boost::uint64_t uint_x2_type; + typedef Big big_int_type; + typedef double fpt_type; + typedef boost::polygon::detail::extended_exponent_fpt<fpt_type> efpt_type; + typedef boost::polygon::detail::ulp_comparison<fpt_type> ulp_cmp_type; + struct to_fpt_converter_type + { + template <class T> + double operator ()(const T& val)const + { + return val; + } + double operator()(const efpt_type& that) const + { + return that.d(); + } + }; + struct to_efpt_converter_type + { + template <class T> + efpt_type operator ()(const T& val)const + { + return efpt_type(val, 0); + } + }; +}; + +std::map<std::string, double> results; +double min_time = (std::numeric_limits<double>::max)(); + +template <class Traits> +double test(const char* name) +{ + typedef boost::polygon::detail::voronoi_predicates<Traits> preds; + typedef boost::polygon::detail::circle_event<boost::int32_t> circle_event; + typedef boost::polygon::detail::site_event<boost::int32_t> site_event; + typedef typename preds::template mp_circle_formation_functor<site_event, circle_event> circle_pred; + + boost::random::uniform_int_distribution<> dist(0, points.size() - 1); + circle_pred pc; + circle_event event; + + stopwatch<boost::chrono::high_resolution_clock> w; + + for(unsigned i = 0; i < 10000; ++i) + { + site_event s1(points[dist(gen)]); + site_event s2(points[dist(gen)]); + site_event s3(points[dist(gen)]); + pc.ppp(s1, s2, s3, event); + pc.pps(s1, s2, s3, 0, event); + pc.pss(s1, s2, s3, 0, event); + pc.sss(s1, s2, s3, event); + } + double d = boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count(); + if(d < min_time) + min_time = d; + results[name] = d; + std::cout << "Time for " << std::setw(30) << std::left << name << " = " << d << std::endl; + return d; +} + +void generate_quickbook() +{ + std::cout << "[table\n[[Integer Type][Relative Performance (Actual time in parenthesis)]]\n"; + + std::map<std::string, double>::const_iterator i(results.begin()), j(results.end()); + + while(i != j) + { + double rel = i->second / min_time; + std::cout << "[[" << i->first << "][" << rel << "(" << i->second << "s)]]\n"; + ++i; + } + + std::cout << "]\n"; +} + + +int main() +{ + boost::random::uniform_int_distribution<> dist((std::numeric_limits<boost::int32_t>::min)() / 2, (std::numeric_limits<boost::int32_t>::max)() / 2); + + for(unsigned i = 0; i < 100; ++i) + { + points.push_back(i_point(dist(gen), dist(gen))); + } + + test<boost::polygon::detail::voronoi_ctype_traits<boost::int32_t> >("extended_int"); + + test<cpp_int_voronoi_traits<boost::multiprecision::int256_t> >("int256_t"); + test<cpp_int_voronoi_traits<boost::multiprecision::int512_t> >("int512_t"); + test<cpp_int_voronoi_traits<boost::multiprecision::int1024_t> >("int1024_t"); + + test<cpp_int_voronoi_traits<boost::multiprecision::checked_int256_t> >("checked_int256_t"); + test<cpp_int_voronoi_traits<boost::multiprecision::checked_int512_t> >("checked_int512_t"); + test<cpp_int_voronoi_traits<boost::multiprecision::checked_int1024_t> >("checked_int1024_t"); + + test<cpp_int_voronoi_traits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<>, boost::multiprecision::et_off> > >("cpp_int"); + +#ifdef TEST_GMP + test<cpp_int_voronoi_traits<boost::multiprecision::number<boost::multiprecision::gmp_int, boost::multiprecision::et_off> > >("mpz_int"); +#endif +#ifdef TEST_TOMMATH + test<cpp_int_voronoi_traits<boost::multiprecision::number<boost::multiprecision::tommath_int, boost::multiprecision::et_off> > >("tom_int"); +#endif + + generate_quickbook(); + + test<native_int_voronoi_traits<boost::int64_t> >("int64_t"); + test<cpp_int_voronoi_traits<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<boost::int64_t>, boost::multiprecision::et_off> > >("number<arithmetic_backend<boost::int64_t>, et_off>"); + //test<cpp_int_voronoi_traits<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<boost::int64_t>, boost::multiprecision::et_on> > >("number<arithmetic_backend<boost::int64_t>, et_on>"); + + return 0; +} + diff --git a/libs/multiprecision/test/Jamfile.v2 b/libs/multiprecision/test/Jamfile.v2 new file mode 100644 index 0000000000..5972b7762e --- /dev/null +++ b/libs/multiprecision/test/Jamfile.v2 @@ -0,0 +1,865 @@ +# copyright John Maddock 2011 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; +import ../../config/checks/config : requires ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local mpfi_path = [ modules.peek : MPFI_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project : requirements + <include>$(gmp_path) + <include>$(gmp_path)/mpfr + <include>$(gmp_path)/gmpfrxx + <include>$(mpfr_path) + <include>$(mpfi_path) + <include>$(mpfi_path)/src + <include>$(tommath_path) + <include>../include + <include>../../.. + # We set these to make it easier to set up and test GMP and MPFR under Win32: + <toolset>msvc:<runtime-link>static + <toolset>msvc:<link>static + <toolset>msvc:<warnings>all + <toolset>msvc:<cxxflags>/fp:precise + <toolset>intel-win:<runtime-link>static + <toolset>intel-win:<link>static + # Speed up compiles: + <toolset>msvc:<debug-symbols>off + <toolset>intel:<debug-symbols>off + <toolset>gcc:<cxxflags>-Wall + <toolset>gcc:<cxxflags>-Wextra + <toolset>intel:<define>SLOW_COMPILER + ; + +local enable-specfun = [ MATCH (--enable-specfun) : [ modules.peek : ARGV ] ] ; +local disable-concepts = [ MATCH (--disable-concepts) : [ modules.peek : ARGV ] ] ; + +lib gmp : : <search>$(gmp_path) ; +lib mpfr : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug ; +lib mpfi : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug <search>$(mpfi_path) <search>$(mpfi_path)/src ; +lib quadmath ; + +if $(tommath_path) +{ + lib tommath : [ GLOB $(tommath_path) : *.c ] ; + TOMMATH = tommath ; +} +else +{ + lib tommath : : <search>$(tommath_path) ; + TOMMATH = tommath ; +} + +run test_arithmetic_backend_concept.cpp ; + +run test_arithmetic_cpp_dec_float_1.cpp ; +run test_arithmetic_cpp_dec_float_2.cpp ; +run test_arithmetic_cpp_dec_float_3.cpp ; + +run test_arithmetic_cpp_bin_float_1.cpp ; +run test_arithmetic_cpp_bin_float_2.cpp ; +run test_arithmetic_cpp_bin_float_3.cpp ; + +run test_arithmetic_mpf_50.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run test_arithmetic_mpf.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run test_arithmetic_mpz.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run test_arithmetic_mpz_br.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; +run test_arithmetic_mpq.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ; + +run test_arithmetic_mpfr.cpp mpfr gmp : : : [ check-target-builds ../config//has_mpfr : : <build>no ] ; +run test_arithmetic_mpfr_50.cpp mpfr gmp : : : [ check-target-builds ../config//has_mpfr : : <build>no ] ; +run test_arithmetic_mpfr_50_static.cpp mpfr gmp : : : [ check-target-builds ../config//has_mpfr : : <build>no ] ; + +run test_arithmetic_tommath.cpp $(TOMMATH) : : : [ check-target-builds ../config//has_tommath : : <build>no ] ; +run test_arithmetic_tommath_br.cpp $(TOMMATH) : : : [ check-target-builds ../config//has_tommath : : <build>no ] ; + +run test_arithmetic_cpp_int_1.cpp ; +run test_arithmetic_cpp_int_2.cpp ; +run test_arithmetic_cpp_int_3.cpp ; +run test_arithmetic_cpp_int_4.cpp ; +run test_arithmetic_cpp_int_5.cpp ; +run test_arithmetic_cpp_int_6.cpp ; +run test_arithmetic_cpp_int_7.cpp ; +run test_arithmetic_cpp_int_8.cpp ; +run test_arithmetic_cpp_int_9.cpp ; +run test_arithmetic_cpp_int_10.cpp ; +run test_arithmetic_cpp_int_11.cpp ; +run test_arithmetic_cpp_int_12.cpp ; +run test_arithmetic_cpp_int_13.cpp ; +run test_arithmetic_cpp_int_14.cpp ; +run test_arithmetic_cpp_int_15.cpp ; +run test_arithmetic_cpp_int_16.cpp ; +run test_arithmetic_cpp_int_17.cpp ; +run test_arithmetic_cpp_int_18.cpp ; +run test_arithmetic_cpp_int_br.cpp ; + +run test_arithmetic_ab_1.cpp ; +run test_arithmetic_ab_2.cpp ; +run test_arithmetic_ab_3.cpp ; + +run test_cpp_dec_float_round.cpp ; + +run test_arithmetic_logged_1.cpp ; +run test_arithmetic_logged_2.cpp ; + +run test_arithmetic_dbg_adptr1.cpp ; +run test_arithmetic_dbg_adptr2.cpp ; + +run test_arithmetic_mpfi_50.cpp mpfi mpfr gmp : : : [ check-target-builds ../config//has_mpfi : : <build>no ] ; + +run test_arithmetic_float_128.cpp quadmath : : : [ check-target-builds ../config//has_float128 : : <build>no ] ; +run test_arithmetic_float_128.cpp : : : [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] [ check-target-builds ../config//has_float128 : <source>quadmath ] : test_arithmetic_intel_quad ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + <define>TEST_BACKEND + : test_numeric_limits_backend_concept ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_numeric_limits_mpf50 ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPF + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_numeric_limits_mpf ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPZ + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_numeric_limits_mpz ; + +run test_numeric_limits.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPQ + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_numeric_limits_mpq ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + <define>TEST_MPFR + [ check-target-builds ../config//has_mpfr : : <build>no ] + : test_numeric_limits_mpfr ; + +run test_numeric_limits.cpp mpfr + : # command line + : # input files + : # requirements + <define>TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : <build>no ] + : test_numeric_limits_mpfr_50 ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_DEC_FLOAT + : test_numeric_limits_cpp_dec_float ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_BIN_FLOAT + : test_numeric_limits_cpp_bin_float ; + +run test_numeric_limits.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + <define>TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : <build>no ] + : test_numeric_limits_tommath ; + +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_INT + : test_numeric_limits_cpp_int ; + +run test_numeric_limits.cpp mpfi mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST_MPFI_50 + [ check-target-builds ../config//has_mpfi : : <build>no ] + : test_numeric_limits_mpfi_50 ; + + +run test_numeric_limits.cpp quadmath + : # command line + : # input files + : # requirements + <define>TEST_FLOAT128 + [ check-target-builds ../config//has_float128 : : <build>no ] + : test_numeric_limits_float128 ; +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + <define>TEST_FLOAT128 + [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] [ check-target-builds ../config//has_float128 : <source>quadmath ] + : test_numeric_limits_intel_quad ; + +for local source in test_exp.cpp test_log.cpp test_pow.cpp test_sinh.cpp test_sqrt.cpp test_cosh.cpp test_tanh.cpp test_sin.cpp test_cos.cpp test_tan.cpp test_asin.cpp test_acos.cpp test_atan.cpp test_round.cpp test_fpclassify.cpp +{ + run $(source) gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + <define>TEST_MPF_50 + : $(source:B)_mpf50 ; + run $(source) mpfr gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfr : : <build>no ] + <define>TEST_MPFR_50 + : $(source:B)_mpfr50 ; + run $(source) mpfi mpfr gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfi : : <build>no ] + <define>TEST_MPFI_50 + : $(source:B)_mpfi50 ; + run $(source) + : # command line + : # input files + : # requirements + <define>TEST_CPP_DEC_FLOAT + : $(source:B)_cpp_dec_float ; + run $(source) + : # command line + : # input files + : # requirements + <define>TEST_CPP_BIN_FLOAT + : $(source:B)_cpp_bin_float ; + run $(source) quadmath + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_float128 : : <build>no ] + <define>TEST_FLOAT128 + : $(source:B)_float128 ; + run $(source) + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] [ check-target-builds ../config//has_float128 : <source>quadmath ] + <define>TEST_FLOAT128 + : $(source:B)_intel_quad ; +} + +run test_gmp_conversions.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] ; + +run test_mpfr_conversions.cpp gmp mpfr + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfr : : <build>no ] ; + +run test_constants.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_constants_mpf50 ; + +run test_constants.cpp mpfr + : # command line + : # input files + : # requirements + <define>TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : <build>no ] + : test_constants_mpfr_50 ; + +run test_constants.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_DEC_FLOAT + : test_constants_cpp_dec_float ; + + +run test_move.cpp mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST_MPFR + [ check-target-builds ../config//has_mpfr : : <build>no ] + : test_move_mpfr ; + +run test_move.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_GMP + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_move_gmp ; + +run test_move.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + <define>TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : <build>no ] + : test_move_tommath ; + +run test_move.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_INT + : test_move_cpp_int ; + +run test_test.cpp ; +run test_cpp_int_lit.cpp ; +compile test_constexpr.cpp : + [ check-target-builds ../config//has_float128 : <define>HAVE_FLOAT128 : ] + [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type <define>HAVE_FLOAT128 : ] + [ requires cxx11_constexpr cxx11_user_defined_literals ] ; + +run test_cpp_bin_float_io.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST_CPP_BIN_FLOAT + <define>TEST1 + release # Otherwise runtime is slow + : test_cpp_bin_float_io_1 + ; + +run test_cpp_bin_float_io.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST_CPP_BIN_FLOAT + <define>TEST2 + release # Otherwise runtime is slow + : test_cpp_bin_float_io_2 + ; + +run test_cpp_bin_float.cpp mpfr gmp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST_MPFR + [ check-target-builds ../config//has_mpfr : : <build>no ] + release # Otherwise runtime is slow + ; + +run test_float_io.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_DEC_FLOAT + release # Otherwise runtime is slow + : test_float_io_cpp_dec_float ; + +run test_float_io.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPF_50 + release # Otherwise runtime is slow + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_float_io_mpf ; + +run test_float_io.cpp mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST_MPFR_50 + release # Otherwise runtime is slow + [ check-target-builds ../config//has_mpfr : : <build>no ] + : test_float_io_mpfr ; + +run test_float_io.cpp mpfi mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST_MPFI_50 + release # Otherwise runtime is slow + [ check-target-builds ../config//has_mpfi : : <build>no ] + : test_float_io_mpfi ; + +run test_float_io.cpp quadmath + : # command line + : # input files + : # requirements + <define>TEST_FLOAT128 + release # Otherwise runtime is slow + [ check-target-builds ../config//has_float128 : : <build>no ] + : test_float_io_float128 ; +run test_float_io.cpp + : # command line + : # input files + : # requirements + <define>TEST_FLOAT128 + release # Otherwise runtime is slow + [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] [ check-target-builds ../config//has_float128 : <source>quadmath ] + : test_float_io_intel_quad ; + +run test_int_io.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + <define>TEST_TOMMATH + release # Otherwise runtime is slow + [ check-target-builds ../config//has_tommath : : <build>no ] + : test_int_io_tommath ; + +run test_int_io.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPZ + release # Otherwise runtime is slow + [ check-target-builds ../config//has_gmp : : <build>no ] + : test_int_io_mpz ; + +run test_int_io.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_INT + release # Otherwise runtime is slow + : test_int_io_cpp_int ; + +run test_cpp_int.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + release # otherwise runtime is too slow!! + <define>TEST1 + : test_cpp_int_1 + ; + +run test_cpp_int.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + release # otherwise runtime is too slow!! + <define>TEST2 + : test_cpp_int_2 + ; + +run test_cpp_int.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + release # otherwise runtime is too slow!! + <define>TEST3 + : test_cpp_int_3 + ; + +run test_checked_cpp_int.cpp ; + +run test_miller_rabin.cpp gmp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + release # otherwise runtime is too slow!! + ; + +run test_rational_io.cpp $(TOMMATH) + : # command line + : # input files + : # requirements + <define>TEST_TOMMATH + [ check-target-builds ../config//has_tommath : : <build>no ] + release # Otherwise runtime is slow + : test_rational_io_tommath ; + +run test_rational_io.cpp gmp + : # command line + : # input files + : # requirements + <define>TEST_MPQ + [ check-target-builds ../config//has_gmp : : <build>no ] + release # Otherwise runtime is slow + : test_rational_io_mpz ; + +run test_rational_io.cpp + : # command line + : # input files + : # requirements + <define>TEST_CPP_INT + release # Otherwise runtime is slow + : test_rational_io_cpp_int ; + +run test_generic_conv.cpp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : <define>TEST_GMP <source>gmp : ] + [ check-target-builds ../config//has_tommath : <define>TEST_TOMMATH <source>$(TOMMATH) : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <source>mpfr : ] + release # Otherwise runtime is slow + ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST1 + release + : test_rat_float_interconv_1 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST2 + release + : test_rat_float_interconv_2 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST3 + release + : test_rat_float_interconv_3 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + <define>TEST4 + release + : test_rat_float_interconv_4 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST5 + [ check-target-builds ../config//has_mpfr : : <build>no ] + release + : test_rat_float_interconv_5 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST6 + [ check-target-builds ../config//has_mpfr : : <build>no ] + release + : test_rat_float_interconv_6 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST7 + [ check-target-builds ../config//has_mpfr : : <build>no ] + release + : test_rat_float_interconv_7 ; + +run test_rat_float_interconv.cpp /boost/system//boost_system /boost/chrono//boost_chrono mpfr gmp + : # command line + : # input files + : # requirements + <define>TEST8 + [ check-target-builds ../config//has_mpfr : : <build>no ] + release + : test_rat_float_interconv_8 ; + +build-project ../example ; + + +run test_cpp_int_conv.cpp ; +run test_native_integer.cpp ; + +run test_mixed_cpp_int.cpp ; +run test_mixed_float.cpp + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : <define>TEST_GMP <library>gmp : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <library>mpfr <library>gmp : ] ; + + +compile include_test/mpfr_include_test.cpp + : # requirements + [ check-target-builds ../config//has_mpfr : : <build>no ] ; +compile include_test/gmp_include_test.cpp + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] ; +compile include_test/tommath_include_test.cpp + : # requirements + [ check-target-builds ../config//has_tommath : : <build>no ] ; +compile include_test/cpp_int_include_test.cpp ; +compile include_test/cpp_dec_float_include_test.cpp ; +compile include_test/cpp_bin_float_include_test.cpp ; + +run ublas_interop/test1.cpp ublas_interop/test11.cpp ublas_interop/test12.cpp ublas_interop/test13.cpp ; +run ublas_interop/test2.cpp ublas_interop/test21.cpp ublas_interop/test22.cpp ublas_interop/test23.cpp ; +#run ublas_interop/test3.cpp ublas_interop/test31.cpp ublas_interop/test32.cpp ublas_interop/test33.cpp ; +run ublas_interop/test4.cpp ublas_interop/test42.cpp ublas_interop/test43.cpp ; +run ublas_interop/test5.cpp ublas_interop/test52.cpp ublas_interop/test53.cpp ; +run ublas_interop/test6.cpp ublas_interop/test62.cpp ublas_interop/test63.cpp ; +#run ublas_interop/test7.cpp ublas_interop/test71.cpp ublas_interop/test72.cpp ublas_interop/test73.cpp ; + +run ublas_interop/test1.cpp ublas_interop/test11.cpp ublas_interop/test12.cpp ublas_interop/test13.cpp : : : <define>TEST_ET=1 : ublas1_et ; +run ublas_interop/test2.cpp ublas_interop/test21.cpp ublas_interop/test22.cpp ublas_interop/test23.cpp : : : <define>TEST_ET=1 : ublas2_et ; +#run ublas_interop/test3.cpp ublas_interop/test31.cpp ublas_interop/test32.cpp ublas_interop/test33.cpp : : : <define>TEST_ET=1 : ublas3_et ; +run ublas_interop/test4.cpp ublas_interop/test42.cpp ublas_interop/test43.cpp : : : <define>TEST_ET=1 : ublas3_et ; +run ublas_interop/test5.cpp ublas_interop/test52.cpp ublas_interop/test53.cpp : : : <define>TEST_ET=1 : ublas4_et ; +run ublas_interop/test6.cpp ublas_interop/test62.cpp ublas_interop/test63.cpp : : : <define>TEST_ET=1 : ublas5_et ; +#run ublas_interop/test7.cpp ublas_interop/test71.cpp ublas_interop/test72.cpp ublas_interop/test73.cpp : : : <define>TEST_ET=1 : ublas6_et ; + +# +# Serialization tests, run in release mode so we cycle through more values: +# +path-constant here : . ; +run test_cpp_int_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST1 : test_cpp_int_serial_1 ; +run test_cpp_int_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST2 : test_cpp_int_serial_2 ; +run test_cpp_int_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST3 : test_cpp_int_serial_3 ; +run test_cpp_int_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST4 : test_cpp_int_serial_4 ; +run test_cpp_int_deserial.cpp ../../serialization/build//boost_serialization ../../filesystem/build//boost_filesystem : $(here) : : release ; +run test_cpp_rat_serial.cpp ../../serialization/build//boost_serialization : : : release ; +run test_adapt_serial.cpp ../../serialization/build//boost_serialization : : : release ; +run test_cpp_dec_float_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST1 : test_cpp_dec_float_serial_1 ; +run test_cpp_dec_float_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST2 : test_cpp_dec_float_serial_2 ; +run test_float128_serial.cpp ../../serialization/build//boost_serialization quadmath : : : release [ check-target-builds ../config//has_float128 : : <build>no ] ; +run test_cpp_bin_float_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST1 : test_bin_dec_float_serial_1 ; +run test_cpp_bin_float_serial.cpp ../../serialization/build//boost_serialization : : : release <define>TEST2 : test_bin_dec_float_serial_2 ; + + +if $(enable-specfun) +{ + + for local source in [ glob math/*.cpp ] + { + run $(source) mpfr gmp + /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_mpfr/<link>static + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_mpfr : : <build>no ] + <define>TEST_MPFR_50 + <optimization>speed + <define>BOOST_ALL_NO_LIB + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_mpfr ; + run $(source) gmp + /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_mpf/<link>static + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_gmp : : <build>no ] + <optimization>speed + <define>TEST_MPF_50 + <define>BOOST_ALL_NO_LIB + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_mpf ; + run $(source) /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_cpp_dec_float/<link>static + : # command line + : # input files + : # requirements + <define>TEST_CPP_DEC_FLOAT + <define>BOOST_ALL_NO_LIB + <optimization>speed + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_cpp_dec_float ; + run $(source) /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_cpp_bin_float/<link>static + : # command line + : # input files + : # requirements + <define>TEST_CPP_BIN_FLOAT + <define>BOOST_ALL_NO_LIB + <optimization>speed + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_cpp_bin_float ; + run $(source) quadmath + /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_float128/<link>static + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_float128 : : <build>no ] + <optimization>speed + <define>TEST_FLOAT128 + <define>BOOST_ALL_NO_LIB + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_float128 ; + run $(source) + /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + math/instances//test_instances_intel_quad/<link>static + : # command line + : # input files + : # requirements + [ check-target-builds ../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] [ check-target-builds ../config//has_float128 : <source>quadmath ] + <optimization>speed + <define>TEST_FLOAT128 + <define>BOOST_ALL_NO_LIB + <toolset>msvc:<cxxflags>-bigobj + release + : $(source:B)_intel_quad ; + } + # + # High precision tests are rather different, as they test only one + # multiprecision type and are more a test of Boost.Math: + # + for local source in [ glob math/high_prec/*.cpp ] + { + run $(source) + /boost/test//boost_unit_test_framework/<link>static + /boost/regex//boost_regex/<link>static + : # command line + : # input files + : # requirements + <optimization>speed + <define>BOOST_ALL_NO_LIB + <toolset>msvc:<cxxflags>-bigobj + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <source>gmp <source>mpfr : ] + release ; + } +} + +for local source in [ glob compile_fail/*.cpp ] +{ + compile-fail $(source) + : + [ check-target-builds ../config//has_gmp : <define>TEST_GMP <debug-symbols>off : ] + [ check-target-builds ../config//has_mpfr : <define>TEST_MPFR <debug-symbols>off : ] + ; +} + +if ! $(disable-concepts) +{ + + for local source in [ glob concepts/*.cpp ] + { + + compile $(source) mpfr + : # requirements + <define>TEST_MPFR_50 + [ check-target-builds ../config//has_mpfr : : <build>no ] + <debug-symbols>off + : $(source:B)_mpfr_50 ; + + compile $(source) mpfr + : # requirements + <define>TEST_MPFR_6 + [ check-target-builds ../config//has_mpfr : : <build>no ] + <debug-symbols>off + : $(source:B)_mpfr_6 ; + + compile $(source) mpfr + : # requirements + <define>TEST_MPFR_15 + [ check-target-builds ../config//has_mpfr : : <build>no ] + <debug-symbols>off + : $(source:B)_mpfr_15 ; + + compile $(source) mpfr + : # requirements + <define>TEST_MPFR_17 + [ check-target-builds ../config//has_mpfr : : <build>no ] + <debug-symbols>off + : $(source:B)_mpfr_17 ; + + compile $(source) mpfr + : # requirements + <define>TEST_MPFR_30 + [ check-target-builds ../config//has_mpfr : : <build>no ] + <debug-symbols>off + : $(source:B)_mpfr_30 ; + + compile $(source) gmp + : # requirements + <define>TEST_MPF_50 + [ check-target-builds ../config//has_gmp : : <build>no ] + <debug-symbols>off + : $(source:B)_mpf50 ; + + compile $(source) + : # requirements + <define>TEST_CPP_DEC_FLOAT + <debug-symbols>off + : $(source:B)_cpp_dec_float ; + + compile $(source) + : # requirements + <define>TEST_CPP_BIN_FLOAT + <debug-symbols>off + : $(source:B)_cpp_bin_float ; + + compile $(source) + : # requirements + <define>TEST_CPP_DEC_FLOAT_NO_ET + <debug-symbols>off + : $(source:B)_cpp_dec_float_no_et ; + + compile $(source) + : # requirements + <define>TEST_BACKEND + <debug-symbols>off + : $(source:B)_backend_concept ; + + compile $(source) + : # requirements + <define>TEST_LOGGED_ADAPTER + <debug-symbols>off + : $(source:B)_logged_adaptor ; + } +} + + + + + + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_01.cpp b/libs/multiprecision/test/compile_fail/conv_fail_01.cpp new file mode 100644 index 0000000000..c5edc3b0ed --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_01.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +void foo(cpp_int i) +{ +} + +int main() +{ + foo(2.3); // conversion from float is explicit +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_02.cpp b/libs/multiprecision/test/compile_fail/conv_fail_02.cpp new file mode 100644 index 0000000000..79ffff2f84 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_02.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i == 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_03.cpp b/libs/multiprecision/test/compile_fail/conv_fail_03.cpp new file mode 100644 index 0000000000..0fe8932019 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_03.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i != 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_04.cpp b/libs/multiprecision/test/compile_fail/conv_fail_04.cpp new file mode 100644 index 0000000000..6bd72119bc --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_04.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i <= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_05.cpp b/libs/multiprecision/test/compile_fail/conv_fail_05.cpp new file mode 100644 index 0000000000..23f49022e8 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_05.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i >= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_06.cpp b/libs/multiprecision/test/compile_fail/conv_fail_06.cpp new file mode 100644 index 0000000000..78fea0f7c1 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_06.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i > 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_07.cpp b/libs/multiprecision/test/compile_fail/conv_fail_07.cpp new file mode 100644 index 0000000000..af4286f481 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_07.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i < 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_08.cpp b/libs/multiprecision/test/compile_fail/conv_fail_08.cpp new file mode 100644 index 0000000000..d741c6138a --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_08.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i = 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_09.cpp b/libs/multiprecision/test/compile_fail/conv_fail_09.cpp new file mode 100644 index 0000000000..29ce8b7bf7 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_09.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i += 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_10.cpp b/libs/multiprecision/test/compile_fail/conv_fail_10.cpp new file mode 100644 index 0000000000..d4376a2b84 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_10.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i -= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_11.cpp b/libs/multiprecision/test/compile_fail/conv_fail_11.cpp new file mode 100644 index 0000000000..b07a8b89e4 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_11.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i *= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_12.cpp b/libs/multiprecision/test/compile_fail/conv_fail_12.cpp new file mode 100644 index 0000000000..fbaf8fae9b --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_12.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i /= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_13.cpp b/libs/multiprecision/test/compile_fail/conv_fail_13.cpp new file mode 100644 index 0000000000..1d705e7f2f --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_13.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i %= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_14.cpp b/libs/multiprecision/test/compile_fail/conv_fail_14.cpp new file mode 100644 index 0000000000..54b8623253 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_14.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i |= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_15.cpp b/libs/multiprecision/test/compile_fail/conv_fail_15.cpp new file mode 100644 index 0000000000..e225a870f0 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_15.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i ^= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_16.cpp b/libs/multiprecision/test/compile_fail/conv_fail_16.cpp new file mode 100644 index 0000000000..0ba8c25ba7 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_16.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 2; + i &= 2.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_17.cpp b/libs/multiprecision/test/compile_fail/conv_fail_17.cpp new file mode 100644 index 0000000000..0649a64de1 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_17.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(a); +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_18.cpp b/libs/multiprecision/test/compile_fail/conv_fail_18.cpp new file mode 100644 index 0000000000..4335d9755b --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_18.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(2); + i = a; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_19.cpp b/libs/multiprecision/test/compile_fail/conv_fail_19.cpp new file mode 100644 index 0000000000..2315252e47 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_19.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(a + b); +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_20.cpp b/libs/multiprecision/test/compile_fail/conv_fail_20.cpp new file mode 100644 index 0000000000..24a63fa246 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_20.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i = a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_21.cpp b/libs/multiprecision/test/compile_fail/conv_fail_21.cpp new file mode 100644 index 0000000000..8c845f1083 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_21.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i += a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_22.cpp b/libs/multiprecision/test/compile_fail/conv_fail_22.cpp new file mode 100644 index 0000000000..d35e837e27 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_22.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i -= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_23.cpp b/libs/multiprecision/test/compile_fail/conv_fail_23.cpp new file mode 100644 index 0000000000..3e5a9f5340 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_23.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i *= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_24.cpp b/libs/multiprecision/test/compile_fail/conv_fail_24.cpp new file mode 100644 index 0000000000..a2581052da --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_24.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i /= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_25.cpp b/libs/multiprecision/test/compile_fail/conv_fail_25.cpp new file mode 100644 index 0000000000..694ee71290 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_25.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i %= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_26.cpp b/libs/multiprecision/test/compile_fail/conv_fail_26.cpp new file mode 100644 index 0000000000..0df397f42d --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_26.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i &= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_27.cpp b/libs/multiprecision/test/compile_fail/conv_fail_27.cpp new file mode 100644 index 0000000000..3995389ddc --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_27.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i |= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_28.cpp b/libs/multiprecision/test/compile_fail/conv_fail_28.cpp new file mode 100644 index 0000000000..4133aa1462 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_28.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2), b(3); + cpp_int i(3); + i ^= a * b; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_29.cpp b/libs/multiprecision/test/compile_fail/conv_fail_29.cpp new file mode 100644 index 0000000000..854118fbad --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_29.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i + 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_30.cpp b/libs/multiprecision/test/compile_fail/conv_fail_30.cpp new file mode 100644 index 0000000000..4ba78fe5a6 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_30.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 + i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_31.cpp b/libs/multiprecision/test/compile_fail/conv_fail_31.cpp new file mode 100644 index 0000000000..56a1482804 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_31.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 - i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_32.cpp b/libs/multiprecision/test/compile_fail/conv_fail_32.cpp new file mode 100644 index 0000000000..1769185f5f --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_32.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i - 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_33.cpp b/libs/multiprecision/test/compile_fail/conv_fail_33.cpp new file mode 100644 index 0000000000..36758318a6 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_33.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i * 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_34.cpp b/libs/multiprecision/test/compile_fail/conv_fail_34.cpp new file mode 100644 index 0000000000..7d178c4874 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_34.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 * i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_35.cpp b/libs/multiprecision/test/compile_fail/conv_fail_35.cpp new file mode 100644 index 0000000000..67f6bdc82d --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_35.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 / i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_36.cpp b/libs/multiprecision/test/compile_fail/conv_fail_36.cpp new file mode 100644 index 0000000000..3b175be85b --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_36.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i / 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_37.cpp b/libs/multiprecision/test/compile_fail/conv_fail_37.cpp new file mode 100644 index 0000000000..164db0b9df --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_37.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i % 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_38.cpp b/libs/multiprecision/test/compile_fail/conv_fail_38.cpp new file mode 100644 index 0000000000..a905e20e2e --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_38.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 % i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_39.cpp b/libs/multiprecision/test/compile_fail/conv_fail_39.cpp new file mode 100644 index 0000000000..fa495d702b --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_39.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 & i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_40.cpp b/libs/multiprecision/test/compile_fail/conv_fail_40.cpp new file mode 100644 index 0000000000..f3ccf05b65 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_40.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i & 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_41.cpp b/libs/multiprecision/test/compile_fail/conv_fail_41.cpp new file mode 100644 index 0000000000..67c30945f3 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_41.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i | 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_42.cpp b/libs/multiprecision/test/compile_fail/conv_fail_42.cpp new file mode 100644 index 0000000000..6ebe5f5bf6 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_42.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 | i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_43.cpp b/libs/multiprecision/test/compile_fail/conv_fail_43.cpp new file mode 100644 index 0000000000..cac2c02054 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_43.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = 3.3 ^ i; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_44.cpp b/libs/multiprecision/test/compile_fail/conv_fail_44.cpp new file mode 100644 index 0000000000..32a27593c0 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_44.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(3), j; + j = i ^ 3.3; +} diff --git a/libs/multiprecision/test/compile_fail/conv_fail_45.cpp b/libs/multiprecision/test/compile_fail/conv_fail_45.cpp new file mode 100644 index 0000000000..5e2f813aa8 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_45.cpp @@ -0,0 +1,24 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include <boost/multiprecision/gmp.hpp> + +using namespace boost::multiprecision; + +void foo(mpz_int i); + +int main() +{ + mpf_t f + foo(f); +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_46.cpp b/libs/multiprecision/test/compile_fail/conv_fail_46.cpp new file mode 100644 index 0000000000..11530eb1b7 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_46.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include <boost/multiprecision/gmp.hpp> + +using namespace boost::multiprecision; + +int main() +{ + mpf_t f; + mpz_int i; + i = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_47.cpp b/libs/multiprecision/test/compile_fail/conv_fail_47.cpp new file mode 100644 index 0000000000..b385e98855 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_47.cpp @@ -0,0 +1,24 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include <boost/multiprecision/gmp.hpp> + +using namespace boost::multiprecision; + +void foo(mpf_float_50); + +int main() +{ + mpf_float_100 f(2); + foo(f); +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_48.cpp b/libs/multiprecision/test/compile_fail/conv_fail_48.cpp new file mode 100644 index 0000000000..66828ca36f --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_48.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_GMP + +#include <boost/multiprecision/gmp.hpp> + +using namespace boost::multiprecision; + +int main() +{ + mpf_float_100 f(2); + mpf_float_50 f2; + f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_49.cpp b/libs/multiprecision/test/compile_fail/conv_fail_49.cpp new file mode 100644 index 0000000000..7f4bd612a7 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_49.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_MPFR + +#include <boost/multiprecision/mpfr.hpp> + +using namespace boost::multiprecision; + +int main() +{ + mpfr_float_100 f(2); + mpfr_float_50 f2; + f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_50.cpp b/libs/multiprecision/test/compile_fail/conv_fail_50.cpp new file mode 100644 index 0000000000..d0a52a58ee --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_50.cpp @@ -0,0 +1,22 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef TEST_MPFR + +#include <boost/multiprecision/mpfr.hpp> + +using namespace boost::multiprecision; + +int main() +{ + mpfr_float_100 f(2); + mpfr_float_50 f2 = f; +} + +#else + +#error "Nothing to test without GMP!" + +#endif diff --git a/libs/multiprecision/test/compile_fail/conv_fail_51.cpp b/libs/multiprecision/test/compile_fail/conv_fail_51.cpp new file mode 100644 index 0000000000..77441672fe --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_51.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_100 f(2); + cpp_dec_float_50 f2 = f; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_52.cpp b/libs/multiprecision/test/compile_fail/conv_fail_52.cpp new file mode 100644 index 0000000000..0f9edfb55d --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_52.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_100 f(2); + cpp_dec_float_50 f2; + f2 = f; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_53.cpp b/libs/multiprecision/test/compile_fail/conv_fail_53.cpp new file mode 100644 index 0000000000..cd48feea08 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_53.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + int128_t j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_54.cpp b/libs/multiprecision/test/compile_fail/conv_fail_54.cpp new file mode 100644 index 0000000000..f75833637c --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_54.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + int128_t j; + j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_55.cpp b/libs/multiprecision/test/compile_fail/conv_fail_55.cpp new file mode 100644 index 0000000000..680306f1f0 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_55.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + uint256_t j; + j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_56.cpp b/libs/multiprecision/test/compile_fail/conv_fail_56.cpp new file mode 100644 index 0000000000..f33e832d07 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_56.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + int256_t i = 3; + uint256_t j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_57.cpp b/libs/multiprecision/test/compile_fail/conv_fail_57.cpp new file mode 100644 index 0000000000..04dcb4cf42 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_57.cpp @@ -0,0 +1,15 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 3; + int256_t j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_58.cpp b/libs/multiprecision/test/compile_fail/conv_fail_58.cpp new file mode 100644 index 0000000000..00e0906092 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_58.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i = 3; + int256_t j; + j = i; +} + diff --git a/libs/multiprecision/test/compile_fail/conv_fail_59.cpp b/libs/multiprecision/test/compile_fail/conv_fail_59.cpp new file mode 100644 index 0000000000..0870a7b4dd --- /dev/null +++ b/libs/multiprecision/test/compile_fail/conv_fail_59.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_int i(1), j(3); + void* p = i * j; +} diff --git a/libs/multiprecision/test/compile_fail/cpp_int_complement.cpp b/libs/multiprecision/test/compile_fail/cpp_int_complement.cpp new file mode 100644 index 0000000000..195d94e71b --- /dev/null +++ b/libs/multiprecision/test/compile_fail/cpp_int_complement.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + checked_int256_t i; + i = ~i; +} diff --git a/libs/multiprecision/test/compile_fail/cpp_int_negate_1.cpp b/libs/multiprecision/test/compile_fail/cpp_int_negate_1.cpp new file mode 100644 index 0000000000..35fa0abcce --- /dev/null +++ b/libs/multiprecision/test/compile_fail/cpp_int_negate_1.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + checked_uint256_t i; + i = -i; +} diff --git a/libs/multiprecision/test/compile_fail/cpp_int_negate_2.cpp b/libs/multiprecision/test/compile_fail/cpp_int_negate_2.cpp new file mode 100644 index 0000000000..5b75cf09eb --- /dev/null +++ b/libs/multiprecision/test/compile_fail/cpp_int_negate_2.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + number<cpp_int_backend<32, 32, unsigned_magnitude>, et_on> i; + i = -i; +} diff --git a/libs/multiprecision/test/compile_fail/operator_fail_01.cpp b/libs/multiprecision/test/compile_fail/operator_fail_01.cpp new file mode 100644 index 0000000000..8b13b385b9 --- /dev/null +++ b/libs/multiprecision/test/compile_fail/operator_fail_01.cpp @@ -0,0 +1,17 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +int main() +{ + number<cpp_dec_float<50>, et_on> a(2); + number<cpp_dec_float<50>, et_off> b(2); + + a = a + b; +} + diff --git a/libs/multiprecision/test/compile_fail/operator_fail_02.cpp b/libs/multiprecision/test/compile_fail/operator_fail_02.cpp new file mode 100644 index 0000000000..cd422e74ba --- /dev/null +++ b/libs/multiprecision/test/compile_fail/operator_fail_02.cpp @@ -0,0 +1,18 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +int main() +{ + cpp_dec_float_50 a(2); + cpp_int b(2); + + a = a + b; +} + diff --git a/libs/multiprecision/test/concepts/number_concept_check.cpp b/libs/multiprecision/test/concepts/number_concept_check.cpp new file mode 100644 index 0000000000..5749765f58 --- /dev/null +++ b/libs/multiprecision/test/concepts/number_concept_check.cpp @@ -0,0 +1,255 @@ +// Copyright John Maddock 2011. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +#include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/concepts/real_type_concept.hpp> + +template <class T> +void test_extra(T) +{ + T t = 1; + t = abs(t); + t = abs(t*t); + + t = fabs(t); + t = fabs(t*t); + + t = sqrt(t); + t = sqrt(t*t); + + t = floor(t); + t = floor(t*t); + + t = ceil(t); + t = ceil(t*t); + + t = trunc(t); + t = trunc(t*t); + + t = round(t); + t = round(t*t); + + t = exp(t); + t = exp(t*t); + + t = log(t); + t = log(t*t); + + t = log10(t); + t = log10(t*t); + + t = cos(t); + t = cos(t*t); + + t = sin(t); + t = sin(t*t); + + t = tan(t); + t = tan(t*t); + + t = asin(t); + t = asin(t*t); + + t = atan(t); + t = atan(t*t); + + t = acos(t); + t = acos(t*t); + + t = cosh(t); + t = cosh(t*t); + + t = sinh(t); + t = sinh(t*t); + + t = tanh(t); + t = tanh(t*t); + + double dval = 2; + t = pow(t, t); + t = pow(t, t*t); + t = pow(t, dval); + t = pow(t*t, t); + t = pow(t*t, t*t); + t = pow(t*t, dval); + t = pow(dval, t); + t = pow(dval, t*t); + + t = atan2(t, t); + t = atan2(t, t*t); + t = atan2(t, dval); + t = atan2(t*t, t); + t = atan2(t*t, t*t); + t = atan2(t*t, dval); + t = atan2(dval, t); + t = atan2(dval, t*t); + + t = fmod(t, t); + t = fmod(t, t*t); + t = fmod(t, dval); + t = fmod(t*t, t); + t = fmod(t*t, t*t); + t = fmod(t*t, dval); + t = fmod(dval, t); + t = fmod(dval, t*t); + + typedef typename T::backend_type backend_type; + typedef typename backend_type::exponent_type exp_type; + exp_type e = 0; + int i = 0; + + t = ldexp(t, i); + t = ldexp(t*t, i); + t = ldexp(t, e); + t = ldexp(t*t, e); + + t = frexp(t, &i); + t = frexp(t*t, &i); + t = frexp(t, &e); + t = frexp(t*t, &e); + + t = scalbn(t, i); + t = scalbn(t*t, i); + t = scalbn(t, e); + t = scalbn(t*t, e); + + t = logb(t); + t = logb(t*t); + e = ilogb(t); + e = ilogb(t*t); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +} + +int main() +{ +#ifdef TEST_BACKEND + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::concepts::mp_number_float_architype>)); +#endif +#ifdef TEST_MPF_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::mpf_float_50>)); +#endif +#ifdef TEST_MPFR_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::mpfr_float_50>)); +#endif +#ifdef TEST_MPFR_6 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> > >)); +#endif +#ifdef TEST_MPFR_15 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> > >)); +#endif +#ifdef TEST_MPFR_17 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> > >)); +#endif +#ifdef TEST_MPFR_30 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> > >)); +#endif +#ifdef TEST_MPFR_50 + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::mpfr_float_50>)); +#endif +#ifdef TEST_CPP_DEC_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::cpp_dec_float_50>)); +#endif +#ifdef TEST_CPP_BIN_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept<boost::multiprecision::cpp_bin_float_50>)); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif + +} diff --git a/libs/multiprecision/test/concepts/sf_concept_check_basic.cpp b/libs/multiprecision/test/concepts/sf_concept_check_basic.cpp new file mode 100644 index 0000000000..2d79d0725c --- /dev/null +++ b/libs/multiprecision/test/concepts/sf_concept_check_basic.cpp @@ -0,0 +1,167 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) \ + && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +#include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/special_functions.hpp> + +template <class T> +void test_extra(T) +{ + T v1, v2, v3; + int i; + (boost::math::fpclassify)(v1); + (boost::math::isfinite)(v1); + (boost::math::isnormal)(v1); + (boost::math::isnan)(v1); + (boost::math::isinf)(v1); + (boost::math::signbit)(v1); + (boost::math::copysign)(v1, v2); + (boost::math::changesign)(v1); + (boost::math::sign)(v1); + boost::math::log1p(v1); + boost::math::expm1(v1); + boost::math::cbrt(v1); + boost::math::sqrt1pm1(v1); + boost::math::powm1(v1, v2); + boost::math::hypot(v1, v2); + boost::math::sinc_pi(v1); + boost::math::sinhc_pi(v1); + boost::math::asinh(v1); + boost::math::acosh(v1); + boost::math::atanh(v1); + boost::math::sin_pi(v1); + boost::math::cos_pi(v1); + boost::math::trunc(v1); + boost::math::itrunc(v1); + boost::math::ltrunc(v1); + boost::math::round(v1); + boost::math::iround(v1); + boost::math::lround(v1); + boost::math::modf(v1, &v1); + boost::math::modf(v1, &i); + long l; + boost::math::modf(v1, &l); +#ifdef BOOST_HAS_LONG_LONG + boost::math::lltrunc(v1); + boost::math::llround(v1); + boost::long_long_type ll; + boost::math::modf(v1, &ll); +#endif + boost::math::pow<2>(v1); + boost::math::nextafter(v1, v1); + boost::math::float_next(v1); + boost::math::float_prior(v1); + boost::math::float_distance(v1, v1); + // Misc functions that don't fit elsewhere: + boost::math::expint(v1); + boost::math::expint(i); + boost::math::expint(i, v2); + boost::math::expint(i, i); + boost::math::zeta(v1); + boost::math::zeta(i); + boost::math::owens_t(v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif +} + +int main() +{ + foo(); +} diff --git a/libs/multiprecision/test/concepts/sf_concept_check_bessel.cpp b/libs/multiprecision/test/concepts/sf_concept_check_bessel.cpp new file mode 100644 index 0000000000..8743419f0b --- /dev/null +++ b/libs/multiprecision/test/concepts/sf_concept_check_bessel.cpp @@ -0,0 +1,135 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +# include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/special_functions.hpp> + +template <class T> +void test_extra(T) +{ + T v1, v2, v3; + int i(0); + boost::math::cyl_neumann(v1, v2); + boost::math::cyl_neumann(i, v2); +#ifndef SLOW_COMPILER + boost::math::cyl_bessel_j(v1, v2); + boost::math::cyl_bessel_j(i, v2); + boost::math::cyl_bessel_i(v1, v2); + boost::math::cyl_bessel_i(i, v2); + boost::math::cyl_bessel_k(v1, v2); + boost::math::cyl_bessel_k(i, v2); + boost::math::sph_bessel(i, v2); + boost::math::sph_bessel(i, 1); + boost::math::sph_neumann(i, v2); + boost::math::sph_neumann(i, i); + boost::math::airy_ai(v1); + boost::math::airy_bi(v1); + boost::math::airy_ai_prime(v1); + boost::math::airy_bi_prime(v1); +#endif +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif +} + +int main() +{ + foo(); +} diff --git a/libs/multiprecision/test/concepts/sf_concept_check_elliptic.cpp b/libs/multiprecision/test/concepts/sf_concept_check_elliptic.cpp new file mode 100644 index 0000000000..0bd6d6f76c --- /dev/null +++ b/libs/multiprecision/test/concepts/sf_concept_check_elliptic.cpp @@ -0,0 +1,139 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +#include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/special_functions.hpp> + +template <class T> +void test_extra(T) +{ + T v1, v2, v3; + boost::math::ellint_1(v1); + boost::math::ellint_1(v1, v2); + boost::math::ellint_2(v1); + boost::math::ellint_2(v1, v2); + boost::math::ellint_3(v1, v2); + boost::math::ellint_3(v1, v2, v3); + boost::math::ellint_rc(v1, v2); + boost::math::ellint_rd(v1, v2, v3); + boost::math::ellint_rf(v1, v2, v3); + boost::math::ellint_rj(v1, v2, v3, v1); + boost::math::jacobi_elliptic(v1, v2, &v1, &v2); + boost::math::jacobi_cd(v1, v2); + boost::math::jacobi_cn(v1, v2); + boost::math::jacobi_cs(v1, v2); + boost::math::jacobi_dc(v1, v2); + boost::math::jacobi_dn(v1, v2); + boost::math::jacobi_ds(v1, v2); + boost::math::jacobi_nc(v1, v2); + boost::math::jacobi_nd(v1, v2); + boost::math::jacobi_ns(v1, v2); + boost::math::jacobi_sc(v1, v2); + boost::math::jacobi_sd(v1, v2); + boost::math::jacobi_sn(v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif +} + +int main() +{ + foo(); +} diff --git a/libs/multiprecision/test/concepts/sf_concept_check_gamma.cpp b/libs/multiprecision/test/concepts/sf_concept_check_gamma.cpp new file mode 100644 index 0000000000..fd07db1c4b --- /dev/null +++ b/libs/multiprecision/test/concepts/sf_concept_check_gamma.cpp @@ -0,0 +1,157 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +#include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/special_functions.hpp> + +template <class T> +void test_extra(T) +{ + T v1, v2, v3; + int i; + boost::math::tgamma(v1); + boost::math::tgamma1pm1(v1); + boost::math::lgamma(v1); + boost::math::lgamma(v1, &i); + boost::math::digamma(v1); + boost::math::tgamma_ratio(v1, v2); + boost::math::tgamma_delta_ratio(v1, v2); + boost::math::factorial<T>(i); + boost::math::unchecked_factorial<T>(i); + i = boost::math::max_factorial<T>::value; + boost::math::double_factorial<T>(i); + boost::math::rising_factorial(v1, i); + boost::math::falling_factorial(v1, i); +#ifndef SLOW_COMPILER + boost::math::tgamma(v1, v2); + boost::math::tgamma_lower(v1, v2); + boost::math::gamma_p(v1, v2); + boost::math::gamma_q(v1, v2); + boost::math::gamma_p_inv(v1, v2); + boost::math::gamma_q_inv(v1, v2); + boost::math::gamma_p_inva(v1, v2); + boost::math::gamma_q_inva(v1, v2); + boost::math::erf(v1); + boost::math::erfc(v1); + boost::math::erf_inv(v1); + boost::math::erfc_inv(v1); + boost::math::beta(v1, v2); + boost::math::beta(v1, v2, v3); + boost::math::betac(v1, v2, v3); + boost::math::ibeta(v1, v2, v3); + boost::math::ibetac(v1, v2, v3); + boost::math::ibeta_inv(v1, v2, v3); + boost::math::ibetac_inv(v1, v2, v3); + boost::math::ibeta_inva(v1, v2, v3); + boost::math::ibetac_inva(v1, v2, v3); + boost::math::ibeta_invb(v1, v2, v3); + boost::math::ibetac_invb(v1, v2, v3); + boost::math::gamma_p_derivative(v2, v3); + boost::math::ibeta_derivative(v1, v2, v3); +#endif +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif +} + +int main() +{ + foo(); +} diff --git a/libs/multiprecision/test/concepts/sf_concept_check_poly.cpp b/libs/multiprecision/test/concepts/sf_concept_check_poly.cpp new file mode 100644 index 0000000000..44414b9a2c --- /dev/null +++ b/libs/multiprecision/test/concepts/sf_concept_check_poly.cpp @@ -0,0 +1,130 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// +// This tests that cpp_dec_float_50 meets our +// conceptual requirements when used with Boost.Math. +// +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +# pragma warning(disable:4800) +# pragma warning(disable:4512) +# pragma warning(disable:4127) +# pragma warning(disable:4512) +# pragma warning(disable:4503) // decorated name length exceeded, name was truncated +#endif + +#include <libs/math/test/compile_test/poison.hpp> + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ + && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR_50 +# define TEST_MPFR_6 +# define TEST_MPFR_15 +# define TEST_MPFR_17 +# define TEST_MPFR_30 +# define TEST_CPP_DEC_FLOAT +# define TEST_CPP_DEC_FLOAT_NO_ET +# define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_CPP_BIN_FLOAT) +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_LOGGED_ADAPTER +#include <boost/multiprecision/logged_adaptor.hpp> +#endif + +#include <boost/math/special_functions.hpp> + +template <class T> +void test_extra(T) +{ + T v1, v2, v3; + boost::math::legendre_p(1, v1); + boost::math::legendre_p(1, 0, v1); + boost::math::legendre_q(1, v1); + boost::math::legendre_next(2, v1, v2, v3); + boost::math::legendre_next(2, 2, v1, v2, v3); + boost::math::laguerre(1, v1); + boost::math::laguerre(2, 1, v1); + boost::math::laguerre(2u, 1u, v1); + boost::math::laguerre_next(2, v1, v2, v3); + boost::math::laguerre_next(2, 1, v1, v2, v3); + boost::math::hermite(1, v1); + boost::math::hermite_next(2, v1, v2, v3); + boost::math::spherical_harmonic_r(2, 1, v1, v2); + boost::math::spherical_harmonic_i(2, 1, v1, v2); +} + +void foo() +{ +#ifdef TEST_BACKEND + test_extra(boost::multiprecision::concepts::mp_number_float_architype()); +#endif +#ifdef TEST_MPF_50 + test_extra(boost::multiprecision::mpf_float_50()); +#endif +#ifdef TEST_MPFR_50 + test_extra(boost::multiprecision::mpfr_float_50()); +#endif +#ifdef TEST_MPFR_6 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<6> >()); +#endif +#ifdef TEST_MPFR_15 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<15> >()); +#endif +#ifdef TEST_MPFR_17 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<17> >()); +#endif +#ifdef TEST_MPFR_30 + test_extra(boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> >()); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test_extra(boost::multiprecision::cpp_dec_float_50()); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif +#ifdef TEST_CPP_DEC_FLOAT_NO_ET + test_extra(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_off>()); +#endif +#ifdef TEST_LOGGED_ADAPTER + typedef boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > num_t; + test_extra(num_t()); +#endif +} + +int main() +{ + foo(); +} diff --git a/libs/multiprecision/test/coverage/Makefile b/libs/multiprecision/test/coverage/Makefile new file mode 100644 index 0000000000..d3825ea759 --- /dev/null +++ b/libs/multiprecision/test/coverage/Makefile @@ -0,0 +1,313 @@ +# copyright John Maddock 2012 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + + +SOURCES=\ +../../../../boost/multiprecision/mpfr.hpp\ +../../../../boost/multiprecision/tommath.hpp\ +../../../../boost/multiprecision/number.hpp\ +../../../../boost/multiprecision/cpp_dec_float.hpp\ +../../../../boost/multiprecision/gmp.hpp\ +../../../../boost/multiprecision/random.hpp\ +../../../../boost/multiprecision/cpp_int.hpp\ +../../../../boost/multiprecision/miller_rabin.hpp\ +../../../../boost/multiprecision/rational_adaptor.hpp\ +../../../../boost/multiprecision/concepts/mp_number_archetypes.hpp\ +../../../../boost/multiprecision/detail/big_lanczos.hpp\ +../../../../boost/multiprecision/detail/digits.hpp\ +../../../../boost/multiprecision/detail/no_et_ops.hpp\ +../../../../boost/multiprecision/detail/number_base.hpp\ +../../../../boost/multiprecision/detail/generic_interconvert.hpp\ +../../../../boost/multiprecision/detail/number_compare.hpp\ +../../../../boost/multiprecision/detail/default_ops.hpp\ +../../../../boost/multiprecision/detail/integer_ops.hpp\ +../../../../boost/multiprecision/detail/functions/constants.hpp\ +../../../../boost/multiprecision/detail/functions/pow.hpp\ +../../../../boost/multiprecision/detail/functions/trig.hpp\ +../../../../boost/multiprecision/traits/explicit_conversion.hpp\ +../../../../boost/multiprecision/traits/is_restricted_conversion.hpp + +coverage : run + gcov test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 \ + gcov test_arithmetic_cpp_int_4 test_arithmetic_cpp_int_5 test_arithmetic_cpp_int_6 \ + gcov test_arithmetic_cpp_int_7 test_arithmetic_cpp_int_8 test_arithmetic_cpp_int_9 \ + gcov test_arithmetic_cpp_int_10 test_arithmetic_cpp_int_11 test_arithmetic_cpp_int_12 \ + gcov test_arithmetic_cpp_int_13 test_arithmetic_cpp_int_14 test_arithmetic_cpp_int_15 \ + gcov test_arithmetic_cpp_int_16 test_arithmetic_cpp_int_17 test_arithmetic_cpp_int_18 \ + test_arithmetic_cpp_dec_float_1 test_arithmetic_cpp_dec_float_2 test_arithmetic_cpp_dec_float_3\ + test_arithmetic_concept test_arithmetic_mpz test_arithmetic_mpf \ + test_arithmetic_mpf_50 test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 test_cpp_int \ + test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + +test_arithmetic_cpp_int_1.o : ../test_arithmetic_cpp_int_1.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_1 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_1.o -c ../test_arithmetic_cpp_int_1.cpp + +test_arithmetic_cpp_int_1 : test_arithmetic_cpp_int_1.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_1.o + +test_arithmetic_cpp_int_2.o : ../test_arithmetic_cpp_int_2.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_2 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_2.o -c ../test_arithmetic_cpp_int_2.cpp + +test_arithmetic_cpp_int_2 : test_arithmetic_cpp_int_2.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_2.o + +test_arithmetic_cpp_int_3.o : ../test_arithmetic_cpp_int_3.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_3.o -c ../test_arithmetic_cpp_int_3.cpp + +test_arithmetic_cpp_int_3 : test_arithmetic_cpp_int_3.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_3 test_arithmetic_cpp_int_3.o + +test_arithmetic_cpp_int_4.o : ../test_arithmetic_cpp_int_4.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_4.o -c ../test_arithmetic_cpp_int_4.cpp + +test_arithmetic_cpp_int_4 : test_arithmetic_cpp_int_4.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_4 test_arithmetic_cpp_int_4.o + +test_arithmetic_cpp_int_5.o : ../test_arithmetic_cpp_int_5.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_5.o -c ../test_arithmetic_cpp_int_5.cpp + +test_arithmetic_cpp_int_5 : test_arithmetic_cpp_int_5.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_5 test_arithmetic_cpp_int_5.o + +test_arithmetic_cpp_int_6.o : ../test_arithmetic_cpp_int_6.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_6.o -c ../test_arithmetic_cpp_int_6.cpp + +test_arithmetic_cpp_int_6 : test_arithmetic_cpp_int_6.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_6 test_arithmetic_cpp_int_6.o + +test_arithmetic_cpp_int_7.o : ../test_arithmetic_cpp_int_7.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_7.o -c ../test_arithmetic_cpp_int_7.cpp + +test_arithmetic_cpp_int_7 : test_arithmetic_cpp_int_7.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_7 test_arithmetic_cpp_int_7.o + +test_arithmetic_cpp_int_8.o : ../test_arithmetic_cpp_int_8.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_8.o -c ../test_arithmetic_cpp_int_8.cpp + +test_arithmetic_cpp_int_8 : test_arithmetic_cpp_int_8.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_8 test_arithmetic_cpp_int_8.o + +test_arithmetic_cpp_int_9.o : ../test_arithmetic_cpp_int_9.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_9.o -c ../test_arithmetic_cpp_int_9.cpp + +test_arithmetic_cpp_int_9 : test_arithmetic_cpp_int_9.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_9 test_arithmetic_cpp_int_9.o + +test_arithmetic_cpp_int_10.o : ../test_arithmetic_cpp_int_10.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_10.o -c ../test_arithmetic_cpp_int_10.cpp + +test_arithmetic_cpp_int_10 : test_arithmetic_cpp_int_10.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_10 test_arithmetic_cpp_int_10.o + +test_arithmetic_cpp_int_11.o : ../test_arithmetic_cpp_int_11.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_11.o -c ../test_arithmetic_cpp_int_12.cpp + +test_arithmetic_cpp_int_11 : test_arithmetic_cpp_int_11.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_11 test_arithmetic_cpp_int_11.o + +test_arithmetic_cpp_int_12.o : ../test_arithmetic_cpp_int_12.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_12.o -c ../test_arithmetic_cpp_int_12.cpp + +test_arithmetic_cpp_int_12 : test_arithmetic_cpp_int_12.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_12 test_arithmetic_cpp_int_12.o + +test_arithmetic_cpp_int_13.o : ../test_arithmetic_cpp_int_13.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_13.o -c ../test_arithmetic_cpp_int_13.cpp + +test_arithmetic_cpp_int_13 : test_arithmetic_cpp_int_13.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_13 test_arithmetic_cpp_int_13.o + +test_arithmetic_cpp_int_14.o : ../test_arithmetic_cpp_int_14.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_14.o -c ../test_arithmetic_cpp_int_14.cpp + +test_arithmetic_cpp_int_14 : test_arithmetic_cpp_int_14.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_14 test_arithmetic_cpp_int_14.o + +test_arithmetic_cpp_int_15.o : ../test_arithmetic_cpp_int_15.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_15.o -c ../test_arithmetic_cpp_int_15.cpp + +test_arithmetic_cpp_int_15 : test_arithmetic_cpp_int_15.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_15 test_arithmetic_cpp_int_15.o + +test_arithmetic_cpp_int_16.o : ../test_arithmetic_cpp_int_16.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_16.o -c ../test_arithmetic_cpp_int_16.cpp + +test_arithmetic_cpp_int_16 : test_arithmetic_cpp_int_16.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_16 test_arithmetic_cpp_int_16.o + +test_arithmetic_cpp_int_17.o : ../test_arithmetic_cpp_int_17.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_17.o -c ../test_arithmetic_cpp_int_17.cpp + +test_arithmetic_cpp_int_17 : test_arithmetic_cpp_int_17.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_17 test_arithmetic_cpp_int_17.o + +test_arithmetic_cpp_int_18.o : ../test_arithmetic_cpp_int_18.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_INT_3 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_int_18.o -c ../test_arithmetic_cpp_int_18.cpp + +test_arithmetic_cpp_int_18 : test_arithmetic_cpp_int_18.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_int_18 test_arithmetic_cpp_int_18.o + +test_arithmetic_cpp_dec_float_1.o : ../test_arithmetic_cpp_dec_float_1.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_DEC_FLOAT --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_dec_float_1.o -c ../test_arithmetic_cpp_dec_float_1.cpp + +test_arithmetic_cpp_dec_float_1 : test_arithmetic_cpp_dec_float_1.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_dec_float_1 test_arithmetic_cpp_dec_float_1.o + +test_arithmetic_cpp_dec_float_2.o : ../test_arithmetic_cpp_dec_float_2.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_DEC_FLOAT --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_dec_float_2.o -c ../test_arithmetic_cpp_dec_float_2.cpp + +test_arithmetic_cpp_dec_float_2 : test_arithmetic_cpp_dec_float_2.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_dec_float_2 test_arithmetic_cpp_dec_float_2.o + +test_arithmetic_cpp_dec_float_3.o : ../test_arithmetic_cpp_dec_float_3.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_CPP_DEC_FLOAT --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_cpp_dec_float_3.o -c ../test_arithmetic_cpp_dec_float_3.cpp + +test_arithmetic_cpp_dec_float_3 : test_arithmetic_cpp_dec_float_3.o + g++ -std=gnu++0x --coverage -o test_arithmetic_cpp_dec_float_3 test_arithmetic_cpp_dec_float_3.o + +test_arithmetic_concept.o : ../test_arithmetic_backend_concept.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_BACKEND --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_concept.o -c ../test_arithmetic_backend_concept.cpp + +test_arithmetic_concept : test_arithmetic_concept.o + g++ -std=gnu++0x --coverage -o test_arithmetic_concept test_arithmetic_concept.o + +test_arithmetic_mpz.o : ../test_arithmetic_mpz.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPZ --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpz.o -c ../test_arithmetic_mpz.cpp + +test_arithmetic_mpz : test_arithmetic_mpz.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpz test_arithmetic_mpz.o -lgmp + +test_arithmetic_mpf.o : ../test_arithmetic_mpf.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPF --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpf.o -c ../test_arithmetic_mpf.cpp + +test_arithmetic_mpf : test_arithmetic_mpf.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpf test_arithmetic_mpf.o -lgmp + +test_arithmetic_mpf_50.o : ../test_arithmetic_mpf_50.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPF_50 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpf_50.o -c ../test_arithmetic_mpf_50.cpp + +test_arithmetic_mpf_50 : test_arithmetic_mpf_50.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpf_50 test_arithmetic_mpf_50.o -lgmp + +test_arithmetic_mpq.o : ../test_arithmetic_mpq.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPQ --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpq.o -c ../test_arithmetic_mpq.cpp + +test_arithmetic_mpq : test_arithmetic_mpq.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpq test_arithmetic_mpq.o -lgmp + +test_arithmetic_mpfr.o : ../test_arithmetic_mpfr.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPFR --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpfr.o -c ../test_arithmetic_mpfr.cpp + +test_arithmetic_mpfr : test_arithmetic_mpfr.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpfr test_arithmetic_mpfr.o -lmpfr -lgmp + +test_arithmetic_mpfr_50.o : ../test_arithmetic_mpfr_50.cpp $(SOURCES) + g++ -std=gnu++0x -DTEST_MPFR_50 --coverage -g -I../../../.. -I../../../../../../trunk -o test_arithmetic_mpfr_50.o -c ../test_arithmetic_mpfr_50.cpp + +test_arithmetic_mpfr_50 : test_arithmetic_mpfr_50.o + g++ -std=gnu++0x --coverage -o test_arithmetic_mpfr_50 test_arithmetic_mpfr_50.o -lmpfr -lgmp + +test_cpp_int.o : ../test_cpp_int.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_cpp_int.o -c ../test_cpp_int.cpp + +test_cpp_int : test_cpp_int.o + g++ -std=gnu++0x --coverage -o test_cpp_int test_cpp_int.o -lgmp + +test_int_io.o : ../test_int_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -DTEST_MPZ -DTEST_CPP_INT -g -I../../../.. -I../../../../../../trunk -o test_int_io.o -c ../test_int_io.cpp + +test_int_io : test_int_io.o + g++ -std=gnu++0x --coverage -o test_int_io test_int_io.o -lgmp + +test_float_io.o : ../test_float_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -DTEST_MPF_50 -DTEST_CPP_DEC_FLOAT -DTEST_MPFR_50 -I../../../.. -I../../../../../../trunk -o test_float_io.o -c ../test_float_io.cpp + +test_float_io : test_float_io.o + g++ -std=gnu++0x --coverage -o test_float_io test_float_io.o -lmpfr -lgmp + +test_rational_io.o : ../test_rational_io.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -DTEST_MPQ -DTEST_CPP_INT -g -I../../../.. -I../../../../../../trunk -o test_rational_io.o -c ../test_rational_io.cpp + +test_rational_io : test_rational_io.o + g++ -std=gnu++0x --coverage -o test_rational_io test_rational_io.o -lgmp + +test_gmp_conversions.o : ../test_gmp_conversions.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_gmp_conversions.o -c ../test_gmp_conversions.cpp + +test_gmp_conversions : test_gmp_conversions.o + g++ -std=gnu++0x --coverage -o test_gmp_conversions test_gmp_conversions.o -lgmp + +test_mpfr_conversions.o : ../test_mpfr_conversions.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_mpfr_conversions.o -c ../test_mpfr_conversions.cpp + +test_mpfr_conversions : test_mpfr_conversions.o + g++ -std=gnu++0x --coverage -o test_mpfr_conversions test_mpfr_conversions.o -lmpfr -lgmp + +test_cpp_int_conv.o : ../test_cpp_int_conv.cpp $(SOURCES) + g++ -std=gnu++0x --coverage -g -I../../../.. -I../../../../../../trunk -o test_cpp_int_conv.o -c ../test_cpp_int_conv.cpp + +test_cpp_int_conv : test_cpp_int_conv.o + g++ -std=gnu++0x --coverage -o test_cpp_int_conv test_cpp_int_conv.o + +run : test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 \ + test_arithmetic_cpp_int_4 test_arithmetic_cpp_int_5 test_arithmetic_cpp_int_6 \ + test_arithmetic_cpp_int_7 test_arithmetic_cpp_int_8 test_arithmetic_cpp_int_9 \ + test_arithmetic_cpp_int_10 test_arithmetic_cpp_int_11 test_arithmetic_cpp_int_12 \ + test_arithmetic_cpp_int_13 test_arithmetic_cpp_int_14 test_arithmetic_cpp_int_15 \ + test_arithmetic_cpp_int_16 test_arithmetic_cpp_int_17 test_arithmetic_cpp_int_18 \ + test_arithmetic_cpp_dec_float_1 test_arithmetic_cpp_dec_float_2 test_arithmetic_cpp_dec_float_3 test_arithmetic_concept \ + test_arithmetic_mpz test_arithmetic_mpf test_arithmetic_mpf_50 test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 \ + test_cpp_int test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + ./test_arithmetic_cpp_int_1 + ./test_arithmetic_cpp_int_2 + ./test_arithmetic_cpp_int_3 + ./test_arithmetic_cpp_int_4 + ./test_arithmetic_cpp_int_5 + ./test_arithmetic_cpp_int_6 + ./test_arithmetic_cpp_int_7 + ./test_arithmetic_cpp_int_8 + ./test_arithmetic_cpp_int_9 + ./test_arithmetic_cpp_int_10 + ./test_arithmetic_cpp_int_11 + ./test_arithmetic_cpp_int_12 + ./test_arithmetic_cpp_int_13 + ./test_arithmetic_cpp_int_14 + ./test_arithmetic_cpp_int_15 + ./test_arithmetic_cpp_int_16 + ./test_arithmetic_cpp_int_17 + ./test_arithmetic_cpp_int_18 + ./test_arithmetic_cpp_dec_float_1 + ./test_arithmetic_cpp_dec_float_2 + ./test_arithmetic_cpp_dec_float_3 + ./test_arithmetic_concept + ./test_arithmetic_mpz + ./test_arithmetic_mpf + ./test_arithmetic_mpf_50 + ./test_arithmetic_mpq + ./test_arithmetic_mpfr + ./test_arithmetic_mpfr_50 + ./test_cpp_int + ./test_int_io + ./test_float_io + ./test_rational_io + ./test_gmp_conversions + ./test_mpfr_conversions + ./test_cpp_int_conv + +clean : + rm -rf *.o *.gc* test_arithmetic_cpp_int_1 test_arithmetic_cpp_int_2 test_arithmetic_cpp_int_3 \ + test_arithmetic_cpp_int_4 test_arithmetic_cpp_int_5 test_arithmetic_cpp_int_6 \ + test_arithmetic_cpp_int_7 test_arithmetic_cpp_int_8 test_arithmetic_cpp_int_9 \ + test_arithmetic_cpp_int_10 test_arithmetic_cpp_int_11 test_arithmetic_cpp_int_12 \ + test_arithmetic_cpp_int_13 test_arithmetic_cpp_int_14 test_arithmetic_cpp_int_15 \ + test_arithmetic_cpp_int_16 test_arithmetic_cpp_int_17 test_arithmetic_cpp_int_18 \ + test_arithmetic_cpp_dec_float test_arithmetic_concept test_arithmetic_mpz \ + test_arithmetic_mpf test_arithmetic_mpf_50 test_arithmetic_mpq test_arithmetic_mpfr test_arithmetic_mpfr_50 test_cpp_int\ + test_int_io test_float_io test_rational_io test_gmp_conversions test_mpfr_conversions test_cpp_int_conv + + + + + diff --git a/libs/multiprecision/test/cpp_int1024_serial32.txt b/libs/multiprecision/test/cpp_int1024_serial32.txt new file mode 100644 index 0000000000..d9e8452cb3 --- /dev/null +++ b/libs/multiprecision/test/cpp_int1024_serial32.txt @@ -0,0 +1 @@ +22 serialization::archive 10 0 0 0 0 0 108 240 216 207 212 25 178 183 244 196 236 95 147 174 198 156 135 30 192 249 71 150 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0 0 0 0 0 0 0 8 58 0 224 93 1 0 0 0 1 8 58 0 224 93 1 0 0 0 0 8 61 170 163 0 0 0 0 0 1 8 61 170 163 0 0 0 0 0 0 8 16 0 0 0 0 0 0 0 1 8 16 0 0 0 0 0 0 0 0 8 19 80 184 100 0 136 17 0 1 8 19 80 184 100 0 136 17 0 0 8 141 166 59 0 0 0 0 0 1 8 141 166 59 0 0 0 0 0 0 8 1 0 0 0 0 0 0 0 1 8 1 0 0 0 0 0 0 0 0 8 106 120 1 0 0 0 0 0 1 8 106 120 1 0 0 0 0 0 0 8 24 0 0 0 0 0 0 0 1 8 24 0 0 0 0 0 0 0 0 8 250 206 237 235 100 45 220 2 1 8 250 206 237 235 100 45 220 2 0 8 104 0 0 0 0 0 0 0 1 8 104 0 0 0 0 0 0 0 0 8 45 124 107 88 59 188 20 0 1 8 45 124 107 88 59 188 20 0 0 8 133 86 244 174 225 3 0 0 1 8 133 86 244 174 225 3 0 0 0 8 10 106 7 0 0 0 0 0 1 8 10 106 7 0 0 0 0 0 0 8 198 151 96 192 44 105 0 0 1 8 198 151 96 192 44 105 0 0 0 8 18 6 0 0 0 0 0 0 1 8 18 6 0 0 0 0 0 0 0 8 139 29 156 22 238 7 0 0 1 8 139 29 156 22 238 7 0 0 0 8 223 115 28 171 0 0 0 0 1 8 223 115 28 171 0 0 0 0 0 8 221 148 185 62 0 0 0 0 1 8 221 148 185 62 0 0 0 0 0 8 61 47 108 1 0 0 0 0 1 8 61 47 108 1 0 0 0 0 0 8 87 157 178 141 10 0 0 0 1 8 87 157 178 141 10 0 0 0 0 8 86 94 188 134 23 82 0 0 1 8 86 94 188 134 23 82 0 0 0 8 179 64 23 0 0 0 0 0 1 8 179 64 23 0 0 0 0 0 0 8 113 45 10 0 0 0 0 0 1 8 113 45 10 0 0 0 0 0 0 8 204 227 150 219 42 98 0 0 1 8 204 227 150 219 42 98 0 0 0 8 72 207 3 4 107 1 0 0 1 8 72 207 3 4 107 1 0 0 0 8 242 22 0 0 0 0 0 0 1 8 242 22 0 0 0 0 0 0 0 8 43 248 193 8 8 37 19 0 1 8 43 248 193 8 8 37 19 0 0 8 135 156 114 210 151 8 0 0 1 8 135 156 114 210 151 8 0 0 0 8 126 63 25 0 0 0 0 0 1 8 126 63 25 0 0 0 0 0 0 8 94 41 0 0 0 0 0 0 1 8 94 41 0 0 0 0 0 0 0 8 132 46 67 3 0 0 0 0 1 8 132 46 67 3 0 0 0 0 0 8 12 53 213 1 0 0 0 0 1 8 12 53 213 1 0 0 0 0 0 8 224 181 149 0 0 0 0 0 1 8 224 181 149 0 0 0 0 0 0 8 214 73 249 129 122 0 0 0 1 8 214 73 249 129 122 0 0 0 0 8 141 160 27 51 90 159 14 0 1 8 141 160 27 51 90 159 14 0 0 8 123 185 72 150 135 30 2 0 1 8 123 185 72 150 135 30 2 0 0 8 132 79 251 109 16 13 0 0 1 8 132 79 251 109 16 13 0 0 0 8 187 0 0 0 0 0 0 0 1 8 187 0 0 0 0 0 0 0 0 8 26 47 114 1 0 0 0 0 1 8 26 47 114 1 0 0 0 0 0 8 36 142 132 192 11 54 198 0 1 8 36 142 132 192 11 54 198 0 0 8 167 191 148 125 0 0 0 0 1 8 167 191 148 125 0 0 0 0 0 8 234 206 244 113 18 198 0 0 1 8 234 206 244 113 18 198 0 0 0 8 3 143 18 0 0 0 0 0 1 8 3 143 18 0 0 0 0 0 0 8 62 157 58 195 0 0 0 0 1 8 62 157 58 195 0 0 0 0 0 8 172 170 222 106 83 163 194 4 1 8 172 170 222 106 83 163 194 4 0 8 88 220 20 57 0 0 0 0 1 8 88 220 20 57 0 0 0 0 0 8 167 245 187 129 1 0 0 0 1 8 167 245 187 129 1 0 0 0 0 8 164 130 167 36 0 0 0 0 1 8 164 130 167 36 0 0 0 0 0 8 61 130 34 172 248 118 0 0 1 8 61 130 34 172 248 118 0 0 0 8 40 22 12 0 0 0 0 0 1 8 40 22 12 0 0 0 0 0 0 8 209 1 0 0 0 0 0 0 1 8 209 1 0 0 0 0 0 0 0 8 170 133 218 207 1 0 0 0 1 8 170 133 218 207 1 0 0 0 0 8 223 195 71 3 0 0 0 0 1 8 223 195 71 3 0 0 0 0 0 8 197 87 218 147 1 0 0 0 1 8 197 87 218 147 1 0 0 0 0 8 210 1 234 57 242 124 45 0 1 8 210 1 234 57 242 124 45 0 0 8 119 110 205 24 176 195 21 0 1 8 119 110 205 24 176 195 21 0 0 8 71 104 194 0 0 0 0 0 1 8 71 104 194 0 0 0 0 0 0 8 53 164 236 57 255 127 4 0 1 8 53 164 236 57 255 127 4 0 0 8 218 132 146 91 132 77 213 4 1 8 218 132 146 91 132 77 213 4 0 8 133 79 247 151 252 1 0 0 1 8 133 79 247 151 252 1 0 0 0 8 203 243 153 55 2 0 0 0 1 8 203 243 153 55 2 0 0 0 0 8 197 193 53 2 0 0 0 0 1 8 197 193 53 2 0 0 0 0 0 8 84 5 0 0 0 0 0 0 1 8 84 5 0 0 0 0 0 0 0 8 177 187 206 97 141 85 1 0 1 8 177 187 206 97 141 85 1 0 0 8 166 94 0 0 0 0 0 0 1 8 166 94 0 0 0 0 0 0 0 8 190 247 33 10 10 0 0 0 1 8 190 247 33 10 10 0 0 0 0 8 61 186 120 114 110 34 74 14 1 8 61 186 120 114 110 34 74 14 0 8 48 152 216 0 0 0 0 0 1 8 48 152 216 0 0 0 0 0 0 8 157 24 37 230 113 32 156 61 1 8 157 24 37 230 113 32 156 61 0 8 26 71 250 167 179 175 252 27 1 8 26 71 250 167 179 175 252 27 0 8 138 11 1 0 0 0 0 0 1 8 138 11 1 0 0 0 0 0 0 8 64 228 47 79 174 153 235 1 1 8 64 228 47 79 174 153 235 1 0 8 12 0 0 0 0 0 0 0 1 8 12 0 0 0 0 0 0 0 0 8 227 20 33 239 16 0 0 0 1 8 227 20 33 239 16 0 0 0 0 8 89 117 39 6 0 0 0 0 1 8 89 117 39 6 0 0 0 0 0 8 56 143 170 210 159 0 0 0 1 8 56 143 170 210 159 0 0 0 0 8 83 94 139 170 42 227 7 0 1 8 83 94 139 170 42 227 7 0 0 8 158 24 234 182 90 0 0 0 1 8 158 24 234 182 90 0 0 0 0 8 184 250 218 70 0 0 0 0 1 8 184 250 218 70 0 0 0 0 0 8 199 13 0 0 0 0 0 0 1 8 199 13 0 0 0 0 0 0 0 8 162 245 210 10 15 0 0 0 1 8 162 245 210 10 15 0 0 0 0 8 163 218 24 0 0 0 0 0 1 8 163 218 24 0 0 0 0 0 0 8 14 0 0 0 0 0 0 0 1 8 14 0 0 0 0 0 0 0 0 8 167 97 145 202 0 0 0 0 1 8 167 97 145 202 0 0 0 0 0 8 207 69 56 26 219 188 172 2 1 8 207 69 56 26 219 188 172 2 0 8 19 245 0 0 0 0 0 0 1 8 19 245 0 0 0 0 0 0 0 8 101 116 0 0 0 0 0 0 1 8 101 116 0 0 0 0 0 0 0 8 144 67 225 251 217 0 96 0 1 8 144 67 225 251 217 0 96 0 0 8 141 129 40 88 123 180 46 1 1 8 141 129 40 88 123 180 46 1 0 8 83 65 0 0 0 0 0 0 1 8 83 65 0 0 0 0 0 0 0 8 1 71 241 42 0 0 0 0 1 8 1 71 241 42 0 0 0 0 0 8 201 82 0 0 0 0 0 0 1 8 201 82 0 0 0 0 0 0 0 8 143 3 0 0 0 0 0 0 1 8 143 3 0 0 0 0 0 0 0 8 140 29 0 0 0 0 0 0 1 8 140 29 0 0 0 0 0 0 0 8 209 38 0 0 0 0 0 0 1 8 209 38 0 0 0 0 0 0 0 8 34 69 0 0 0 0 0 0 1 8 34 69 0 0 0 0 0 0 0 8 221 163 103 107 78 53 11 0 1 8 221 163 103 107 78 53 11 0 0 8 210 46 149 42 0 0 0 0 1 8 210 46 149 42 0 0 0 0 0 8 48 85 36 205 0 0 0 0 1 8 48 85 36 205 0 0 0 0 0 8 37 35 35 0 0 0 0 0 1 8 37 35 35 0 0 0 0 0 0 8 13 0 0 0 0 0 0 0 1 8 13 0 0 0 0 0 0 0 0 8 46 173 250 215 165 229 166 2 1 8 46 173 250 215 165 229 166 2 0 8 67 188 30 254 109 2 0 0 1 8 67 188 30 254 109 2 0 0 0 8 137 152 11 16 0 0 0 0 1 8 137 152 11 16 0 0 0 0 0 8 152 52 243 192 36 1 0 0 1 8 152 52 243 192 36 1 0 0 0 8 129 59 0 0 0 0 0 0 1 8 129 59 0 0 0 0 0 0 0 8 201 94 53 127 56 0 0 0 1 8 201 94 53 127 56 0 0 0 0 8 73 236 21 75 203 154 66 5 1 8 73 236 21 75 203 154 66 5 0 8 196 244 167 127 116 213 0 0 1 8 196 244 167 127 116 213 0 0 0 8 63 43 243 86 100 247 101 30 1 8 63 43 243 86 100 247 101 30 0 8 179 18 79 0 0 0 0 0 1 8 179 18 79 0 0 0 0 0 0 8 62 229 32 2 0 0 0 0 1 8 62 229 32 2 0 0 0 0 0 8 191 161 29 68 10 28 0 0 1 8 191 161 29 68 10 28 0 0 0 8 157 0 0 0 0 0 0 0 1 8 157 0 0 0 0 0 0 0 0 8 177 110 144 211 209 51 0 0 1 8 177 110 144 211 209 51 0 0 0 8 38 140 6 0 0 0 0 0 1 8 38 140 6 0 0 0 0 0 0 8 230 31 0 0 0 0 0 0 1 8 230 31 0 0 0 0 0 0 0 8 240 94 116 15 0 0 0 0 1 8 240 94 116 15 0 0 0 0 0 8 182 7 0 0 0 0 0 0 1 8 182 7 0 0 0 0 0 0 0 8 1 177 12 133 96 0 0 0 1 8 1 177 12 133 96 0 0 0 0 8 240 7 185 0 0 0 0 0 1 8 240 7 185 0 0 0 0 0 0 8 243 73 7 0 0 0 0 0 1 8 243 73 7 0 0 0 0 0 0 8 26 0 0 0 0 0 0 0 1 8 26 0 0 0 0 0 0 0 0 8 103 9 1 204 46 0 0 0 1 8 103 9 1 204 46 0 0 0 0 8 98 214 177 103 24 96 0 0 1 8 98 214 177 103 24 96 0 0 0 8 81 174 115 76 247 124 0 0 1 8 81 174 115 76 247 124 0 0 0 8 61 12 0 0 0 0 0 0 1 8 61 12 0 0 0 0 0 0 0 8 85 161 0 0 0 0 0 0 1 8 85 161 0 0 0 0 0 0 0 8 101 4 40 150 22 103 32 0 1 8 101 4 40 150 22 103 32 0 0 8 103 2 0 0 0 0 0 0 1 8 103 2 0 0 0 0 0 0 0 8 60 153 25 0 0 0 0 0 1 8 60 153 25 0 0 0 0 0 0 8 143 111 7 0 0 0 0 0 1 8 143 111 7 0 0 0 0 0 0 8 80 120 24 232 225 5 0 0 1 8 80 120 24 232 225 5 0 0 0 8 174 134 41 0 0 0 0 0 1 8 174 134 41 0 0 0 0 0 0 8 113 152 62 21 0 0 0 0 1 8 113 152 62 21 0 0 0 0 0 8 241 24 81 31 0 0 0 0 1 8 241 24 81 31 0 0 0 0 0 8 82 153 37 103 160 93 6 0 1 8 82 153 37 103 160 93 6 0 0 8 40 224 161 201 3 0 0 0 1 8 40 224 161 201 3 0 0 0 0 8 19 3 0 0 0 0 0 0 1 8 19 3 0 0 0 0 0 0 0 8 82 0 0 0 0 0 0 0 1 8 82 0 0 0 0 0 0 0 0 8 64 200 218 23 94 23 70 119 1 8 64 200 218 23 94 23 70 119 0 8 15 139 7 0 0 0 0 0 1 8 15 139 7 0 0 0 0 0 0 8 18 20 0 0 0 0 0 0 1 8 18 20 0 0 0 0 0 0 0 8 128 37 176 212 38 112 1 0 1 8 128 37 176 212 38 112 1 0 0 8 13 125 43 146 204 213 0 0 1 8 13 125 43 146 204 213 0 0 0 8 14 0 0 0 0 0 0 0 1 8 14 0 0 0 0 0 0 0 0 8 70 145 5 0 0 0 0 0 1 8 70 145 5 0 0 0 0 0 0 8 186 122 94 51 73 69 56 8 1 8 186 122 94 51 73 69 56 8 0 8 77 183 3 0 0 0 0 0 1 8 77 183 3 0 0 0 0 0 0 8 217 138 24 241 155 207 0 0 1 8 217 138 24 241 155 207 0 0 0 8 150 0 0 0 0 0 0 0 1 8 150 0 0 0 0 0 0 0 0 8 196 49 182 125 0 0 0 0 1 8 196 49 182 125 0 0 0 0 0 8 133 3 165 0 0 0 0 0 1 8 133 3 165 0 0 0 0 0 0 8 0 245 2 102 53 0 0 0 1 8 0 245 2 102 53 0 0 0 0 8 35 187 7 0 0 0 0 0 1 8 35 187 7 0 0 0 0 0 0 8 217 58 0 0 0 0 0 0 1 8 217 58 0 0 0 0 0 0 0 8 93 4 23 102 114 100 3 1 1 8 93 4 23 102 114 100 3 1 0 8 18 224 241 10 0 0 0 0 1 8 18 224 241 10 0 0 0 0 0 8 100 120 0 0 0 0 0 0 1 8 100 120 0 0 0 0 0 0 diff --git a/libs/multiprecision/test/include_test/cpp_bin_float_include_test.cpp b/libs/multiprecision/test/include_test/cpp_bin_float_include_test.cpp new file mode 100644 index 0000000000..b36c89e1be --- /dev/null +++ b/libs/multiprecision/test/include_test/cpp_bin_float_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_bin_float.hpp> + +using namespace boost::multiprecision; + +cpp_bin_float<50> a; + + diff --git a/libs/multiprecision/test/include_test/cpp_dec_float_include_test.cpp b/libs/multiprecision/test/include_test/cpp_dec_float_include_test.cpp new file mode 100644 index 0000000000..bdf09e83f0 --- /dev/null +++ b/libs/multiprecision/test/include_test/cpp_dec_float_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace boost::multiprecision; + +cpp_dec_float<50> a; + + diff --git a/libs/multiprecision/test/include_test/cpp_int_include_test.cpp b/libs/multiprecision/test/include_test/cpp_int_include_test.cpp new file mode 100644 index 0000000000..e374261233 --- /dev/null +++ b/libs/multiprecision/test/include_test/cpp_int_include_test.cpp @@ -0,0 +1,16 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/cpp_int.hpp> + +using namespace boost::multiprecision; + +number<cpp_int_backend<> > a; +number<cpp_int_backend<>, et_off> b; +number<cpp_int_backend<64, 64, signed_magnitude, checked, void>, et_off> c; +number<cpp_int_backend<128, 128, signed_magnitude, checked, void>, et_off> d; +number<cpp_int_backend<500, 500, signed_magnitude, checked, void>, et_off> e; + + diff --git a/libs/multiprecision/test/include_test/gmp_include_test.cpp b/libs/multiprecision/test/include_test/gmp_include_test.cpp new file mode 100644 index 0000000000..4b07266fe6 --- /dev/null +++ b/libs/multiprecision/test/include_test/gmp_include_test.cpp @@ -0,0 +1,14 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/gmp.hpp> + +using namespace boost::multiprecision; + +mpf_float a; +mpz_int b; +mpq_rational c; + + diff --git a/libs/multiprecision/test/include_test/mpfr_include_test.cpp b/libs/multiprecision/test/include_test/mpfr_include_test.cpp new file mode 100644 index 0000000000..f84cbb959e --- /dev/null +++ b/libs/multiprecision/test/include_test/mpfr_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/mpfr.hpp> + +using namespace boost::multiprecision; + +mpfr_float a; + + diff --git a/libs/multiprecision/test/include_test/tommath_include_test.cpp b/libs/multiprecision/test/include_test/tommath_include_test.cpp new file mode 100644 index 0000000000..bc000fefbd --- /dev/null +++ b/libs/multiprecision/test/include_test/tommath_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/multiprecision/tommath.hpp> + +using namespace boost::multiprecision; + +tom_int a; + + diff --git a/libs/multiprecision/test/math/high_prec/gamma.ipp b/libs/multiprecision/test/math/high_prec/gamma.ipp new file mode 100644 index 0000000000..dae325a5fa --- /dev/null +++ b/libs/multiprecision/test/math/high_prec/gamma.ipp @@ -0,0 +1,505 @@ + static const boost::array<boost::array<typename table_type<T>::type, 3>, 500> gamma = {{ + { SC_(8.45530509948730468750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.11676792084632275714192215809847832812560655161416701540037514678588899552795223636051283861515685855053582939146274240113874531527973814210488207830128530900559599074170389066138081891070712920623473461857632254352617595899153121789055651865429663273105801624222067275035146160407682419814612559770937851333313258174693831239060158272144283644033402005812336141640353704703451805075743457651474500575180336149704581761302422616802534269713673320145810616702623379426577267381016596640646036780085640e+00), SC_(1.10438728442867816609665916944098399086765601795314917615577669041382221945245269046345957164829024229823010663264720601624809651655116368339246859099278886577422386896811750937967494940960029250224075543433744666205413027910764506859493838993507216401131983731121529344952082060498119577899781093069658373786189150246027769179901839580061229387653730476486565832292623869480613925012343335744507187985817127088673548820437219886661135524261767270766239756270078148544872782377812888609878714473093021e-01) }, + { 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SC_(4.11917442852952711543741507530337656290736016465506639741742101611014731373074855727222493539896474697110498858504643770565949929474195415135105179617700802945752394424643368615173443852328593935472829240359653696116395379824510508393155403134258111311673599669939241747207061523079182632547737365431783702760141194142731371171480274286029170854076168498596924110170468837240766315428782766656743993971526078852137464960957958084824518999844115962290565276220206898969535823972967013864671556923956906e+00) } + }}; +//#undef SC_ + + diff --git a/libs/multiprecision/test/math/high_prec/readme.txt b/libs/multiprecision/test/math/high_prec/readme.txt new file mode 100644 index 0000000000..e52652f18d --- /dev/null +++ b/libs/multiprecision/test/math/high_prec/readme.txt @@ -0,0 +1,3 @@ +These tests are designed to test Boost.Math's code at really rather high precision +- 500 decimal digits or so. As such they use their own test data, and take rather +a long time to run. diff --git a/libs/multiprecision/test/math/high_prec/test_gamma.cpp b/libs/multiprecision/test/math/high_prec/test_gamma.cpp new file mode 100644 index 0000000000..fd04bfcc41 --- /dev/null +++ b/libs/multiprecision/test/math/high_prec/test_gamma.cpp @@ -0,0 +1,81 @@ +// (C) Copyright John Maddock 2006. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include "test_gamma.hpp" +#ifdef TEST_MPFR +#include <boost/multiprecision/mpfr.hpp> +#else +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + const char* largest_type; +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >()) + { + largest_type = "(long\\s+)?double"; + } + else + { + largest_type = "long double"; + } +#else + largest_type = "(long\\s+)?double"; +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*near 1.*", // test data group + ".*lgamma.*", 100000000000LL, 100000000000LL); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*near 0.*", // test data group + ".*lgamma.*", 300000, 100000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 100000, 50000); // test function + + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + expected_results(); + BOOST_MATH_CONTROL_FP; + +#ifdef TEST_MPFR + typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<450> > mp_type; + const char* name = "number<mpfr_float_backend<450> >"; +#else + typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<450> > mp_type; + const char* name = "number<cpp_bin_float<450> >"; +#endif + + test_gamma(mp_type(0), name); +} + + + + diff --git a/libs/multiprecision/test/math/high_prec/test_gamma.hpp b/libs/multiprecision/test/math/high_prec/test_gamma.hpp new file mode 100644 index 0000000000..fa5c9e548d --- /dev/null +++ b/libs/multiprecision/test/math/high_prec/test_gamma.hpp @@ -0,0 +1,92 @@ +// Copyright John Maddock 2006. +// Copyright Paul A. Bristow 2007, 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error + +#include <boost/math/special_functions/gamma.hpp> +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> +#include <boost/test/floating_point_comparison.hpp> +#include <boost/math/tools/stats.hpp> +#include <boost/math/tools/test.hpp> +#include <boost/math/constants/constants.hpp> +#include <boost/type_traits/is_floating_point.hpp> +#include <boost/array.hpp> +#include "libs/math/test/functor.hpp" + +#include "libs/math/test/handle_test_result.hpp" +#include "../table_type.hpp" + +#ifndef SC_ +#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L)) +#endif + +template <class Real, class T> +void do_test_gamma(const T& data, const char* type_name, const char* test_name) +{ + typedef typename T::value_type row_type; + typedef Real value_type; + + typedef value_type (*pg)(value_type); +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + pg funcp = boost::math::tgamma<value_type>; +#else + pg funcp = boost::math::tgamma; +#endif + + boost::math::tools::test_result<value_type> result; + + std::cout << "Testing " << test_name << " with type " << type_name + << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; + + // + // test tgamma against data: + // + result = boost::math::tools::test_hetero<Real>( + data, + bind_func<Real>(funcp, 0), + extract_result<Real>(1)); + handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma", test_name); + + // + // test lgamma against data: + // +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + funcp = boost::math::lgamma<value_type>; +#else + funcp = boost::math::lgamma; +#endif + result = boost::math::tools::test_hetero<Real>( + data, + bind_func<Real>(funcp, 0), + extract_result<Real>(2)); + handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::lgamma", test_name); + + std::cout << std::endl; +} + +template <class T> +void test_gamma(T, const char* name) +{ +# include "gamma.ipp" + + do_test_gamma<T>(gamma, name, "random values"); + +# include "gamma_1_2.ipp" + + do_test_gamma<T>(gamma_1_2, name, "Values near 1 and 2"); + +# include "gamma_0.ipp" + + do_test_gamma<T>(gamma_0, name, "Values near 0"); + +# include "gamma_neg.ipp" + + do_test_gamma<T>(gamma_neg, name, "Negative arguments"); + +} + + diff --git a/libs/multiprecision/test/math/instances/Jamfile.v2 b/libs/multiprecision/test/math/instances/Jamfile.v2 new file mode 100644 index 0000000000..9e6aa4729e --- /dev/null +++ b/libs/multiprecision/test/math/instances/Jamfile.v2 @@ -0,0 +1,81 @@ +# copyright John Maddock 2013 +# Distributed under the Boost Software License, Version 1.0. +# (See accompanying file LICENSE_1_0.txt or copy at +# http://www.boost.org/LICENSE_1_0.txt. + +import modules ; +import path ; + +local ntl-path = [ modules.peek : NTL_PATH ] ; +local gmp_path = [ modules.peek : GMP_PATH ] ; +local mpfr_path = [ modules.peek : MPFR_PATH ] ; +local mpfi_path = [ modules.peek : MPFI_PATH ] ; +local tommath_path = [ modules.peek : TOMMATH_PATH ] ; + +project : requirements + <include>$(gmp_path) + <include>$(gmp_path)/mpfr + <include>$(gmp_path)/gmpfrxx + <include>$(mpfr_path) + <include>$(mpfi_path) + <include>$(mpfi_path)/src + <include>$(tommath_path) + <include>../../.. + # We set these to make it easier to set up and test GMP and MPFR under Win32: + #<toolset>msvc:<runtime-link>static + #<toolset>msvc:<link>static + #<toolset>msvc:<warnings>all + #<toolset>intel-win:<runtime-link>static + #<toolset>intel-win:<link>static + # Speed up compiles: + #<toolset>msvc:<debug-symbols>off + #<toolset>intel:<debug-symbols>off + <toolset>gcc:<cxxflags>-Wall + <toolset>gcc:<cxxflags>-Wextra + <toolset>intel:<define>SLOW_COMPILER + ; + +lib gmp : : <search>$(gmp_path) ; +lib mpfr : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug ; +lib mpfi : : <search>$(gmp_path) <search>$(mpfr_path) <search>$(mpfr_path)/build.vc10/lib/Win32/Debug <search>$(mpfi_path) <search>$(mpfi_path)/src ; +lib quadmath ; + +rule generate_objs ( suffix : variant_count : build_opts * ) +{ + local result ; + switch $(variant_count) + { + case "1" : variant_list = 1 ; + case "2" : variant_list = 1 2 ; + case "3" : variant_list = 1 2 3 ; + case "4" : variant_list = 1 2 3 4 ; + case "5" : variant_list = 1 2 3 4 5 ; + case "6" : variant_list = 1 2 3 4 5 6 ; + } + + for group_id in 1 2 3 4 5 6 7 8 9 10 + { + for variant_id in $(variant_list) + { + name = "test_instances$(suffix)_$(group_id)_$(variant_id)" ; + obj $(name) : instances.cpp : release <define>BOOST_MATH_TEST_TYPE=test_type_$(variant_id) <define>TEST_GROUP_$(group_id) $(build_opts) ; + result += $(name) ; + } + } + return $(result) ; +} + +lib test_instances_mpf : [ generate_objs "_mpf" : 4 : <define>TEST_MPF_50 ] : [ check-target-builds ../../../config//has_gmp : : <build>no ] ; +lib test_instances_mpfr : [ generate_objs "_mpfr" : 3 : <define>TEST_MPFR_50 ] : [ check-target-builds ../../../config//has_mpfr : : <build>no ] ; +lib test_instances_cpp_dec_float : [ generate_objs "_cpp_dec_float" : 3 : <define>TEST_CPP_DEC_FLOAT ] : ; +lib test_instances_cpp_bin_float : [ generate_objs "_cpp_bin_float" : 1 : <define>TEST_CPP_BIN_FLOAT ] : ; +lib test_instances_float128 : [ generate_objs "_float128" : 1 : <define>TEST_FLOAT128 ] : [ check-target-builds ../../../config//has_float128 : : <build>no ] ; +lib test_instances_intel_quad : [ generate_objs "_intel_quad" : 1 : <define>TEST_FLOAT128 <cxxflags>-Qoption,cpp,--extended_float_type ] : [ check-target-builds ../../../config//has_intel_quad : <cxxflags>-Qoption,cpp,--extended_float_type : <build>no ] ; + +explicit test_instances_mpf ; +explicit test_instances_mpfr ; +explicit test_instances_cpp_dec_float ; +explicit test_instances_cpp_bin_float ; +explicit test_instances_float128 ; +explicit test_instances_intel_quad ; + diff --git a/libs/multiprecision/test/math/instances/instances.cpp b/libs/multiprecision/test/math/instances/instances.cpp new file mode 100644 index 0000000000..7b4b845fae --- /dev/null +++ b/libs/multiprecision/test/math/instances/instances.cpp @@ -0,0 +1,14 @@ +// Copyright John Maddock 2013. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include <boost/math/special_functions.hpp> + +#include "../setup.hpp" + +//#define BOOST_MATH_TEST_TYPE double +//#define TEST_GROUP_1 +#include "../../../../math/test/test_instances/test_instances.hpp" + diff --git a/libs/multiprecision/test/math/log1p_expm1_test.cpp b/libs/multiprecision/test/math/log1p_expm1_test.cpp new file mode 100644 index 0000000000..29767e13a0 --- /dev/null +++ b/libs/multiprecision/test/math/log1p_expm1_test.cpp @@ -0,0 +1,101 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +//#include <boost/math/special_functions/log1p.hpp> +//#include <boost/math/special_functions/expm1.hpp> +#include <boost/math/special_functions/math_fwd.hpp> + +#include "table_type.hpp" + +#include "libs/math/test/log1p_expm1_test.hpp" + +// +// DESCRIPTION: +// ~~~~~~~~~~~~ +// +// This file tests the functions log1p and expm1. The accuracy tests +// use values generated with NTL::RR at 1000-bit precision +// and our generic versions of these functions. +// +// Note that when this file is first run on a new platform many of +// these tests will fail: the default accuracy is 1 epsilon which +// is too tight for most platforms. In this situation you will +// need to cast a human eye over the error rates reported and make +// a judgement as to whether they are acceptable. Either way please +// report the results to the Boost mailing list. Acceptable rates of +// error are marked up below as a series of regular expressions that +// identify the compiler/stdlib/platform/data-type/test-data/test-function +// along with the maximum expected peek and RMS mean errors for that +// test. +// + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + + // + // Catch all cases come last: + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*", // test data group + ".*", // test function + 500, // Max Peek error + 100); // Max mean error + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", // test function + 500, // Max Peek error + 100); // Max mean error + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", // test function + 8, // Max Peek error + 5); // Max mean error + + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/powm1_sqrtp1m1_test.cpp b/libs/multiprecision/test/math/powm1_sqrtp1m1_test.cpp new file mode 100644 index 0000000000..d0c6b54236 --- /dev/null +++ b/libs/multiprecision/test/math/powm1_sqrtp1m1_test.cpp @@ -0,0 +1,97 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" + +#include <boost/test/floating_point_comparison.hpp> +#include <boost/math/special_functions/math_fwd.hpp> + +#include "table_type.hpp" + +#include "libs/math/test/powm1_sqrtp1m1_test.hpp" + +// +// DESCRIPTION: +// ~~~~~~~~~~~~ +// +// This file tests the functions log1p and expm1. The accuracy tests +// use values generated with NTL::RR at 1000-bit precision +// and our generic versions of these functions. +// +// Note that when this file is first run on a new platform many of +// these tests will fail: the default accuracy is 1 epsilon which +// is too tight for most platforms. In this situation you will +// need to cast a human eye over the error rates reported and make +// a judgement as to whether they are acceptable. Either way please +// report the results to the Boost mailing list. Acceptable rates of +// error are marked up below as a series of regular expressions that +// identify the compiler/stdlib/platform/data-type/test-data/test-function +// along with the maximum expected peek and RMS mean errors for that +// test. +// + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + + // + // Catch all cases come last: + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", // test function + 300, // Max Peek error + 50); // Max mean error + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", // test function + 15, // Max Peek error + 5); // Max mean error + + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_powm1_sqrtp1m1(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // We test two different precisions: + // 18 decimal digits triggers Boost.Math's 64-bit long double support. + // 30 decimal digits triggers Boost.Math's 128-bit long double support. + // 35 decimal digits triggers true arbitrary precision support. + // + ALL_SMALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/readme.txt b/libs/multiprecision/test/math/readme.txt new file mode 100644 index 0000000000..c0a6d92144 --- /dev/null +++ b/libs/multiprecision/test/math/readme.txt @@ -0,0 +1,7 @@ +These tests verify that the multiprecision types can interoperate with Boost.Math. + +We use Boost.Math's own test data for these and test at various precisions which trigger +different code inside the Math lib. We don't test at very high precision here as +Boost.Math's test data doesn't go much beyond 35 digits (for good reason, some compilers +choke when attempting to parse higher precision numbers as double's). + diff --git a/libs/multiprecision/test/math/setup.hpp b/libs/multiprecision/test/math/setup.hpp new file mode 100644 index 0000000000..ea019f3125 --- /dev/null +++ b/libs/multiprecision/test/math/setup.hpp @@ -0,0 +1,143 @@ +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_MATH_SETUP_HPP +#define BOOST_MP_MATH_SETUP_HPP + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#define BOOST_MATH_SMALL_CONSTANT(x) x + +#if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) \ + && !defined(TEST_MPFR_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> + +#define MPF_TESTS test(number<gmp_float<18> >(), "number<gmp_float<18> >");\ + test(number<gmp_float<30> >(), "number<gmp_float<30> >");\ + test(number<gmp_float<35> >(), "number<gmp_float<35> >");\ + /* there should be at least one test with expression templates off: */ \ + test(number<gmp_float<35>, et_off>(), "number<gmp_float<35>, et_off>"); +#define MPF_SMALL_TESTS /*test(number<gmp_float<18> >(), "number<gmp_float<18> >");*/\ + test(number<gmp_float<30> >(), "number<gmp_float<30> >");\ + test(number<gmp_float<35> >(), "number<gmp_float<35> >");\ + /* there should be at least one test with expression templates off: */ \ + test(number<gmp_float<35>, et_off>(), "number<gmp_float<35>, et_off>"); + +typedef boost::multiprecision::number<boost::multiprecision::gmp_float<18> > test_type_1; +typedef boost::multiprecision::number<boost::multiprecision::gmp_float<30> > test_type_2; +typedef boost::multiprecision::number<boost::multiprecision::gmp_float<35> > test_type_3; +typedef boost::multiprecision::number<boost::multiprecision::gmp_float<35>, boost::multiprecision::et_off> test_type_4; + +#else + +#define MPF_TESTS +#define MPF_SMALL_TESTS + +#endif + +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> + +#define MPFR_TESTS test(number<mpfr_float_backend<18> >(), "number<mpfr_float_backend<18> >");\ + test(number<mpfr_float_backend<30> >(), "number<mpfr_float_backend<30> >");\ + test(number<mpfr_float_backend<35> >(), "number<mpfr_float_backend<35> >"); + +typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<18> > test_type_1; +typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<30> > test_type_2; +typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<35> > test_type_3; + +#else + +#define MPFR_TESTS + +#endif + +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> + +#define CPP_DEC_FLOAT_TESTS test(number<cpp_dec_float<18> >(), "number<cpp_dec_float<18> >");\ + test(number<cpp_dec_float<30> >(), "number<cpp_dec_float<30> >");\ + test(number<cpp_dec_float<35, long long, std::allocator<void> > >(), "number<cpp_dec_float<35, long long, std::allocator<void> > >"); + +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > test_type_1; +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<30> > test_type_2; +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<35, long long, std::allocator<void> > > test_type_3; + +#else + +#define CPP_DEC_FLOAT_TESTS + +#endif + +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> + +#define CPP_BIN_FLOAT_TESTS test(cpp_bin_float_quad(), "cpp_bin_float_quad"); + +typedef boost::multiprecision::cpp_bin_float_quad test_type_1; + +#else + +#define CPP_BIN_FLOAT_TESTS + +#endif + +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> + +#define FLOAT128_TESTS test(float128(), "float128"); + +typedef boost::multiprecision::float128 test_type_1; + +#else + +#define FLOAT128_TESTS + +#endif + + +#ifndef BOOST_MATH_TEST_TYPE +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> +#include <boost/test/floating_point_comparison.hpp> +#endif + +#define ALL_TESTS \ + MPF_TESTS\ + MPFR_TESTS\ + CPP_DEC_FLOAT_TESTS\ + FLOAT128_TESTS\ + CPP_BIN_FLOAT_TESTS + +#define ALL_SMALL_TESTS\ + MPF_SMALL_TESTS\ + MPFR_TESTS\ + CPP_DEC_FLOAT_TESTS\ + FLOAT128_TESTS\ + CPP_BIN_FLOAT_TESTS + +#endif + diff --git a/libs/multiprecision/test/math/table_type.hpp b/libs/multiprecision/test/math/table_type.hpp new file mode 100644 index 0000000000..0b78ec0fdf --- /dev/null +++ b/libs/multiprecision/test/math/table_type.hpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_TABLE_TYPE + +#include <libs/math/test/table_type.hpp> +#include <boost/multiprecision/number.hpp> + +struct string_table_entry +{ +private: + const char* m_data; +public: + string_table_entry(const char* p) : m_data(p) {} + + template <class T> + operator T () const + { + return static_cast<T>(m_data); + } +}; + +inline std::ostream& operator << (std::ostream& os, string_table_entry const & what) +{ + return os << static_cast<const char*>(what); +} + +template <class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> +struct table_type<boost::multiprecision::number<Backend, ExpressionTemplates> > +{ + typedef string_table_entry type; +}; + +#define SC_(x) string_table_entry(BOOST_STRINGIZE(x)) + +#endif + diff --git a/libs/multiprecision/test/math/test_bessel_i.cpp b/libs/multiprecision/test/math/test_bessel_i.cpp new file mode 100644 index 0000000000..0e13862ee5 --- /dev/null +++ b/libs/multiprecision/test/math/test_bessel_i.cpp @@ -0,0 +1,68 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" + +#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_STRINGIZE(x)) + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_bessel_i.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + + // + // Catch all cases come last: + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", // test function + 500, // Max Peek error + 200); // Max mean error + + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_bessel(t, p); +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 9 decimal digits: tests the least wide arbitrary precision code + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_SMALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_bessel_j.cpp b/libs/multiprecision/test/math/test_bessel_j.cpp new file mode 100644 index 0000000000..0a07f6022e --- /dev/null +++ b/libs/multiprecision/test/math/test_bessel_j.cpp @@ -0,0 +1,123 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_bessel_j.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*J0.*Tricky.*", // test data group + ".*", 10000000000L, 5000000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*J0.*Tricky.*", // test data group + ".*", 400000000, 400000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*J1.*Tricky.*", // test data group + ".*", 1000000000L, 500000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*J1.*Tricky.*", // test data group + ".*", 10000000, 5000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*JN.*Integer.*", // test data group + ".*", 500000, 150000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*JN.*Integer.*", // test data group + ".*", 50000, 15000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*(JN|j).*|.*Tricky.*", // test data group + ".*", 70000, 7000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*(JN|j).*|.*Tricky.*", // test data group + ".*", 500000, 200000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*(JN|j).*|.*Tricky.*", // test data group + ".*", 7000, 3000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 40, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_bessel(t, p); +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_bessel_k.cpp b/libs/multiprecision/test/math/test_bessel_k.cpp new file mode 100644 index 0000000000..0608326e00 --- /dev/null +++ b/libs/multiprecision/test/math/test_bessel_k.cpp @@ -0,0 +1,95 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_bessel_k.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp.*", // test type(s) + ".*", // test data group + ".*", 2000, 1500); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*float128.*", // test type(s) + ".*", // test data group + ".*", 300, 100); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 3000, 1000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*large.*", // test data group + ".*", 80, 50); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*", // test data group + ".*", 300, 150); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 50, 15); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_bessel(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_bessel_y.cpp b/libs/multiprecision/test/math/test_bessel_y.cpp new file mode 100644 index 0000000000..a5bca85cf1 --- /dev/null +++ b/libs/multiprecision/test/math/test_bessel_y.cpp @@ -0,0 +1,135 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_bessel_y.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*(Y[nv]|y).*Random.*", // test data group + ".*", 200000, 10000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*(Y[nv]|y).*Random.*", // test data group + ".*", 2000000, 1000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*(Y[nv]|y).*Random.*", // test data group + ".*", 70000, 4000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*Y0.*", // test data group + ".*", 3000, 2000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*Y0.*", // test data group + ".*", 40000, 20000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*Y0.*", // test data group + ".*", 800, 400); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*Yn.*", // test data group + ".*", 400000, 70000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*Yn.*", // test data group + ".*", 400000, 200000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*Yn.*", // test data group + ".*", 1700, 600); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 15000, 4000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*", // test data group + ".*", 50000, 20000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 150, 60); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_bessel(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_SMALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_beta.cpp b/libs/multiprecision/test/math/test_beta.cpp new file mode 100644 index 0000000000..88858f3705 --- /dev/null +++ b/libs/multiprecision/test/math/test_beta.cpp @@ -0,0 +1,93 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_beta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp.*", // test type(s) + "Beta Function: Medium.*", // test data group + "boost::math::beta", 2300, 1000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp.*", // test type(s) + "Beta Function: Divergent.*", // test data group + "boost::math::beta", 2200, 1000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + "Beta Function: Small.*", // test data group + "boost::math::beta", 1000, 750); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "Beta Function: Small.*", // test data group + "boost::math::beta", 8, 5); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "Beta Function: Medium.*", // test data group + "boost::math::beta", 1000, 750); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "Beta Function: Divergent.*", // test data group + "boost::math::beta", 1000, 700); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_binomial_coeff.cpp b/libs/multiprecision/test/math/test_binomial_coeff.cpp new file mode 100644 index 0000000000..334ddeff6f --- /dev/null +++ b/libs/multiprecision/test/math/test_binomial_coeff.cpp @@ -0,0 +1,73 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_binomial_coeff.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp.*", // test type(s) + ".*", // test data group + ".*", 3000, 1500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 750, 150); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 100, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_binomial(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + + diff --git a/libs/multiprecision/test/math/test_carlson.cpp b/libs/multiprecision/test/math/test_carlson.cpp new file mode 100644 index 0000000000..58cbee63c6 --- /dev/null +++ b/libs/multiprecision/test/math/test_carlson.cpp @@ -0,0 +1,61 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_carlson.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*RJ.*", // test data group + ".*", 2700, 250); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 40, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_spots(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_cbrt.cpp b/libs/multiprecision/test/math/test_cbrt.cpp new file mode 100644 index 0000000000..c7854b5f01 --- /dev/null +++ b/libs/multiprecision/test/math/test_cbrt.cpp @@ -0,0 +1,54 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_cbrt.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 5, 3); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_cbrt(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + + + diff --git a/libs/multiprecision/test/math/test_digamma.cpp b/libs/multiprecision/test/math/test_digamma.cpp new file mode 100644 index 0000000000..e3a1bd56d4 --- /dev/null +++ b/libs/multiprecision/test/math/test_digamma.cpp @@ -0,0 +1,66 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_digamma.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*Negative.*", // test data group + ".*", 20000, 2000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*Negative.*", // test data group + ".*", 350, 40); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 80, 30); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_digamma(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ellint_1.cpp b/libs/multiprecision/test/math/test_ellint_1.cpp new file mode 100644 index 0000000000..fc158ff371 --- /dev/null +++ b/libs/multiprecision/test/math/test_ellint_1.cpp @@ -0,0 +1,59 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ellint_1.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 1000, 200); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 40, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_spots(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ellint_2.cpp b/libs/multiprecision/test/math/test_ellint_2.cpp new file mode 100644 index 0000000000..775c30f6b2 --- /dev/null +++ b/libs/multiprecision/test/math/test_ellint_2.cpp @@ -0,0 +1,52 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ellint_2.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 300, 200); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_spots(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ellint_3.cpp b/libs/multiprecision/test/math/test_ellint_3.cpp new file mode 100644 index 0000000000..21e12bd544 --- /dev/null +++ b/libs/multiprecision/test/math/test_ellint_3.cpp @@ -0,0 +1,82 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ellint_3.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*", // test data group + ".*", 3000, 500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 10000, 3000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*Large.*", // test data group + ".*", 75, 40); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*float128.*", // test type(s) + ".*", // test data group + ".*", 200, 30); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 60, 30); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_spots(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_erf.cpp b/libs/multiprecision/test/math/test_erf.cpp new file mode 100644 index 0000000000..054ed663f9 --- /dev/null +++ b/libs/multiprecision/test/math/test_erf.cpp @@ -0,0 +1,90 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_erf.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + "Erf Function:.*", // test data group + "boost::math::erfc?", 2200, 1500);// test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + "Inverse Erf.*", // test data group + "boost::math::erfc?_inv", 2200, 1500); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "float128", // test type(s) + "Erf Function:.*", // test data group + "boost::math::erfc?", 15000, 1000); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + "Erf Function:.*", // test data group + "boost::math::erfc?", 3000, 1000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "Erf Function:.*", // test data group + "boost::math::erfc?", 300, 200); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "Inverse Erf.*", // test data group + "boost::math::erfc?_inv", 60, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_erf(t, p); +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_expint.cpp b/libs/multiprecision/test/math/test_expint.cpp new file mode 100644 index 0000000000..c4899648ab --- /dev/null +++ b/libs/multiprecision/test/math/test_expint.cpp @@ -0,0 +1,89 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_expint.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*", // test data group + ".*", 2500, 1500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 1000, 500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float.*", // test type(s) + ".*", // test data group + ".*", 250, 100); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "float128", // test type(s) + ".*", // test data group + ".*", 4500, 1000); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*cpp_bin_float.*", // test type(s) + ".*", // test data group + ".*", 5000, 2000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 250, 50); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_expint(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_gamma.cpp b/libs/multiprecision/test/math/test_gamma.cpp new file mode 100644 index 0000000000..d752f7a2a1 --- /dev/null +++ b/libs/multiprecision/test/math/test_gamma.cpp @@ -0,0 +1,96 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_gamma.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*", // test data group + "boost::math::tgamma", 4000, 2500); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "factorials", // test data group + "boost::math::tgamma", 140, 70); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "factorials", // test data group + "boost::math::lgamma", 750, 100); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "float128", // test type(s) + ".*near -.*", // test data group + ".*", 150000L, 30000L); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "near.*", // test data group + "boost::math::tgamma", 200, 100); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "near.*", // test data group + "boost::math::lgamma", 10000000, 10000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + "tgamma1pm1.*", // test data group + "boost::math::tgamma1pm1", 1000, 150); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_gamma(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_hermite.cpp b/libs/multiprecision/test/math/test_hermite.cpp new file mode 100644 index 0000000000..766642c623 --- /dev/null +++ b/libs/multiprecision/test/math/test_hermite.cpp @@ -0,0 +1,61 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_hermite.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "float128", // test type(s) + ".*", // test data group + "boost::math::hermite", 70, 25); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + "boost::math::hermite", 10, 5); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_hermite(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta.cpp b/libs/multiprecision/test/math/test_ibeta.cpp new file mode 100644 index 0000000000..72badb0fca --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta.cpp @@ -0,0 +1,92 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 1 + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*gmp_float<18>.*", // test type(s) + "(?i).*small.*", // test data group + ".*", 3000, 1000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + "(?i).*small.*", // test data group + ".*", 2000, 500); // test function +#ifdef BOOST_INTEL + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + "float128", // test type(s) + "(?i).*small.*", // test data group + ".*", 500, 100); // test function +#endif + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*small.*", // test data group + ".*", 90, 25); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 150, 50); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*large.*", // test data group + ".*", 5000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta_2.cpp b/libs/multiprecision/test/math/test_ibeta_2.cpp new file mode 100644 index 0000000000..485548b7ed --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta_2.cpp @@ -0,0 +1,91 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 2 + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*gmp_float<18>.*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 4000, 1000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 20000, 1000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*small.*", // test data group + ".*", 90, 25); // test function +#ifdef BOOST_INTEL + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + "float128", // test type(s) + "(?i).*medium.*", // test data group + ".*", 5000, 500); // test function +#endif + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 200, 50); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*large.*", // test data group + ".*", 5000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta_3.cpp b/libs/multiprecision/test/math/test_ibeta_3.cpp new file mode 100644 index 0000000000..4c51aef610 --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta_3.cpp @@ -0,0 +1,68 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 3 + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*small.*", // test data group + ".*", 90, 25); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 200, 50); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*large.*", // test data group + ".*", 6000000, 500000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta_4.cpp b/libs/multiprecision/test/math/test_ibeta_4.cpp new file mode 100644 index 0000000000..f9064a5b80 --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta_4.cpp @@ -0,0 +1,76 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 4 + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*small.*", // test data group + ".*", 4000, 1000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*small.*", // test data group + ".*", 90, 25); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*medium.*", // test data group + ".*", 200, 50); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + ".*", // test type(s) + "(?i).*large.*", // test data group + ".*", 5000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta_inv_1.cpp b/libs/multiprecision/test/math/test_ibeta_inv_1.cpp new file mode 100644 index 0000000000..160fff5c38 --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta_inv_1.cpp @@ -0,0 +1,61 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 4 + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta_inv.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 50000000, 7000000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 1000000, 100000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_SMALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_ibeta_inv_ab_4.cpp b/libs/multiprecision/test/math/test_ibeta_inv_ab_4.cpp new file mode 100644 index 0000000000..ed83082dd8 --- /dev/null +++ b/libs/multiprecision/test/math/test_ibeta_inv_ab_4.cpp @@ -0,0 +1,55 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#define TEST_DATA 4 +#define FULL_TEST + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_ibeta_inv_ab.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 10000, 1000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_beta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_igamma.cpp b/libs/multiprecision/test/math/test_igamma.cpp new file mode 100644 index 0000000000..75982d5083 --- /dev/null +++ b/libs/multiprecision/test/math/test_igamma.cpp @@ -0,0 +1,58 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_igamma.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*large.*", // test data group + ".*", 20000000L, 1000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 7000, 2000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_gamma(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_igamma_inv.cpp b/libs/multiprecision/test/math/test_igamma_inv.cpp new file mode 100644 index 0000000000..b245305ee8 --- /dev/null +++ b/libs/multiprecision/test/math/test_igamma_inv.cpp @@ -0,0 +1,73 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_igamma_inv.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*small.*", // test data group + ".*", 2000000000L, 300000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*small.*", // test data group + ".*", 30000000L, 20000000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*small.*", // test data group + ".*", 10000000L, 2500000L); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 7000, 2000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_gamma(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_igamma_inva.cpp b/libs/multiprecision/test/math/test_igamma_inva.cpp new file mode 100644 index 0000000000..42eeb946c5 --- /dev/null +++ b/libs/multiprecision/test/math/test_igamma_inva.cpp @@ -0,0 +1,52 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_igamma_inva.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 7000, 2000); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_gamma(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_laguerre.cpp b/libs/multiprecision/test/math/test_laguerre.cpp new file mode 100644 index 0000000000..83b84174c7 --- /dev/null +++ b/libs/multiprecision/test/math/test_laguerre.cpp @@ -0,0 +1,52 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_laguerre.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 7000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_laguerre(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_legendre.cpp b/libs/multiprecision/test/math/test_legendre.cpp new file mode 100644 index 0000000000..787a192b12 --- /dev/null +++ b/libs/multiprecision/test/math/test_legendre.cpp @@ -0,0 +1,52 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_legendre.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 6000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_legendre_p(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_tgamma_ratio.cpp b/libs/multiprecision/test/math/test_tgamma_ratio.cpp new file mode 100644 index 0000000000..1ef7641e61 --- /dev/null +++ b/libs/multiprecision/test/math/test_tgamma_ratio.cpp @@ -0,0 +1,66 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_tgamma_ratio.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*gmp_float<18>.*", // test type(s) + ".*", // test data group + ".*", 4000, 2000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*mpfr_float_backend<18>.*", // test type(s) + ".*", // test data group + ".*", 20000, 7000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 2000, 500); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_tgamma_ratio(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/math/test_zeta.cpp b/libs/multiprecision/test/math/test_zeta.cpp new file mode 100644 index 0000000000..b9ae5f6c9c --- /dev/null +++ b/libs/multiprecision/test/math/test_zeta.cpp @@ -0,0 +1,69 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include "setup.hpp" +#include "table_type.hpp" +#define TEST_UDT + +#include <boost/math/special_functions/math_fwd.hpp> +#include "libs/math/test/test_zeta.hpp" + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*Random values less than 1", // test data group + ".*", 6000, 3000); // test function +#ifdef BOOST_INTEL + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "float128", // test type(s) + ".*close to and less than 1.*", // test data group + ".*", 10000000L, 2000000L); // test function +#endif + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + ".*", // test type(s) + ".*", // test data group + ".*", 1000, 200); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + +template <class T> +void test(T t, const char* p) +{ + test_zeta(t, p); +} + +BOOST_AUTO_TEST_CASE( test_main ) +{ + using namespace boost::multiprecision; + expected_results(); + // + // Test at: + // 9 decimal digits: tests the least wide arbitrary precision code + // 18 decimal digits: tests 80-bit long double approximations + // 30 decimal digits: tests 128-bit long double approximations + // 35 decimal digits: tests arbitrary precision code + // + ALL_TESTS +} + diff --git a/libs/multiprecision/test/sincos.ipp b/libs/multiprecision/test/sincos.ipp new file mode 100644 index 0000000000..2273549d11 --- /dev/null +++ b/libs/multiprecision/test/sincos.ipp @@ -0,0 +1,358 @@ +#ifndef SC_ +# define SC_(x) static_cast<T>(BOOST_STRINGIZE(x)) +#endif + static const boost::array<boost::array<T, 3>, 351> sincos = {{ + { SC_(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), 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SC_(8.13845084031492640613386104575625537797314524719600723400961398682265346258342553800702435865044529994514493269349360241716452021150170976184564475930349320327294213744778471680231255567737036617811154621323506663548592662785646800499829866106486293702489790533055529549635178889628268927391706714202367178496631902276183977618547547514283224465880040875138298723442763757980830113435205370560834162520016704500157651115626101042762031082967251945734212875798186029500136459910061696644610683824984172e-02) }, + { 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SC_(7.96093014102787857311853897169714896003178997833084509746261920212282904923245728708338229611953838785802609515963050682205601178649541846223606669995712553087046533525243208438038611435636700879519384389078441175165514979582616566905525683674375742838422423588917802839236707296641241280017877960271241566981191179744385341858916524101345194801390243168621344421220012275921118083354308199733352187061121123492182523906644632947523518443805234926530481306985017526225224799204564632165926385889633624e-02) }, + { SC_(1.49469184875488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.97105451691637836980566977886191495470310625478984302514468734081978317004712365179572388160094873766545892259684126612171730371334431713402903857531243843855031719141960805464286066705907297221591074259625271788178601626673326754719816154765918422856170761025895221537060495081964634143881365727528637573199554544101393148199185537988251924073321046398397270592899501388280072694753480150196648362062195285790390273399747995245778399713979670854796624214784952767383795902013605892666997263955330095e-01), SC_(7.60310344978606994311454252807960986535803469428379193529425796476644344334413001865738243975566508261589698713562091901145249736705485695273728137391377751615494502695150924195446763383201607951069471691560757133118887684442353070862022248337360915742210326532477359739395822627983312298986859616214217003217070111399151039551118513567199164797534425187953687276545896053419230138261452230491054544837629498576689887971671483487696900902095055042924520918068327882892863731988941436799798706418513466e-02) } + }}; +//#undef SC_ + diff --git a/libs/multiprecision/test/string_data.ipp b/libs/multiprecision/test/string_data.ipp new file mode 100644 index 0000000000..2676149a42 --- /dev/null +++ b/libs/multiprecision/test/string_data.ipp @@ -0,0 +1,45 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + + {{ "1e+08", "1.e+08", "+1e+08", "1.2e+08", "+1.2e+08", "1.2e+08", "123456789.0", "123456789.0", "+123456789.0", "1.2e+08", "1.2e+08", "+1.2e+08", "1.23e+08", "+1.23e+08", "1.23e+08", "123456789.00", "123456789.00", "+123456789.00", "1.23e+08", "1.23e+08", "+1.23e+08", "1.235e+08", "+1.235e+08", "1.235e+08", "123456789.000", "123456789.000", "+123456789.000", "1.235e+08", "1.235e+08", "+1.235e+08", "1.2346e+08", "+1.2346e+08", "1.2346e+08", "123456789.0000", "123456789.0000", "+123456789.0000", "1.2346e+08", "1.2346e+08", "+1.2346e+08", "1.23457e+08", "+1.23457e+08", "1.23457e+08", "123456789.00000", "123456789.00000", "+123456789.00000", "1.23457e+08", "1.23457e+08", "+1.23457e+08", "1.234568e+08", "+1.234568e+08", "1.234568e+08", "123456789.000000", "123456789.000000", "+123456789.000000", "1.234568e+08", "1.234568e+08", "+1.234568e+08", "1.2345679e+08", "+1.2345679e+08", "1.2345679e+08", 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+/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifndef BOOST_MULTIPRECISION_TEST_HPP +#define BOOST_MULTIPRECISION_TEST_HPP + +#include <limits> +#include <cmath> +#include <typeinfo> + +#include <boost/detail/lightweight_test.hpp> +#include <boost/current_function.hpp> +#include <boost/static_assert.hpp> +#include <boost/utility/enable_if.hpp> +#include <boost/type_traits/is_unsigned.hpp> +#include <boost/multiprecision/number.hpp> + +namespace detail{ + +template <class T> +inline typename boost::disable_if_c<boost::is_unsigned<T>::value || boost::multiprecision::is_unsigned_number<T>::value, T>::type + abs(const T& a) +{ + return a < 0 ? -a : a; +} + +template <class T> +inline typename boost::enable_if_c<boost::is_unsigned<T>::value || boost::multiprecision::is_unsigned_number<T>::value, T>::type + abs(const T& a) +{ + return a; +} + +} + +template <class T> +typename boost::enable_if_c<boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_integer, T>::type relative_error(T a, T b) +{ + return a > b ? a - b : b - a; +} + +template <class T> +typename boost::disable_if_c<(boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_integer) || boost::multiprecision::is_interval_number<T>::value, T>::type relative_error(T a, T b) +{ + using std::abs; + using detail::abs; + + T min_val = (std::numeric_limits<T>::min)(); + T max_val = (std::numeric_limits<T>::max)(); + + if((a != 0) && (b != 0)) + { + if(a == b) + return 0; + + // TODO: use isfinite: + if(abs(b) >= max_val) + { + if(abs(a) >= max_val) + return 0; // one infinity is as good as another! + } + // If the result is denormalised, treat all denorms as equivalent: + if((a < min_val) && (a > 0)) + a = min_val; + else if((a > -min_val) && (a < 0)) + a = -min_val; + if((b < min_val) && (b > 0)) + b = min_val; + else if((b > -min_val) && (b < 0)) + b = -min_val; + + return (std::max)(abs(T((a-b)/a)), abs(T((a-b)/b))) / std::numeric_limits<T>::epsilon(); + } + + // Handle special case where one or both are zero: + if(min_val == 0) + return abs(T(a-b)); + if(abs(a) < min_val) + a = min_val; + if(abs(b) < min_val) + b = min_val; + + return (std::max)(abs(T((a-b)/a)), abs(T((a-b)/b))) / std::numeric_limits<T>::epsilon(); +} + +template <class T, class U> +typename boost::mpl::if_c<boost::is_convertible<T, U>::value, U, T>::type + relative_error(T a, U b) +{ + typedef typename boost::mpl::if_c<boost::is_convertible<T, U>::value, U, T>::type cast_type; + return relative_error<cast_type>(static_cast<cast_type>(a), static_cast<cast_type>(b)); +} + +template <class T> +typename boost::enable_if_c<boost::multiprecision::is_interval_number<T>::value, T>::type relative_error(T a, T b) +{ + typename boost::multiprecision::component_type<T>::type am = median(a); + typename boost::multiprecision::component_type<T>::type bm = median(b); + return relative_error<typename boost::multiprecision::component_type<T>::type>(am, bm); +} + + +enum +{ + warn_on_fail, + error_on_fail, + abort_on_fail +}; + +template <class T> +inline T epsilon_of(const T&) +{ + BOOST_STATIC_ASSERT(std::numeric_limits<T>::is_specialized); + return std::numeric_limits<T>::is_integer ? 1 : std::numeric_limits<T>::epsilon(); +} + +template <class T> +inline int digits_of(const T&) +{ + return std::numeric_limits<T>::is_specialized ? std::numeric_limits<T>::digits10 + 2 : std::numeric_limits<long double>::digits10 + 2; +} + +inline std::ostream& report_where(const char* file, int line, const char* function) +{ + if(function) + BOOST_LIGHTWEIGHT_TEST_OSTREAM << "In function: "<< function << std::endl; + BOOST_LIGHTWEIGHT_TEST_OSTREAM << file << ":" << line; + return BOOST_LIGHTWEIGHT_TEST_OSTREAM; +} + +#define BOOST_MP_REPORT_WHERE report_where(__FILE__, __LINE__, BOOST_CURRENT_FUNCTION) + +inline void report_severity(int severity) +{ + if(severity == error_on_fail) + ++boost::detail::test_errors(); + else if(severity == abort_on_fail) + { + ++boost::detail::test_errors(); + abort(); + } +} + +#define BOOST_MP_REPORT_SEVERITY(severity) report_severity(severity) + +template <class E> +void report_unexpected_exception(const E& e, int severity, const char* file, int line, const char* function) +{ + report_where(file, line, function) << " Unexpected exception of type " << typeid(e).name() << std::endl; + BOOST_LIGHTWEIGHT_TEST_OSTREAM << "Errot message was: " << e.what() << std::endl; + BOOST_MP_REPORT_SEVERITY(severity); +} + +#define BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) \ + catch(const std::exception& e) \ + { report_unexpected_exception(e, severity, __FILE__, __LINE__, BOOST_CURRENT_FUNCTION); }\ + catch(...)\ + { std::cout << "Exception of unknown type was thrown" << std::endl; report_severity(severity); } + + +#define BOOST_CHECK_IMP(x, severity)\ + try{ if(x){}else{\ + BOOST_MP_REPORT_WHERE << " Failed predicate: " << BOOST_STRINGIZE(x) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_CHECK(x) BOOST_CHECK_IMP(x, error_on_fail) +#define BOOST_WARN(x) BOOST_CHECK_IMP(x, warn_on_fail) +#define BOOST_REQUIRE(x) BOOST_CHECK_IMP(x, abort_on_fail) + +#define BOOST_CLOSE_IMP(x, y, tol, severity)\ + try{ if(relative_error(x, y) > tol){\ + BOOST_MP_REPORT_WHERE << " Failed check for closeness: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(5) << std::fixed\ + << "Relative error was: " << relative_error(x, y) << "eps\n"\ + << "Tolerance was: " << tol << "eps" << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_EQUAL_IMP(x, y, severity)\ + try{ if(!((x) == (y))){\ + BOOST_MP_REPORT_WHERE << " Failed check for equality: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << (x) << "\n"\ + << "Value of RHS was: " << (y) << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_NE_IMP(x, y, severity)\ + try{ if(!(x != y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for non-equality: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_LT_IMP(x, y, severity)\ + try{ if(!(x < y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for less than: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_GT_IMP(x, y, severity)\ + try{ if(!(x > y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for greater than: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_LE_IMP(x, y, severity)\ + try{ if(!(x <= y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for less-than-equal-to: \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_GE_IMP(x, y, severity)\ + try{ if(!(x >= y)){\ + BOOST_MP_REPORT_WHERE << " Failed check for greater-than-equal-to \n" \ + << std::setprecision(digits_of(x)) << std::scientific\ + << "Value of LHS was: " << x << "\n"\ + << "Value of RHS was: " << y << "\n"\ + << std::setprecision(3) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + }BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_MT_CHECK_THROW_IMP(x, E, severity)\ + try{ \ + x;\ + BOOST_MP_REPORT_WHERE << " Expected exception not thrown in expression " << BOOST_STRINGIZE(x) << std::endl;\ + BOOST_MP_REPORT_SEVERITY(severity);\ + }\ + catch(const E&){}\ + BOOST_MP_UNEXPECTED_EXCEPTION_CHECK(severity) + +#define BOOST_CHECK_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, ((tol / (100 * epsilon_of(x)))), error_on_fail) +#define BOOST_WARN_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (100 * epsilon_of(x))), warn_on_fail) +#define BOOST_REQUIRE_CLOSE(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (100 * epsilon_of(x))), abort_on_fail) + +#define BOOST_CHECK_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, ((tol / (epsilon_of(x)))), error_on_fail) +#define BOOST_WARN_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (epsilon_of(x))), warn_on_fail) +#define BOOST_REQUIRE_CLOSE_FRACTION(x, y, tol) BOOST_CLOSE_IMP(x, y, (tol / (epsilon_of(x))), abort_on_fail) + +#define BOOST_CHECK_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, error_on_fail) +#define BOOST_WARN_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_EQUAL(x, y) BOOST_EQUAL_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_NE(x, y) BOOST_NE_IMP(x, y, error_on_fail) +#define BOOST_WARN_NE(x, y) BOOST_NE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_NE(x, y) BOOST_NE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_LT(x, y) BOOST_LT_IMP(x, y, error_on_fail) +#define BOOST_WARN_LT(x, y) BOOST_LT_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_LT(x, y) BOOST_LT_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_GT(x, y) BOOST_GT_IMP(x, y, error_on_fail) +#define BOOST_WARN_GT(x, y) BOOST_GT_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_GT(x, y) BOOST_GT_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_LE(x, y) BOOST_LE_IMP(x, y, error_on_fail) +#define BOOST_WARN_LE(x, y) BOOST_LE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_LE(x, y) BOOST_LE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_GE(x, y) BOOST_GE_IMP(x, y, error_on_fail) +#define BOOST_WARN_GE(x, y) BOOST_GE_IMP(x, y, warn_on_fail) +#define BOOST_REQUIRE_GE(x, y) BOOST_GE_IMP(x, y, abort_on_fail) + +#define BOOST_CHECK_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, error_on_fail) +#define BOOST_WARN_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, warn_on_fail) +#define BOOST_REQUIRE_THROW(x, E) BOOST_MT_CHECK_THROW_IMP(x, E, abort_on_fail) + +#endif diff --git a/libs/multiprecision/test/test_acos.cpp b/libs/multiprecision/test/test_acos.cpp new file mode 100644 index 0000000000..2881121264 --- /dev/null +++ b/libs/multiprecision/test/test_acos.cpp @@ -0,0 +1,148 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array<boost::array<T, 2>, 13> exact_data = + {{ + {{ 0.5, static_cast<T>("1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550442743555") }}, + {{ 0.25, static_cast<T>("1.31811607165281796574566425464604046984639096659071471685354851741333314266208327690226867044304393238598144034722708676") }}, + {{0.75, static_cast<T>("0.722734247813415611178377352641333362025218486424440267626754132583707381914630264964827610939101303690078815991333621490") }}, + {{1 - std::ldexp(1.0, -20), static_cast<T>("0.00138106804176241718210883847756746694048570648553426714212025111150044290934710742282266738617709904634187850607042604204") }}, + {{std::ldexp(1.0, -20), static_cast<T>("1.57079537312058021283676140197495835299636605165647561806789944133748780804448843729970624018104090863783682329820313127") }}, + {{1, static_cast<T>("0") }}, + + {{0, static_cast<T>("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332") }}, + + {{ -0.5, static_cast<T>("2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539100885487110") }}, + {{ -0.25, static_cast<T>("1.82347658193697527271697912863346241435077843278439110412139607489448326362412572172576615489907313559616664616605521989") }}, + {{-0.75, static_cast<T>("2.41885840577637762728426603063816952217195091295066555334819045972410902437157873366320721440301576429206927052194868516") }}, + {{-1 + std::ldexp(1.0, -20), static_cast<T>("3.14021158554803082128053454480193541725668369288957155383282434119631596337686189120521215795593996893580620800721188061") }}, + {{-std::ldexp(1.0, -20), static_cast<T>("1.57079728046921302562588198130454453120080334771863020290704515097032859824172056132832858516107615934431126321507917538") }}, + {{-1, static_cast<T>("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665") }}, + }}; + unsigned max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = acos(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; +#ifdef TEST_CPP_BIN_FLOAT + BOOST_TEST(max_err < 120); +#else + BOOST_TEST(max_err < 60); +#endif + BOOST_TEST(asin(T(0)) == 0); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_adapt_serial.cpp b/libs/multiprecision/test/test_adapt_serial.cpp new file mode 100644 index 0000000000..33c04a3d0d --- /dev/null +++ b/libs/multiprecision/test/test_adapt_serial.cpp @@ -0,0 +1,163 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/logged_adaptor.hpp> +#include <boost/multiprecision/debug_adaptor.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/timer.hpp> +#include "test.hpp" + +#include <iostream> +#include <iomanip> +#include <sstream> +#include <boost/archive/text_iarchive.hpp> +#include <boost/archive/text_oarchive.hpp> +#include <boost/archive/binary_iarchive.hpp> +#include <boost/archive/binary_oarchive.hpp> +#include <boost/exception/all.hpp> + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +template <class T> +void test_neg(const T& x, const boost::mpl::true_&) +{ + T val = -x; + try + { + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } +} +template <class T> +void test_neg(const T& , const boost::mpl::false_&){} + +template <class T> +void test() +{ + using namespace boost::multiprecision; + + boost::random::mt19937 gen; + boost::uniform_int<> d(3, std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits : 3000); + boost::timer tim; + + while(true) + { + T val = generate_random<T>(d(gen)); + try + { + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + + test_neg(val, boost::mpl::bool_<std::numeric_limits<T>::is_signed>()); + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 30) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + } +} + +int main() +{ + using namespace boost::multiprecision; + test<number<logged_adaptor<cpp_int_backend<> > > >(); + test<number<debug_adaptor<cpp_int_backend<> > > >(); + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_arithmetic.hpp b/libs/multiprecision/test/test_arithmetic.hpp new file mode 100644 index 0000000000..d787f938db --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic.hpp @@ -0,0 +1,1844 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef TEST_VLD +#include <vld.h> +#endif + +#include <boost/math/special_functions/pow.hpp> +#include <boost/math/common_factor_rt.hpp> +#include "test.hpp" + +template <class T> +struct is_boost_rational : public boost::mpl::false_{}; + +#ifdef BOOST_MSVC +// warning C4127: conditional expression is constant +#pragma warning(disable:4127) +#endif + +template <class Target, class Source> +Target checked_lexical_cast(const Source& val) +{ + try + { + return boost::lexical_cast<Target>(val); + } + catch(...) + { + std::cerr << "Error in lexical cast\nSource type = " << typeid(Source).name() << " \"" << val << "\"\n"; + std::cerr << "Target type = " << typeid(Target).name() << std::endl; + throw; + } +} + + +bool isfloat(float){ return true; } +bool isfloat(double){ return true; } +bool isfloat(long double){ return true; } +template <class T> bool isfloat(T){ return false; } + +namespace detail{ + +template<class tag, class Arg1, class Arg2, class Arg3, class Arg4> +typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type + abs(boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4> const& v) +{ + typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type result_type; + return v < 0 ? result_type(-v) : result_type(v); +} + +} + +template <class T> +struct is_twos_complement_integer : public boost::mpl::true_ {}; + +template <class T> +struct related_type +{ + typedef T type; +}; + +template <class Real, class Val> +void test_comparisons(Val, Val, const boost::mpl::false_) +{} + +int normalize_compare_result(int r) +{ + return r > 0 ? 1 : r < 0 ? -1 : 0; +} + +template <class Real, class Val> +void test_comparisons(Val a, Val b, const boost::mpl::true_) +{ + Real r1(a); + Real r2(b); + Real z(1); + + int cr = a < b ? -1 : a > b ? 1 : 0; + + BOOST_CHECK_EQUAL(r1 == r2, a == b); + BOOST_CHECK_EQUAL(r1 != r2, a != b); + BOOST_CHECK_EQUAL(r1 <= r2, a <= b); + BOOST_CHECK_EQUAL(r1 < r2, a < b); + BOOST_CHECK_EQUAL(r1 >= r2, a >= b); + BOOST_CHECK_EQUAL(r1 > r2, a > b); + + BOOST_CHECK_EQUAL(r1 == b, a == b); + BOOST_CHECK_EQUAL(r1 != b, a != b); + BOOST_CHECK_EQUAL(r1 <= b, a <= b); + BOOST_CHECK_EQUAL(r1 < b, a < b); + BOOST_CHECK_EQUAL(r1 >= b, a >= b); + BOOST_CHECK_EQUAL(r1 > b, a > b); + + BOOST_CHECK_EQUAL(a == r2, a == b); + BOOST_CHECK_EQUAL(a != r2, a != b); + BOOST_CHECK_EQUAL(a <= r2, a <= b); + BOOST_CHECK_EQUAL(a < r2, a < b); + BOOST_CHECK_EQUAL(a >= r2, a >= b); + BOOST_CHECK_EQUAL(a > r2, a > b); + + BOOST_CHECK_EQUAL(r1*z == r2, a == b); + BOOST_CHECK_EQUAL(r1*z != r2, a != b); + BOOST_CHECK_EQUAL(r1*z <= r2, a <= b); + BOOST_CHECK_EQUAL(r1*z < r2, a < b); + BOOST_CHECK_EQUAL(r1*z >= r2, a >= b); + BOOST_CHECK_EQUAL(r1*z > r2, a > b); + + BOOST_CHECK_EQUAL(r1 == r2*z, a == b); + BOOST_CHECK_EQUAL(r1 != r2*z, a != b); + BOOST_CHECK_EQUAL(r1 <= r2*z, a <= b); + BOOST_CHECK_EQUAL(r1 < r2*z, a < b); + BOOST_CHECK_EQUAL(r1 >= r2*z, a >= b); + BOOST_CHECK_EQUAL(r1 > r2*z, a > b); + + BOOST_CHECK_EQUAL(r1*z == r2*z, a == b); + BOOST_CHECK_EQUAL(r1*z != r2*z, a != b); + BOOST_CHECK_EQUAL(r1*z <= r2*z, a <= b); + BOOST_CHECK_EQUAL(r1*z < r2*z, a < b); + BOOST_CHECK_EQUAL(r1*z >= r2*z, a >= b); + BOOST_CHECK_EQUAL(r1*z > r2*z, a > b); + + BOOST_CHECK_EQUAL(r1*z == b, a == b); + BOOST_CHECK_EQUAL(r1*z != b, a != b); + BOOST_CHECK_EQUAL(r1*z <= b, a <= b); + BOOST_CHECK_EQUAL(r1*z < b, a < b); + BOOST_CHECK_EQUAL(r1*z >= b, a >= b); + BOOST_CHECK_EQUAL(r1*z > b, a > b); + + BOOST_CHECK_EQUAL(a == r2*z, a == b); + BOOST_CHECK_EQUAL(a != r2*z, a != b); + BOOST_CHECK_EQUAL(a <= r2*z, a <= b); + BOOST_CHECK_EQUAL(a < r2*z, a < b); + BOOST_CHECK_EQUAL(a >= r2*z, a >= b); + BOOST_CHECK_EQUAL(a > r2*z, a > b); + + BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), cr); + BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), -cr); + BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), cr); + BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), -cr); +} + +template <class Real, class Exp> +void test_conditional(Real v, Exp e) +{ + // + // Verify that Exp is usable in Boolean contexts, and has the same value as v: + // + if(e) + { + BOOST_CHECK(v); + } + else + { + BOOST_CHECK(!v); + } + if(!e) + { + BOOST_CHECK(!v); + } + else + { + BOOST_CHECK(v); + } +} + +template <class Real> +void test_complement(Real a, Real b, Real c, const boost::mpl::true_&) +{ + int i = 1020304; + int j = 56789123; + int sign_mask = ~0; + if(std::numeric_limits<Real>::is_signed) + { + BOOST_CHECK_EQUAL(~a , (~i & sign_mask)); + c = a & ~b; + BOOST_CHECK_EQUAL(c , (i & (~j & sign_mask))); + c = ~(a | b); + BOOST_CHECK_EQUAL(c , (~(i | j) & sign_mask)); + } + else + { + BOOST_CHECK_EQUAL((~a & a) , 0); + } +} + +template <class Real> +void test_complement(Real, Real, Real, const boost::mpl::false_&) +{ +} + +template <class Real, class T> +void test_integer_ops(const T&){} + +template <class Real> +void test_rational(const boost::mpl::true_&) +{ + Real a(2); + a /= 3; + BOOST_CHECK_EQUAL(numerator(a) , 2); + BOOST_CHECK_EQUAL(denominator(a) , 3); + Real b(4); + b /= 6; + BOOST_CHECK_EQUAL(a , b); + + // + // Check IO code: + // + std::stringstream ss; + ss << a; + ss >> b; + BOOST_CHECK_EQUAL(a, b); +} + +template <class Real> +void test_rational(const boost::mpl::false_&) +{ + Real a(2); + a /= 3; + BOOST_CHECK_EQUAL(numerator(a) , 2); + BOOST_CHECK_EQUAL(denominator(a) , 3); + Real b(4); + b /= 6; + BOOST_CHECK_EQUAL(a , b); + + BOOST_CHECK_THROW(Real(a / 0), std::overflow_error); + BOOST_CHECK_THROW(Real("3.14"), std::runtime_error); + b = Real("2/3"); + BOOST_CHECK_EQUAL(a, b); + // + // Check IO code: + // + std::stringstream ss; + ss << a; + ss >> b; + BOOST_CHECK_EQUAL(a, b); +} + +template <class Real> +void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&) +{ + test_rational<Real>(is_boost_rational<Real>()); +} + +template <class Real> +void test_signed_integer_ops(const boost::mpl::true_&) +{ + Real a(20); + Real b(7); + Real c(5); + BOOST_CHECK_EQUAL(-a % c , 0); + BOOST_CHECK_EQUAL(-a % b , -20 % 7); + BOOST_CHECK_EQUAL(-a % -b , -20 % -7); + BOOST_CHECK_EQUAL(a % -b , 20 % -7); + BOOST_CHECK_EQUAL(-a % 7 , -20 % 7); + BOOST_CHECK_EQUAL(-a % -7 , -20 % -7); + BOOST_CHECK_EQUAL(a % -7 , 20 % -7); + BOOST_CHECK_EQUAL(-a % 7u , -20 % 7); + BOOST_CHECK_EQUAL(-a % a , 0); + BOOST_CHECK_EQUAL(-a % 5 , 0); + BOOST_CHECK_EQUAL(-a % -5 , 0); + BOOST_CHECK_EQUAL(a % -5 , 0); + + b = -b; + BOOST_CHECK_EQUAL(a % b , 20 % -7); + a = -a; + BOOST_CHECK_EQUAL(a % b , -20 % -7); + BOOST_CHECK_EQUAL(a % -7 , -20 % -7); + b = 7; + BOOST_CHECK_EQUAL(a % b , -20 % 7); + BOOST_CHECK_EQUAL(a % 7 , -20 % 7); + BOOST_CHECK_EQUAL(a % 7u , -20 % 7); + + a = 20; + a %= b; + BOOST_CHECK_EQUAL(a , 20 % 7); + a = -20; + a %= b; + BOOST_CHECK_EQUAL(a , -20 % 7); + a = 20; + a %= -b; + BOOST_CHECK_EQUAL(a , 20 % -7); + a = -20; + a %= -b; + BOOST_CHECK_EQUAL(a , -20 % -7); + a = 5; + a %= b - a; + BOOST_CHECK_EQUAL(a , 5 % (7-5)); + a = -20; + a %= 7; + BOOST_CHECK_EQUAL(a , -20 % 7); + a = 20; + a %= -7; + BOOST_CHECK_EQUAL(a , 20 % -7); + a = -20; + a %= -7; + BOOST_CHECK_EQUAL(a , -20 % -7); +#ifndef BOOST_NO_LONG_LONG + a = -20; + a %= 7uLL; + BOOST_CHECK_EQUAL(a , -20 % 7); + a = 20; + a %= -7LL; + BOOST_CHECK_EQUAL(a , 20 % -7); + a = -20; + a %= -7LL; + BOOST_CHECK_EQUAL(a , -20 % -7); +#endif + a = 400; + b = 45; + BOOST_CHECK_EQUAL(gcd(a, -45) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(a, -45) , boost::math::lcm(400, 45)); + BOOST_CHECK_EQUAL(gcd(-400, b) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(-400, b) , boost::math::lcm(400, 45)); + a = -20; + BOOST_CHECK_EQUAL(abs(a) , 20); + BOOST_CHECK_EQUAL(abs(-a) , 20); + BOOST_CHECK_EQUAL(abs(+a) , 20); + a = 20; + BOOST_CHECK_EQUAL(abs(a) , 20); + BOOST_CHECK_EQUAL(abs(-a) , 20); + BOOST_CHECK_EQUAL(abs(+a) , 20); + a = -400; + b = 45; + BOOST_CHECK_EQUAL(gcd(a, b) , boost::math::gcd(-400, 45)); + BOOST_CHECK_EQUAL(lcm(a, b) , boost::math::lcm(-400, 45)); + BOOST_CHECK_EQUAL(gcd(a, 45) , boost::math::gcd(-400, 45)); + BOOST_CHECK_EQUAL(lcm(a, 45) , boost::math::lcm(-400, 45)); + BOOST_CHECK_EQUAL(gcd(-400, b) , boost::math::gcd(-400, 45)); + BOOST_CHECK_EQUAL(lcm(-400, b) , boost::math::lcm(-400, 45)); + Real r; + divide_qr(a, b, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + BOOST_CHECK_EQUAL(integer_modulus(a, 57) , abs(a % 57)); + b = -57; + divide_qr(a, b, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + BOOST_CHECK_EQUAL(integer_modulus(a, -57) , abs(a % -57)); + a = 458; + divide_qr(a, b, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + BOOST_CHECK_EQUAL(integer_modulus(a, -57) , abs(a % -57)); +} +template <class Real> +void test_signed_integer_ops(const boost::mpl::false_&) +{ +} + +template <class Real> +void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&) +{ + test_signed_integer_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>()); + + Real a(20); + Real b(7); + Real c(5); + BOOST_CHECK_EQUAL(a % b , 20 % 7); + BOOST_CHECK_EQUAL(a % 7 , 20 % 7); + BOOST_CHECK_EQUAL(a % 7u , 20 % 7); + BOOST_CHECK_EQUAL(a % a , 0); + BOOST_CHECK_EQUAL(a % c , 0); + BOOST_CHECK_EQUAL(a % 5 , 0); + a = a % (b + 0); + BOOST_CHECK_EQUAL(a , 20 % 7); + a = 20; + c = (a + 2) % (a - 1); + BOOST_CHECK_EQUAL(c , 22 % 19); + c = 5; + a = b % (a - 15); + BOOST_CHECK_EQUAL(a , 7 % 5); + a = 20; + + a = 20; + a %= 7; + BOOST_CHECK_EQUAL(a , 20 % 7); +#ifndef BOOST_NO_LONG_LONG + a = 20; + a %= 7uLL; + BOOST_CHECK_EQUAL(a , 20 % 7); +#endif + a = 20; + BOOST_CHECK_EQUAL(++a , 21); + BOOST_CHECK_EQUAL(--a , 20); + BOOST_CHECK_EQUAL(a++ , 20); + BOOST_CHECK_EQUAL(a , 21); + BOOST_CHECK_EQUAL(a-- , 21); + BOOST_CHECK_EQUAL(a , 20); + a = 2000; + a <<= 20; + BOOST_CHECK_EQUAL(a , 2000L << 20); + a >>= 20; + BOOST_CHECK_EQUAL(a , 2000); + a <<= 20u; + BOOST_CHECK_EQUAL(a , 2000L << 20); + a >>= 20u; + BOOST_CHECK_EQUAL(a , 2000); + BOOST_CHECK_THROW(a <<= -20, std::out_of_range); + BOOST_CHECK_THROW(a >>= -20, std::out_of_range); + BOOST_CHECK_THROW(Real(a << -20), std::out_of_range); + BOOST_CHECK_THROW(Real(a >> -20), std::out_of_range); +#ifndef BOOST_NO_LONG_LONG + if(sizeof(long long) > sizeof(std::size_t)) + { + // extreme values should trigger an exception: + BOOST_CHECK_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_CHECK_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_CHECK_THROW(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_CHECK_THROW(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_CHECK_THROW(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + BOOST_CHECK_THROW(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range); + // Unless they fit within range: + a = 2000L; + BOOST_CHECK_EQUAL((a <<= 20uLL) , (2000L << 20)); + a = 2000; + BOOST_CHECK_EQUAL((a <<= 20LL) , (2000L << 20)); + + BOOST_CHECK_THROW(Real(a >> (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_CHECK_THROW(Real(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_CHECK_THROW(Real(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_CHECK_THROW(Real(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_CHECK_THROW(Real(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + BOOST_CHECK_THROW(Real(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range); + // Unless they fit within range: + a = 2000L; + BOOST_CHECK_EQUAL(Real(a << 20uLL) , (2000L << 20)); + a = 2000; + BOOST_CHECK_EQUAL(Real(a << 20LL) , (2000L << 20)); + } +#endif + a = 20; + b = a << 20; + BOOST_CHECK_EQUAL(b , (20 << 20)); + b = a >> 2; + BOOST_CHECK_EQUAL(b , (20 >> 2)); + b = (a + 2) << 10; + BOOST_CHECK_EQUAL(b , (22 << 10)); + b = (a + 3) >> 3; + BOOST_CHECK_EQUAL(b , (23 >> 3)); + // + // Bit fiddling: + // + int i = 1020304; + int j = 56789123; + int k = 4523187; + a = i; + b = j; + c = a; + c &= b; + BOOST_CHECK_EQUAL(c , (i & j)); + c = a; + c &= j; + BOOST_CHECK_EQUAL(c , (i & j)); + c = a; + c &= a + b; + BOOST_CHECK_EQUAL(c , (i & (i + j))); + BOOST_CHECK_EQUAL((a & b) , (i & j)); + c = k; + a = a & (b + k); + BOOST_CHECK_EQUAL(a , (i & (j + k))); + a = i; + a = (b + k) & a; + BOOST_CHECK_EQUAL(a , (i & (j + k))); + a = i; + c = a & b & k; + BOOST_CHECK_EQUAL(c , (i&j&k)); + c = a; + c &= (c+b); + BOOST_CHECK_EQUAL(c , (i & (i+j))); + c = a & (b | 1); + BOOST_CHECK_EQUAL(c , (i & (j | 1))); + + test_complement<Real>(a, b, c, typename is_twos_complement_integer<Real>::type()); + + a = i; + b = j; + c = a; + c |= b; + BOOST_CHECK_EQUAL(c , (i | j)); + c = a; + c |= j; + BOOST_CHECK_EQUAL(c , (i | j)); + c = a; + c |= a + b; + BOOST_CHECK_EQUAL(c , (i | (i + j))); + BOOST_CHECK_EQUAL((a | b) , (i | j)); + c = k; + a = a | (b + k); + BOOST_CHECK_EQUAL(a , (i | (j + k))); + a = i; + a = (b + k) | a; + BOOST_CHECK_EQUAL(a , (i | (j + k))); + a = i; + c = a | b | k; + BOOST_CHECK_EQUAL(c , (i|j|k)); + c = a; + c |= (c + b); + BOOST_CHECK_EQUAL(c , (i | (i+j))); + c = a | (b | 1); + BOOST_CHECK_EQUAL(c , (i | (j | 1))); + + a = i; + b = j; + c = a; + c ^= b; + BOOST_CHECK_EQUAL(c , (i ^ j)); + c = a; + c ^= j; + BOOST_CHECK_EQUAL(c , (i ^ j)); + c = a; + c ^= a + b; + BOOST_CHECK_EQUAL(c , (i ^ (i + j))); + BOOST_CHECK_EQUAL((a ^ b) , (i ^ j)); + c = k; + a = a ^ (b + k); + BOOST_CHECK_EQUAL(a , (i ^ (j + k))); + a = i; + a = (b + k) ^ a; + BOOST_CHECK_EQUAL(a , (i ^ (j + k))); + a = i; + c = a ^ b ^ k; + BOOST_CHECK_EQUAL(c , (i^j^k)); + c = a; + c ^= (c + b); + BOOST_CHECK_EQUAL(c , (i ^ (i+j))); + c = a ^ (b | 1); + BOOST_CHECK_EQUAL(c , (i ^ (j | 1))); + + a = i; + b = j; + c = k; + // + // Non-member functions: + // + a = 400; + b = 45; + BOOST_CHECK_EQUAL(gcd(a, b) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(a, b) , boost::math::lcm(400, 45)); + BOOST_CHECK_EQUAL(gcd(a, 45) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(a, 45) , boost::math::lcm(400, 45)); + BOOST_CHECK_EQUAL(gcd(a, 45u) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(a, 45u) , boost::math::lcm(400, 45)); + BOOST_CHECK_EQUAL(gcd(400, b) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(400, b) , boost::math::lcm(400, 45)); + BOOST_CHECK_EQUAL(gcd(400u, b) , boost::math::gcd(400, 45)); + BOOST_CHECK_EQUAL(lcm(400u, b) , boost::math::lcm(400, 45)); + + // + // Conditionals involving 2 arg functions: + // + test_conditional(Real(gcd(a, b)), gcd(a, b)); + + Real r; + divide_qr(a, b, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + divide_qr(a + 0, b, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + divide_qr(a, b+0, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + divide_qr(a+0, b+0, c, r); + BOOST_CHECK_EQUAL(c , a / b); + BOOST_CHECK_EQUAL(r , a % b); + BOOST_CHECK_EQUAL(integer_modulus(a, 57) , a % 57); + for(unsigned i = 0; i < 20; ++i) + { + if(std::numeric_limits<Real>::is_specialized && (!std::numeric_limits<Real>::is_bounded || ((int)i * 17 < std::numeric_limits<Real>::digits))) + { + BOOST_CHECK_EQUAL(lsb(Real(1) << (i * 17)) , i * 17); + BOOST_CHECK_EQUAL(msb(Real(1) << (i * 17)) , i * 17); + BOOST_CHECK(bit_test(Real(1) << (i * 17), i * 17)); + BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 + 1)); + if(i) + { + BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 - 1)); + } + Real zero(0); + BOOST_CHECK(bit_test(bit_set(zero, i * 17), i * 17)); + zero = 0; + BOOST_CHECK_EQUAL(bit_flip(zero, i*17) , Real(1) << i * 17); + zero = Real(1) << i * 17; + BOOST_CHECK_EQUAL(bit_flip(zero, i * 17) , 0); + zero = Real(1) << i * 17; + BOOST_CHECK_EQUAL(bit_unset(zero, i * 17) , 0); + } + } + // + // pow, powm: + // + BOOST_CHECK_EQUAL(pow(Real(3), 4) , 81); + BOOST_CHECK_EQUAL(pow(Real(3) + Real(0), 4) , 81); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4), 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13) + 0) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13) + 0) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13) + 0) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13) + 0) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13) + 0) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13)) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, 13) , 81 % 13); + BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13) + 0) , 81 % 13); + // + // Conditionals involving 3 arg functions: + // + test_conditional(Real(powm(Real(3), Real(4), Real(13))), powm(Real(3), Real(4), Real(13))); + + // + // Things that are expected errors: + // + BOOST_CHECK_THROW(Real("3.14"), std::runtime_error); + BOOST_CHECK_THROW(Real("3L"), std::runtime_error); + BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error); + // + // Extra tests added for full coverage: + // + a = 20; + b = 7; + c = 20 % b; + BOOST_CHECK_EQUAL(c , (20 % 7)); + c = 20 % (b + 0); + BOOST_CHECK_EQUAL(c , (20 % 7)); + c = a & 10; + BOOST_CHECK_EQUAL(c , (20 & 10)); + c = 10 & a; + BOOST_CHECK_EQUAL(c , (20 & 10)); + c = (a + 0) & (b + 0); + BOOST_CHECK_EQUAL(c , (20 & 7)); + c = 10 & (a + 0); + BOOST_CHECK_EQUAL(c , (20 & 10)); + c = 10 | a; + BOOST_CHECK_EQUAL(c , (20 | 10)); + c = (a + 0) | (b + 0); + BOOST_CHECK(c == (20 | 7)) + c = 20 | (b + 0); + BOOST_CHECK_EQUAL(c , (20 | 7)); + c = a ^ 7; + BOOST_CHECK_EQUAL(c , (20 ^ 7)); + c = 20 ^ b; + BOOST_CHECK_EQUAL(c , (20 ^ 7)); + c = (a + 0) ^ (b + 0); + BOOST_CHECK_EQUAL(c , (20 ^ 7)); + c = 20 ^ (b + 0); + BOOST_CHECK_EQUAL(c , (20 ^ 7)); +} + +template <class Real, class T> +void test_float_funcs(const T&){} + +template <class Real> +void test_float_funcs(const boost::mpl::true_&) +{ + if(boost::multiprecision::is_interval_number<Real>::value) + return; + // + // Test variable reuse in function calls, see https://svn.boost.org/trac/boost/ticket/8326 + // + Real a(2), b(10); + a = pow(a, b); + BOOST_CHECK_EQUAL(a, 1024); + a = 2; + b = pow(a, b); + BOOST_CHECK_EQUAL(b, 1024); + b = 10; + a = pow(a, 10); + BOOST_CHECK_EQUAL(a, 1024); + a = -2; + a = abs(a); + BOOST_CHECK_EQUAL(a, 2); + a = -2; + a = fabs(a); + BOOST_CHECK_EQUAL(a, 2); + a = 2.5; + a = floor(a); + BOOST_CHECK_EQUAL(a, 2); + a = 2.5; + a = ceil(a); + BOOST_CHECK_EQUAL(a, 3); + a = 2.5; + a = trunc(a); + BOOST_CHECK_EQUAL(a, 2); + a = 2.25; + a = round(a); + BOOST_CHECK_EQUAL(a, 2); + a = 2; + a = ldexp(a, 1); + BOOST_CHECK_EQUAL(a, 4); + int i; + a = frexp(a, &i); + BOOST_CHECK_EQUAL(a, 0.5); + + Real tol = std::numeric_limits<Real>::epsilon() * 3; + a = 4; + a = sqrt(a); + BOOST_CHECK_CLOSE_FRACTION(a, 2, tol); + a = 3; + a = exp(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(exp(Real(3))), tol); + a = 3; + a = log(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(log(Real(3))), tol); + a = 3; + a = log10(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(log10(Real(3))), tol); + + a = 0.5; + a = sin(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(sin(Real(0.5))), tol); + a = 0.5; + a = cos(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(cos(Real(0.5))), tol); + a = 0.5; + a = tan(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(tan(Real(0.5))), tol); + a = 0.5; + a = asin(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(asin(Real(0.5))), tol); + a = 0.5; + a = acos(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(acos(Real(0.5))), tol); + a = 0.5; + a = atan(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(atan(Real(0.5))), tol); + a = 0.5; + a = sinh(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(sinh(Real(0.5))), tol); + a = 0.5; + a = cosh(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(cosh(Real(0.5))), tol); + a = 0.5; + a = tanh(a); + BOOST_CHECK_CLOSE_FRACTION(a, Real(tanh(Real(0.5))), tol); + a = 4; + b = 2; + a = fmod(a, b); + BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), Real(2))), tol); + a = 4; + b = fmod(a, b); + BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), Real(2))), tol); + b = 2; + a = atan2(a, b); + BOOST_CHECK_CLOSE_FRACTION(a, Real(atan2(Real(4), Real(2))), tol); + a = 4; + b = atan2(a, b); + BOOST_CHECK_CLOSE_FRACTION(b, Real(atan2(Real(4), Real(2))), tol); +} + +template <class Real, class T> +void test_float_ops(const T&){} + +template <class Real> +void test_float_ops(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&) +{ + BOOST_CHECK_EQUAL(abs(Real(2)) , 2); + BOOST_CHECK_EQUAL(abs(Real(-2)) , 2); + BOOST_CHECK_EQUAL(fabs(Real(2)) , 2); + BOOST_CHECK_EQUAL(fabs(Real(-2)) , 2); + BOOST_CHECK_EQUAL(floor(Real(5) / 2) , 2); + BOOST_CHECK_EQUAL(ceil(Real(5) / 2) , 3); + BOOST_CHECK_EQUAL(floor(Real(-5) / 2) , -3); + BOOST_CHECK_EQUAL(ceil(Real(-5) / 2) , -2); + BOOST_CHECK_EQUAL(trunc(Real(5) / 2) , 2); + BOOST_CHECK_EQUAL(trunc(Real(-5) / 2) , -2); + // + // ldexp and frexp, these pretty much have to be implemented by each backend: + // + BOOST_CHECK_EQUAL(ldexp(Real(2), 5) , 64); + BOOST_CHECK_EQUAL(ldexp(Real(2), -5) , Real(2) / 32); + Real v(512); + int exponent; + Real r = frexp(v, &exponent); + BOOST_CHECK_EQUAL(r , 0.5); + BOOST_CHECK_EQUAL(exponent , 10); + BOOST_CHECK_EQUAL(v , 512); + v = 1 / v; + r = frexp(v, &exponent); + BOOST_CHECK_EQUAL(r , 0.5); + BOOST_CHECK_EQUAL(exponent , -8); + typedef typename Real::backend_type::exponent_type e_type; + BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(5)) , 64); + BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(-5)) , Real(2) / 32); + v = 512; + e_type exp2; + r = frexp(v, &exp2); + BOOST_CHECK_EQUAL(r , 0.5); + BOOST_CHECK_EQUAL(exp2 , 10); + BOOST_CHECK_EQUAL(v , 512); + v = 1 / v; + r = frexp(v, &exp2); + BOOST_CHECK_EQUAL(r , 0.5); + BOOST_CHECK_EQUAL(exp2 , -8); + // + // scalbn and logb, these are the same as ldexp and frexp unless the radix is + // something other than 2: + // + if(std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::radix) + { + BOOST_CHECK_EQUAL(scalbn(Real(2), 5), 2 * pow(double(std::numeric_limits<Real>::radix), 5)); + BOOST_CHECK_EQUAL(scalbn(Real(2), -5), Real(2) / pow(double(std::numeric_limits<Real>::radix), 5)); + Real v(512); + int exponent; + Real r; + exponent = ilogb(v); + r = scalbn(v, -exponent); + BOOST_CHECK(r >= 1); + BOOST_CHECK(r < std::numeric_limits<Real>::radix); + BOOST_CHECK_EQUAL(exponent, logb(v)); + BOOST_CHECK_EQUAL(v, scalbn(r, exponent)); + v = 1 / v; + exponent = ilogb(v); + r = scalbn(v, -exponent); + BOOST_CHECK(r >= 1); + BOOST_CHECK(r < std::numeric_limits<Real>::radix); + BOOST_CHECK_EQUAL(exponent, logb(v)); + BOOST_CHECK_EQUAL(v, scalbn(r, exponent)); + } + // + // pow and exponent: + // + v = 3.25; + r = pow(v, 0); + BOOST_CHECK_EQUAL(r , 1); + r = pow(v, 1); + BOOST_CHECK_EQUAL(r , 3.25); + r = pow(v, 2); + BOOST_CHECK_EQUAL(r , boost::math::pow<2>(3.25)); + r = pow(v, 3); + BOOST_CHECK_EQUAL(r , boost::math::pow<3>(3.25)); + r = pow(v, 4); + BOOST_CHECK_EQUAL(r , boost::math::pow<4>(3.25)); + r = pow(v, 5); + BOOST_CHECK_EQUAL(r , boost::math::pow<5>(3.25)); + r = pow(v, 6); + BOOST_CHECK_EQUAL(r , boost::math::pow<6>(3.25)); + r = pow(v, 25); + BOOST_CHECK_EQUAL(r , boost::math::pow<25>(Real(3.25))); + // + // Things that are expected errors: + // + BOOST_CHECK_THROW(Real("3.14L"), std::runtime_error); + if(std::numeric_limits<Real>::is_specialized) + { + if(std::numeric_limits<Real>::has_infinity) + { + BOOST_CHECK((boost::math::isinf)(Real(20) / 0u)); + } + else + { + BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error); + } + } + + test_float_funcs<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>()); +} + +template <class T> +struct lexical_cast_target_type +{ + typedef typename boost::mpl::if_< + boost::is_signed<T>, + boost::intmax_t, + typename boost::mpl::if_< + boost::is_unsigned<T>, + boost::uintmax_t, + T + >::type + >::type type; +}; + +template <class Real, class Num> +void test_negative_mixed_minmax(boost::mpl::true_ const&) +{ + if(!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits >= std::numeric_limits<Num>::digits)) + { + Real mx1((std::numeric_limits<Num>::max)() - 1); + ++mx1; + Real mx2((std::numeric_limits<Num>::max)()); + BOOST_CHECK_EQUAL(mx1, mx2); + mx1 = (std::numeric_limits<Num>::max)() - 1; + ++mx1; + mx2 = (std::numeric_limits<Num>::max)(); + BOOST_CHECK_EQUAL(mx1, mx2); + + if(!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits > std::numeric_limits<Num>::digits)) + { + Real mx3((std::numeric_limits<Num>::min)() + 1); + --mx3; + Real mx4((std::numeric_limits<Num>::min)()); + BOOST_CHECK_EQUAL(mx3, mx4); + mx3 = (std::numeric_limits<Num>::min)() + 1; + --mx3; + mx4 = (std::numeric_limits<Num>::min)(); + BOOST_CHECK_EQUAL(mx3, mx4); + } + } +} +template <class Real, class Num> +void test_negative_mixed_minmax(boost::mpl::false_ const&) +{ +} + +template <class Real, class Num> +void test_negative_mixed(boost::mpl::true_ const&) +{ + typedef typename lexical_cast_target_type<Num>::type target_type; + typedef typename boost::mpl::if_< + boost::is_convertible<Num, Real>, + typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type, + Real + >::type cast_type; + typedef typename boost::mpl::if_< + boost::is_convertible<Num, Real>, + Num, + Real + >::type simple_cast_type; + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + static const int left_shift = std::numeric_limits<Num>::digits - 1; + Num n1 = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10)); + Num n2 = -1; + Num n3 = 0; + Num n4 = -20; + Num n5 = -8; + + test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>()); + + // Default construct: + BOOST_CHECK_EQUAL(Real(n1) , static_cast<cast_type>(n1)); + BOOST_CHECK_EQUAL(Real(n2) , static_cast<cast_type>(n2)); + BOOST_CHECK_EQUAL(Real(n3) , static_cast<cast_type>(n3)); + BOOST_CHECK_EQUAL(Real(n4) , static_cast<cast_type>(n4)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n1) , Real(n1)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n2) , Real(n2)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n3) , Real(n3)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n4) , Real(n4)); + BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>() , n1); + BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>() , n2); + BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>() , n3); + BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>() , n4); +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)) , n1); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)) , n2); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)) , n3); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)) , n4); +#endif +#if defined(TEST_MPFR) + Num tol = 10 * std::numeric_limits<Num>::epsilon(); +#else + Num tol = 0; +#endif + std::ios_base::fmtflags f = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); + int digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized + ? std::numeric_limits<Num>::digits10 + 5 : 0; + if(std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits) + { + BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol); + } + BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0); + BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0); + BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0); + // Assignment: + Real r(0); + BOOST_CHECK(r != static_cast<cast_type>(n1)); + r = static_cast<simple_cast_type>(n1); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1)); + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2)); + r = static_cast<simple_cast_type>(n3); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n3)); + r = static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4)); + // Addition: + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 + n4)); + BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 + n4)); + r += static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 + n4)); + // subtraction: + r = static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n4 - n5)); + BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n4 - n5)); + r -= static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5)); + // Multiplication: + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 * n4)); + BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 * n4)); + r *= static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 * n4)); + // Division: + r = static_cast<simple_cast_type>(n1); + BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n1 / n5)); + BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n1 / n5)); + r /= static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1 / n5)); + // + // Extra cases for full coverage: + // + r = Real(n4) + static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5)); + r = static_cast<simple_cast_type>(n4) + Real(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5)); + r = Real(n4) - static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5)); + r = static_cast<simple_cast_type>(n4) - Real(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5)); + r = static_cast<simple_cast_type>(n4) * Real(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 * n5)); + r = static_cast<cast_type>(4 * n4) / Real(4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4)); + + Real a, b, c; + a = 20; + b = 30; + c = -a + b; + BOOST_CHECK_EQUAL(c , 10); + c = b + -a; + BOOST_CHECK_EQUAL(c , 10); + n4 = 30; + c = -a + static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , 10); + c = static_cast<cast_type>(n4) + -a; + BOOST_CHECK_EQUAL(c , 10); + c = -a + -b; + BOOST_CHECK_EQUAL(c , -50); + n4 = 4; + c = -(a + b) + static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , -50+4); + n4 = 50; + c = (a + b) - static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , 0); + c = (a + b) - static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , 0); + c = a - -(b + static_cast<cast_type>(n4)); + BOOST_CHECK_EQUAL(c , 20 - -(30 + 50)); + c = -(b + static_cast<cast_type>(n4)) - a; + BOOST_CHECK_EQUAL(c , -(30 + 50) - 20); + c = a - -b; + BOOST_CHECK_EQUAL(c , 50); + c = -a - b; + BOOST_CHECK_EQUAL(c , -50); + c = -a - static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , -20 - 50); + c = static_cast<cast_type>(n4) - -a; + BOOST_CHECK_EQUAL(c , 50 + 20); + c = -(a + b) - Real(n4); + BOOST_CHECK_EQUAL(c , -(20 + 30) - 50); + c = static_cast<cast_type>(n4) - (a + b); + BOOST_CHECK_EQUAL(c , 0); + c = (a + b) * static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , 50 * 50); + c = static_cast<cast_type>(n4) * (a + b); + BOOST_CHECK_EQUAL(c , 50 * 50); + c = a * -(b + static_cast<cast_type>(n4)); + BOOST_CHECK_EQUAL(c , 20 * -(30 + 50)); + c = -(b + static_cast<cast_type>(n4)) * a; + BOOST_CHECK_EQUAL(c , 20 * -(30 + 50)); + c = a * -b; + BOOST_CHECK_EQUAL(c , 20 * -30); + c = -a * b; + BOOST_CHECK_EQUAL(c , 20 * -30); + c = -a * static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , -20 * 50); + c = static_cast<cast_type>(n4) * -a; + BOOST_CHECK_EQUAL(c , -20 * 50); + c = -(a + b) + a; + BOOST_CHECK(-50 + 20); + c = static_cast<cast_type>(n4) - (a + b); + BOOST_CHECK_EQUAL(c , 0); + Real d = 10; + c = (a + b) / d; + BOOST_CHECK_EQUAL(c , 5); + c = (a + b) / (d + 0); + BOOST_CHECK_EQUAL(c , 5); + c = (a + b) / static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , 1); + c = static_cast<cast_type>(n4) / (a + b); + BOOST_CHECK_EQUAL(c , 1); + d = 50; + c = d / -(a + b); + BOOST_CHECK_EQUAL(c , -1); + c = -(a + b) / d; + BOOST_CHECK_EQUAL(c , -1); + d = 2; + c = a / -d; + BOOST_CHECK_EQUAL(c , 20 / -2); + c = -a / d; + BOOST_CHECK_EQUAL(c , 20 / -2); + d = 50; + c = -d / static_cast<cast_type>(n4); + BOOST_CHECK_EQUAL(c , -1); + c = static_cast<cast_type>(n4) / -d; + BOOST_CHECK_EQUAL(c , -1); + c = static_cast<cast_type>(n4) + a; + BOOST_CHECK_EQUAL(c , 70); + c = static_cast<cast_type>(n4) - a; + BOOST_CHECK_EQUAL(c , 30); + c = static_cast<cast_type>(n4) * a; + BOOST_CHECK_EQUAL(c , 50 * 20); + + n1 = -2; + n2 = -3; + n3 = -4; + a = static_cast<cast_type>(n1); + b = static_cast<cast_type>(n2); + c = static_cast<cast_type>(n3); + d = a + b * c; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = static_cast<cast_type>(n1) + b * c; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = a + static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = a + b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + a += static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(a , -2 + -3 * -4); + a = static_cast<cast_type>(n1); + a += b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(a , -2 + -3 * -4); + a = static_cast<cast_type>(n1); + + d = b * c + a; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = b * c + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = static_cast<cast_type>(n2) * c + a; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = b * static_cast<cast_type>(n3) + a; + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -2 + -3 * -4); + + a = -20; + d = a - b * c; + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + n1 = -20; + d = static_cast<cast_type>(n1) - b * c; + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + d = a - static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + d = a - b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , -20 - -3 * -4); + a -= static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(a , -20 - -3 * -4); + a = static_cast<cast_type>(n1); + a -= b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(a , -20 - -3 * -4); + + a = -2; + d = b * c - a; + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + n1 = -2; + d = b * c - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + d = static_cast<cast_type>(n2) * c - a; + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + d = b * static_cast<cast_type>(n3) - a; + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , -3 * -4 - -2); + // + // Conversion from min and max values: + // + test_negative_mixed_minmax<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_integer && std::numeric_limits<Num>::is_integer>()); +} + +template <class Real, class Num> +void test_negative_mixed(boost::mpl::false_ const&) +{ +} + +template <class Real, class Num> +void test_mixed(const boost::mpl::false_&) +{ +} + +template <class Real, class Num> +void test_mixed(const boost::mpl::true_&) +{ + typedef typename lexical_cast_target_type<Num>::type target_type; + typedef typename boost::mpl::if_< + boost::is_convertible<Num, Real>, + typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type, + Real + >::type cast_type; + typedef typename boost::mpl::if_< + boost::is_convertible<Num, Real>, + Num, + Real + >::type simple_cast_type; + + if(std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::is_bounded && std::numeric_limits<Real>::digits < std::numeric_limits<Num>::digits) + return; + + std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl; + static const int left_shift = std::numeric_limits<Num>::digits - 1; + Num n1 = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10)); + Num n2 = 1; + Num n3 = 0; + Num n4 = 20; + Num n5 = 8; + + test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>()); + test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>()); + + // Default construct: + BOOST_CHECK_EQUAL(Real(n1) , static_cast<cast_type>(n1)); + BOOST_CHECK_EQUAL(Real(n2) , static_cast<cast_type>(n2)); + BOOST_CHECK_EQUAL(Real(n3) , static_cast<cast_type>(n3)); + BOOST_CHECK_EQUAL(Real(n4) , static_cast<cast_type>(n4)); + BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>() , n1); + BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>() , n2); + BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>() , n3); + BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>() , n4); +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)) , n1); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)) , n2); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)) , n3); + BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)) , n4); +#endif + BOOST_CHECK_EQUAL(static_cast<cast_type>(n1) , Real(n1)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n2) , Real(n2)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n3) , Real(n3)); + BOOST_CHECK_EQUAL(static_cast<cast_type>(n4) , Real(n4)); +#if defined(TEST_MPFR) + Num tol = 10 * std::numeric_limits<Num>::epsilon(); +#else + Num tol = 0; +#endif + std::ios_base::fmtflags f = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0); + int digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized + ? std::numeric_limits<Num>::digits10 + 5 : 0; + if(std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits) + { + BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol); + } + BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0); + BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0); + BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0); + // Assignment: + Real r(0); + BOOST_CHECK(r != static_cast<cast_type>(n1)); + r = static_cast<simple_cast_type>(n1); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1)); + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2)); + r = static_cast<simple_cast_type>(n3); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n3)); + r = static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4)); + // Addition: + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 + n4)); + BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 + n4)); + r += static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 + n4)); + // subtraction: + r = static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n4 - n5)); + BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n4 - n5)); + r -= static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5)); + // Multiplication: + r = static_cast<simple_cast_type>(n2); + BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 * n4)); + BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 * n4)); + r *= static_cast<simple_cast_type>(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 * n4)); + // Division: + r = static_cast<simple_cast_type>(n1); + BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n1 / n5)); + BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n1 / n5)); + r /= static_cast<simple_cast_type>(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1 / n5)); + // + // special cases for full coverage: + // + r = static_cast<simple_cast_type>(n5) + Real(n4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5)); + r = static_cast<simple_cast_type>(n4) - Real(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5)); + r = static_cast<simple_cast_type>(n4) * Real(n5); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 * n5)); + r = static_cast<cast_type>(4 * n4) / Real(4); + BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4)); + + typedef boost::mpl::bool_< + (!std::numeric_limits<Num>::is_specialized || std::numeric_limits<Num>::is_signed) + && (!std::numeric_limits<Real>::is_specialized || std::numeric_limits<Real>::is_signed)> signed_tag; + + test_negative_mixed<Real, Num>(signed_tag()); + + n1 = 2; + n2 = 3; + n3 = 4; + Real a(n1), b(n2), c(n3), d; + d = a + b * c; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = static_cast<cast_type>(n1) + b * c; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = a + static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = a + b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + a += static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(a , 2 + 3 * 4); + a = static_cast<cast_type>(n1); + a += b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(a , 2 + 3 * 4); + a = static_cast<cast_type>(n1); + + d = b * c + a; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = b * c + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = static_cast<cast_type>(n2) * c + a; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = b * static_cast<cast_type>(n3) + a; + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 2 + 3 * 4); + + a = 20; + d = a - b * c; + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + n1 = 20; + d = static_cast<cast_type>(n1) - b * c; + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + d = a - static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + d = a - b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(d , 20 - 3 * 4); + a -= static_cast<cast_type>(n2) * c; + BOOST_CHECK_EQUAL(a , 20 - 3 * 4); + a = static_cast<cast_type>(n1); + a -= b * static_cast<cast_type>(n3); + BOOST_CHECK_EQUAL(a , 20 - 3 * 4); + + a = 2; + d = b * c - a; + BOOST_CHECK_EQUAL(d , 3 * 4 - 2); + n1 = 2; + d = b * c - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 3 * 4 - 2); + d = static_cast<cast_type>(n2) * c - a; + BOOST_CHECK_EQUAL(d , 3 * 4 - 2); + d = b * static_cast<cast_type>(n3) - a; + BOOST_CHECK_EQUAL(d , 3 * 4 - a); + d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 3 * 4 - 2); + d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1); + BOOST_CHECK_EQUAL(d , 3 * 4 - 2); +} + +template <class Real> +void test_members(Real) +{ + // + // Test sign and zero functions: + // + Real a = 20; + Real b = 30; + BOOST_CHECK(a.sign() > 0); + BOOST_CHECK(!a.is_zero()); + if(std::numeric_limits<Real>::is_signed) + { + a = -20; + BOOST_CHECK(a.sign() < 0); + BOOST_CHECK(!a.is_zero()); + } + a = 0; + BOOST_CHECK_EQUAL(a.sign() , 0); + BOOST_CHECK(a.is_zero()); + + a = 20; + b = 30; + a.swap(b); + BOOST_CHECK_EQUAL(a , 30); + BOOST_CHECK_EQUAL(b , 20); +} + +template <class Real> +void test_members(boost::rational<Real>) +{ +} + +template <class Real> +void test_signed_ops(const boost::mpl::true_&) +{ + Real a(8); + Real b(64); + Real c(500); + Real d(1024); + Real ac; + BOOST_CHECK_EQUAL(-a , -8); + ac = a; + ac = ac - b; + BOOST_CHECK_EQUAL(ac , 8 - 64); + ac = a; + ac -= a + b; + BOOST_CHECK_EQUAL(ac , -64); + ac = a; + ac -= b - a; + BOOST_CHECK_EQUAL(ac , 16 - 64); + ac = -a; + BOOST_CHECK_EQUAL(ac , -8); + ac = a; + ac -= -a; + BOOST_CHECK_EQUAL(ac , 16); + ac = a; + ac += -a; + BOOST_CHECK_EQUAL(ac , 0); + ac = b; + ac /= -a; + BOOST_CHECK_EQUAL(ac , -8); + ac = a; + ac *= -a; + BOOST_CHECK_EQUAL(ac , -64); + ac = a + -b; + BOOST_CHECK_EQUAL(ac , 8 - 64); + ac = -a + b; + BOOST_CHECK_EQUAL(ac , -8+64); + ac = -a + -b; + BOOST_CHECK_EQUAL(ac , -72); + ac = a + - + -b; // lots of unary operators!! + BOOST_CHECK_EQUAL(ac , 72); + test_conditional(Real(-a), -a); +} +template <class Real> +void test_signed_ops(const boost::mpl::false_&) +{ +} + +template <class Real> +void test() +{ +#if !defined(NO_MIXED_OPS) && !defined(SLOW_COMPILER) + boost::multiprecision::is_number<Real> tag; + test_mixed<Real, unsigned char>(tag); + test_mixed<Real, signed char>(tag); + test_mixed<Real, char>(tag); + test_mixed<Real, short>(tag); + test_mixed<Real, unsigned short>(tag); + test_mixed<Real, int>(tag); + test_mixed<Real, unsigned int>(tag); + test_mixed<Real, long>(tag); + test_mixed<Real, unsigned long>(tag); +#ifdef BOOST_HAS_LONG_LONG + test_mixed<Real, long long>(tag); + test_mixed<Real, unsigned long long>(tag); +#endif + test_mixed<Real, float>(tag); + test_mixed<Real, double>(tag); + test_mixed<Real, long double>(tag); + + typedef typename related_type<Real>::type related_type; + boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && !boost::is_same<related_type, Real>::value> tag2; + + test_mixed<Real, related_type>(tag2); + +#endif + // + // Integer only functions: + // + test_integer_ops<Real>(typename boost::multiprecision::number_category<Real>::type()); + // + // Real number only functions: + // + test_float_ops<Real>(typename boost::multiprecision::number_category<Real>::type()); + // + // Test basic arithmetic: + // + Real a(8); + Real b(64); + Real c(500); + Real d(1024); + BOOST_CHECK_EQUAL(a + b , 72); + a += b; + BOOST_CHECK_EQUAL(a , 72); + BOOST_CHECK_EQUAL(a - b , 8); + a -= b; + BOOST_CHECK_EQUAL(a , 8); + BOOST_CHECK_EQUAL(a * b , 8*64L); + a *= b; + BOOST_CHECK_EQUAL(a , 8*64L); + BOOST_CHECK_EQUAL(a / b , 8); + a /= b; + BOOST_CHECK_EQUAL(a , 8); + Real ac(a); + BOOST_CHECK_EQUAL(ac , a); + ac = a * c; + BOOST_CHECK_EQUAL(ac , 8*500L); + ac = 8*500L; + ac = ac + b + c; + BOOST_CHECK_EQUAL(ac , 8*500L+64+500); + ac = a; + ac = b + c + ac; + BOOST_CHECK_EQUAL(ac , 8+64+500); + ac = ac - b + c; + BOOST_CHECK_EQUAL(ac , 8+64+500-64+500); + ac = a; + ac = b + c - ac; + BOOST_CHECK_EQUAL(ac , -8+64+500); + ac = a; + ac = ac * b; + BOOST_CHECK_EQUAL(ac , 8*64); + ac = a; + ac *= b * ac; + BOOST_CHECK_EQUAL(ac , 8*8*64); + ac = b; + ac = ac / a; + BOOST_CHECK_EQUAL(ac , 64/8); + ac = b; + ac /= ac / a; + BOOST_CHECK_EQUAL(ac , 64 / (64/8)); + ac = a; + ac = b + ac * a; + BOOST_CHECK_EQUAL(ac , 64 * 2); + ac = a; + ac = b - ac * a; + BOOST_CHECK_EQUAL(ac , 0); + ac = a; + ac = b * (ac + a); + BOOST_CHECK_EQUAL(ac , 64 * (16)); + ac = a; + ac = b / (ac * 1); + BOOST_CHECK_EQUAL(ac , 64 / 8); + ac = a; + ac = ac + b; + BOOST_CHECK_EQUAL(ac , 8 + 64); + ac = a; + ac = a + ac; + BOOST_CHECK_EQUAL(ac , 16); + ac = a; + ac = a - ac; + BOOST_CHECK_EQUAL(ac , 0); + ac = a; + ac += a + b; + BOOST_CHECK_EQUAL(ac , 80); + ac = a; + ac += b + a; + BOOST_CHECK_EQUAL(ac , 80); + ac = +a; + BOOST_CHECK_EQUAL(ac , 8); + ac = 8; + ac = a * ac; + BOOST_CHECK_EQUAL(ac , 8*8); + ac = a; + ac = a; + ac += +a; + BOOST_CHECK_EQUAL(ac , 16); + ac = a; + ac += b - a; + BOOST_CHECK_EQUAL(ac , 8 + 64-8); + ac = a; + ac += b*c; + BOOST_CHECK_EQUAL(ac , 8 + 64 * 500); + ac = a; + ac = a; + ac -= +a; + BOOST_CHECK_EQUAL(ac , 0); + ac = a; + if(std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value) + { + ac = a; + ac -= c - b; + BOOST_CHECK_EQUAL(ac , 8 - (500-64)); + ac = a; + ac -= b*c; + BOOST_CHECK_EQUAL(ac , 8 - 500*64); + } + ac = a; + ac += ac * b; + BOOST_CHECK_EQUAL(ac , 8 + 8 * 64); + if(std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value) + { + ac = a; + ac -= ac * b; + BOOST_CHECK_EQUAL(ac , 8 - 8 * 64); + } + ac = a * 8; + ac *= +a; + BOOST_CHECK_EQUAL(ac , 64 * 8); + ac = a; + ac *= b * c; + BOOST_CHECK_EQUAL(ac , 8 * 64 * 500); + ac = a; + ac *= b / a; + BOOST_CHECK_EQUAL(ac , 8 * 64 / 8); + ac = a; + ac *= b + c; + BOOST_CHECK_EQUAL(ac , 8 * (64 + 500)); + ac = b; + ac /= +a; + BOOST_CHECK_EQUAL(ac , 8); + ac = b; + ac /= b / a; + BOOST_CHECK_EQUAL(ac , 64 / (64/8)); + ac = b; + ac /= a + Real(0); + BOOST_CHECK_EQUAL(ac , 8); + // + // simple tests with immediate values, these calls can be optimised in many backends: + // + ac = a + b; + BOOST_CHECK_EQUAL(ac , 72); + ac = a + +b; + BOOST_CHECK_EQUAL(ac , 72); + ac = +a + b; + BOOST_CHECK_EQUAL(ac , 72); + ac = +a + +b; + BOOST_CHECK_EQUAL(ac , 72); + ac = a; + ac = b / ac; + BOOST_CHECK_EQUAL(ac , b / a); + // + // Comparisons: + // + BOOST_CHECK_EQUAL((a == b) , false); + BOOST_CHECK_EQUAL((a != b) , true); + BOOST_CHECK_EQUAL((a <= b) , true); + BOOST_CHECK_EQUAL((a < b) , true); + BOOST_CHECK_EQUAL((a >= b) , false); + BOOST_CHECK_EQUAL((a > b) , false); + + BOOST_CHECK_EQUAL((a+b == b) , false); + BOOST_CHECK_EQUAL((a+b != b) , true); + BOOST_CHECK_EQUAL((a+b >= b) , true); + BOOST_CHECK_EQUAL((a+b > b) , true); + BOOST_CHECK_EQUAL((a+b <= b) , false); + BOOST_CHECK_EQUAL((a+b < b) , false); + + BOOST_CHECK_EQUAL((a == b+a) , false); + BOOST_CHECK_EQUAL((a != b+a) , true); + BOOST_CHECK_EQUAL((a <= b+a) , true); + BOOST_CHECK_EQUAL((a < b+a) , true); + BOOST_CHECK_EQUAL((a >= b+a) , false); + BOOST_CHECK_EQUAL((a > b+a) , false); + + BOOST_CHECK_EQUAL((a+b == b+a) , true); + BOOST_CHECK_EQUAL((a+b != b+a) , false); + BOOST_CHECK_EQUAL((a+b <= b+a) , true); + BOOST_CHECK_EQUAL((a+b < b+a) , false); + BOOST_CHECK_EQUAL((a+b >= b+a) , true); + BOOST_CHECK_EQUAL((a+b > b+a) , false); + + BOOST_CHECK_EQUAL((8 == b+a) , false); + BOOST_CHECK_EQUAL((8 != b+a) , true); + BOOST_CHECK_EQUAL((8 <= b+a) , true); + BOOST_CHECK_EQUAL((8 < b+a) , true); + BOOST_CHECK_EQUAL((8 >= b+a) , false); + BOOST_CHECK_EQUAL((8 > b+a) , false); + BOOST_CHECK_EQUAL((800 == b+a) , false); + BOOST_CHECK_EQUAL((800 != b+a) , true); + BOOST_CHECK_EQUAL((800 >= b+a) , true); + BOOST_CHECK_EQUAL((800 > b+a) , true); + BOOST_CHECK_EQUAL((800 <= b+a) , false); + BOOST_CHECK_EQUAL((800 < b+a) , false); + BOOST_CHECK_EQUAL((72 == b+a) , true); + BOOST_CHECK_EQUAL((72 != b+a) , false); + BOOST_CHECK_EQUAL((72 <= b+a) , true); + BOOST_CHECK_EQUAL((72 < b+a) , false); + BOOST_CHECK_EQUAL((72 >= b+a) , true); + BOOST_CHECK_EQUAL((72 > b+a) , false); + + test_members(a); + // + // Use in Boolean context: + // + a = 0; + if(a) + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(!a){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + b = 2; + if(!b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(b){} + else + { + BOOST_ERROR("Unexpected non-zero result"); + } + if(a && b) + { + BOOST_ERROR("Unexpected zero result"); + } + if(!(a || b)) + { + BOOST_ERROR("Unexpected zero result"); + } + if(a + b){} + else + { + BOOST_ERROR("Unexpected zero result"); + } + if(b - 2) + { + BOOST_ERROR("Unexpected non-zero result"); + } + // + // Test iostreams: + // + std::stringstream ss; + a = 20; + b = 2; + ss << a; + ss >> c; + BOOST_CHECK_EQUAL(a , c); + ss.clear(); + ss << a + b; + ss >> c; + BOOST_CHECK_EQUAL(c , 22); + BOOST_CHECK_EQUAL(c , a + b); + // + // More cases for complete code coverage: + // + a = 20; + b = 30; + swap(a, b); + BOOST_CHECK_EQUAL(a , 30); + BOOST_CHECK_EQUAL(b , 20); + a = 20; + b = 30; + std::swap(a, b); + BOOST_CHECK_EQUAL(a , 30); + BOOST_CHECK_EQUAL(b , 20); + a = 20; + b = 30; + a = a + b * 2; + BOOST_CHECK_EQUAL(a , 20 + 30 * 2); + a = 100; + a = a - b * 2; + BOOST_CHECK_EQUAL(a , 100 - 30 * 2); + a = 20; + a = a * (b + 2); + BOOST_CHECK_EQUAL(a , 20 * (32)); + a = 20; + a = (b + 2) * a; + BOOST_CHECK_EQUAL(a , 20 * (32)); + a = 90; + b = 2; + a = a / (b + 0); + BOOST_CHECK_EQUAL(a , 45); + a = 20; + b = 30; + c = (a * b) + 22; + BOOST_CHECK_EQUAL(c , 20 * 30 + 22); + c = 22 + (a * b); + BOOST_CHECK_EQUAL(c , 20 * 30 + 22); + c = 10; + ac = a + b * c; + BOOST_CHECK_EQUAL(ac , 20 + 30 * 10); + ac = b * c + a; + BOOST_CHECK_EQUAL(ac , 20 + 30 * 10); + a = a + b * c; + BOOST_CHECK_EQUAL(a , 20 + 30 * 10); + a = 20; + b = a + b * c; + BOOST_CHECK_EQUAL(b , 20 + 30 * 10); + b = 30; + c = a + b * c; + BOOST_CHECK_EQUAL(c , 20 + 30 * 10); + c = 10; + c = a + b / c; + BOOST_CHECK_EQUAL(c , 20 + 30 / 10); + + // + // Test conditionals: + // + a = 20; + test_conditional(a, +a); + test_conditional(a, (a + 0)); + + test_signed_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>()); + // + // Test move: + // +#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES + Real m(static_cast<Real&&>(a)); + BOOST_CHECK_EQUAL(m, 20); + // Move from already moved from object: + Real m2(static_cast<Real&&>(a)); + // assign from moved from object + // (may result in "a" being left in valid state as implementation artifact): + c = static_cast<Real&&>(a); + // assignment to moved-from objects: + c = static_cast<Real&&>(m); + BOOST_CHECK_EQUAL(c, 20); + m2 = c; + BOOST_CHECK_EQUAL(c, 20); + // Destructor of "a" checks destruction of moved-from-object... + Real m3(static_cast<Real&&>(a)); +#endif +} + diff --git a/libs/multiprecision/test/test_arithmetic_ab_1.cpp b/libs/multiprecision/test/test_arithmetic_ab_1.cpp new file mode 100644 index 0000000000..140d3a190e --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_ab_1.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +# include "../performance/arithmetic_backend.hpp" + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<double> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_ab_2.cpp b/libs/multiprecision/test/test_arithmetic_ab_2.cpp new file mode 100644 index 0000000000..883adecca5 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_ab_2.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +# include "../performance/arithmetic_backend.hpp" + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<int> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_ab_3.cpp b/libs/multiprecision/test/test_arithmetic_ab_3.cpp new file mode 100644 index 0000000000..78bc4cca5b --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_ab_3.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +# include "../performance/arithmetic_backend.hpp" + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<unsigned int> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_backend_concept.cpp b/libs/multiprecision/test/test_arithmetic_backend_concept.cpp new file mode 100644 index 0000000000..680e2edc4c --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_backend_concept.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_bin_float_1.cpp b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_1.cpp new file mode 100644 index 0000000000..75f6b77485 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_1.cpp @@ -0,0 +1,29 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> number_type; + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<((std::numeric_limits<number_type>::digits / 2) > std::numeric_limits<long double>::digits ? Digits / 2 : Digits), DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::cpp_bin_float_50>(); + //test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<21> > >(); + //test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<1000, boost::multiprecision::digit_base_10, std::allocator<void> > > >(); + //test<boost::multiprecision::cpp_bin_float_quad>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_bin_float_2.cpp b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_2.cpp new file mode 100644 index 0000000000..a511b8a310 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_2.cpp @@ -0,0 +1,28 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> number_type; + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<((std::numeric_limits<number_type>::digits / 2) > std::numeric_limits<long double>::digits ? Digits / 2 : Digits), DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> type; +}; + +int main() +{ + //test<boost::multiprecision::cpp_bin_float_50>(); + test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<1000, boost::multiprecision::digit_base_10, std::allocator<void> > > >(); + //test<boost::multiprecision::cpp_bin_float_quad>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_bin_float_3.cpp b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_3.cpp new file mode 100644 index 0000000000..544bf46488 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_bin_float_3.cpp @@ -0,0 +1,28 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> number_type; + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<((std::numeric_limits<number_type>::digits / 2) > std::numeric_limits<long double>::digits ? Digits / 2 : Digits), DigitBase, Allocator, Exponent, MinExponent, MaxExponent>, ET> type; +}; + +int main() +{ + //test<boost::multiprecision::cpp_bin_float_50>(); + //test<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<1000, boost::multiprecision::digit_base_10, std::allocator<void> > > >(); + test<boost::multiprecision::cpp_bin_float_quad>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_dec_float_1.cpp b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_1.cpp new file mode 100644 index 0000000000..49e095f9a2 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_1.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::cpp_dec_float_50>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_dec_float_2.cpp b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_2.cpp new file mode 100644 index 0000000000..dae6fe2ca7 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_2.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100, long long>, boost::multiprecision::et_off> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_dec_float_3.cpp b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_3.cpp new file mode 100644 index 0000000000..d1878a94c0 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_dec_float_3.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_dec_float<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100, long long, std::allocator<void> >, boost::multiprecision::et_on> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_1.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_1.cpp new file mode 100644 index 0000000000..3cd1a30b9b --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_1.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::cpp_int>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_10.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_10.cpp new file mode 100644 index 0000000000..ff44210e02 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_10.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::checked_cpp_rational>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_11.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_11.cpp new file mode 100644 index 0000000000..de413be8b1 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_11.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<0, 0, boost::multiprecision::signed_magnitude, boost::multiprecision::checked>, boost::multiprecision::et_off> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_12.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_12.cpp new file mode 100644 index 0000000000..b132e12f3c --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_12.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<500, 500, boost::multiprecision::signed_magnitude, boost::multiprecision::checked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_13.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_13.cpp new file mode 100644 index 0000000000..d6499133b9 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_13.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_14.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_14.cpp new file mode 100644 index 0000000000..ac3ae9a7bc --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_14.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_15.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_15.cpp new file mode 100644 index 0000000000..124d1c8449 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_15.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<31, 31, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_16.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_16.cpp new file mode 100644 index 0000000000..c15581925b --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_16.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::signed_magnitude, boost::multiprecision::checked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_17.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_17.cpp new file mode 100644 index 0000000000..f31b1ca40e --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_17.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<64, 64, boost::multiprecision::unsigned_magnitude, boost::multiprecision::checked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_18.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_18.cpp new file mode 100644 index 0000000000..f04c79bcbb --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_18.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<31, 31, boost::multiprecision::signed_magnitude, boost::multiprecision::checked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_2.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_2.cpp new file mode 100644 index 0000000000..a4e8f9a434 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_2.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::int512_t >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_3.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_3.cpp new file mode 100644 index 0000000000..3f5d05063b --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_3.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::uint1024_t >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_4.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_4.cpp new file mode 100644 index 0000000000..776218f331 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_4.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::checked_cpp_int>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_5.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_5.cpp new file mode 100644 index 0000000000..fb740366a9 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_5.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::checked_int512_t >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_6.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_6.cpp new file mode 100644 index 0000000000..4ae818c342 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_6.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::checked_uint1024_t >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_7.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_7.cpp new file mode 100644 index 0000000000..fc93e67515 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_7.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::cpp_rational>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_8.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_8.cpp new file mode 100644 index 0000000000..894c9f5681 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_8.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<>, boost::multiprecision::et_off> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_9.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_9.cpp new file mode 100644 index 0000000000..787cf6106c --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_9.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<500, 500, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_cpp_int_br.cpp b/libs/multiprecision/test/test_arithmetic_cpp_int_br.cpp new file mode 100644 index 0000000000..f08a3395f5 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_cpp_int_br.cpp @@ -0,0 +1,33 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct is_twos_complement_integer<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ExpressionTemplates> > : public boost::mpl::false_ {}; + +template <> +struct related_type<boost::multiprecision::cpp_int> +{ + typedef boost::multiprecision::int256_t type; +}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ET> +struct related_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ET> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits/2, MaxBits/2, SignType, Checked, Allocator>, ET> type; +}; + +int main() +{ + test<boost::rational<boost::multiprecision::cpp_int> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_dbg_adptr1.cpp b/libs/multiprecision/test/test_arithmetic_dbg_adptr1.cpp new file mode 100644 index 0000000000..88fdc5aa75 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_dbg_adptr1.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/debug_adaptor.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::debug_adaptor<boost::multiprecision::cpp_dec_float<50> > > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_dbg_adptr2.cpp b/libs/multiprecision/test/test_arithmetic_dbg_adptr2.cpp new file mode 100644 index 0000000000..47b5529aed --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_dbg_adptr2.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/debug_adaptor.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::debug_adaptor<boost::multiprecision::cpp_int_backend<> > > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_float_128.cpp b/libs/multiprecision/test/test_arithmetic_float_128.cpp new file mode 100644 index 0000000000..aa99287b61 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_float_128.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/float128.hpp> + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::float128>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_logged_1.cpp b/libs/multiprecision/test/test_arithmetic_logged_1.cpp new file mode 100644 index 0000000000..4904797194 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_logged_1.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/logged_adaptor.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_dec_float<50> > > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_logged_2.cpp b/libs/multiprecision/test/test_arithmetic_logged_2.cpp new file mode 100644 index 0000000000..2ca2be97f4 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_logged_2.cpp @@ -0,0 +1,19 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/logged_adaptor.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::number<boost::multiprecision::logged_adaptor<boost::multiprecision::cpp_int_backend<> > > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpf.cpp b/libs/multiprecision/test/test_arithmetic_mpf.cpp new file mode 100644 index 0000000000..9f4a9be20e --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpf.cpp @@ -0,0 +1,32 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::gmp_float<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::gmp_float<D/2> > type; +}; +template <> +struct related_type<boost::multiprecision::mpf_float > +{ + typedef boost::multiprecision::mpz_int type; +}; + +int main() +{ + boost::multiprecision::mpf_float::default_precision(1000); + BOOST_CHECK_EQUAL(boost::multiprecision::mpf_float::default_precision() , 1000); + test<boost::multiprecision::mpf_float>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpf_50.cpp b/libs/multiprecision/test/test_arithmetic_mpf_50.cpp new file mode 100644 index 0000000000..4d87dd6704 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpf_50.cpp @@ -0,0 +1,30 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> + +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::gmp_float<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::gmp_float<D/2> > type; +}; +template <> +struct related_type<boost::multiprecision::mpf_float > +{ + typedef boost::multiprecision::mpz_int type; +}; + +int main() +{ + test<boost::multiprecision::mpf_float_50>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpfi_50.cpp b/libs/multiprecision/test/test_arithmetic_mpfi_50.cpp new file mode 100644 index 0000000000..7088dd9bbf --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpfi_50.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/mpfi.hpp> +#define TEST_MPFR +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::mpfi_float_backend<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::mpfi_float_backend<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::mpfi_float_50>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpfr.cpp b/libs/multiprecision/test/test_arithmetic_mpfr.cpp new file mode 100644 index 0000000000..8ce8ef39df --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpfr.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/mpfr.hpp> +#define TEST_MPFR +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::mpfr_float>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpfr_50.cpp b/libs/multiprecision/test/test_arithmetic_mpfr_50.cpp new file mode 100644 index 0000000000..cff50b0cf1 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpfr_50.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/mpfr.hpp> +#define TEST_MPFR +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::mpfr_float_50>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpfr_50_static.cpp b/libs/multiprecision/test/test_arithmetic_mpfr_50_static.cpp new file mode 100644 index 0000000000..5928cd4b77 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpfr_50_static.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/mpfr.hpp> +#define TEST_MPFR +#include "test_arithmetic.hpp" + +template <unsigned D> +struct related_type<boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D> > > +{ + typedef boost::multiprecision::number< boost::multiprecision::mpfr_float_backend<D/2> > type; +}; + +int main() +{ + test<boost::multiprecision::static_mpfr_float_50>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpq.cpp b/libs/multiprecision/test/test_arithmetic_mpq.cpp new file mode 100644 index 0000000000..9c95177401 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpq.cpp @@ -0,0 +1,25 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> + +#include "test_arithmetic.hpp" + +template <> +struct related_type<boost::multiprecision::mpq_rational> +{ + typedef boost::multiprecision::mpz_int type; +}; + +int main() +{ + test<boost::multiprecision::mpq_rational>(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpz.cpp b/libs/multiprecision/test/test_arithmetic_mpz.cpp new file mode 100644 index 0000000000..b1306d3a01 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpz.cpp @@ -0,0 +1,21 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/rational_adaptor.hpp> + +#include "test_arithmetic.hpp" + +int main() +{ + test<boost::multiprecision::mpz_int>(); + test<boost::multiprecision::number<boost::multiprecision::rational_adaptor<boost::multiprecision::gmp_int> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_mpz_br.cpp b/libs/multiprecision/test/test_arithmetic_mpz_br.cpp new file mode 100644 index 0000000000..ff153cb6ba --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_mpz_br.cpp @@ -0,0 +1,32 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> + +#define NO_MIXED_OPS + +#include "test_arithmetic.hpp" +#include <boost/rational.hpp> + +template <class T> +struct is_boost_rational<boost::rational<T> > : public boost::mpl::true_{}; + +namespace boost{ namespace multiprecision{ + +template<> +struct number_category<rational<mpz_int> > : public mpl::int_<number_kind_rational> {}; + +}} + +int main() +{ + test<boost::rational<boost::multiprecision::mpz_int> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_tommath.cpp b/libs/multiprecision/test/test_arithmetic_tommath.cpp new file mode 100644 index 0000000000..3207001c00 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_tommath.cpp @@ -0,0 +1,23 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/tommath.hpp> + +#include "test_arithmetic.hpp" + +template <> +struct is_twos_complement_integer<boost::multiprecision::tom_int> : public boost::mpl::false_ {}; + +int main() +{ + test<boost::multiprecision::tom_int>(); + test<boost::multiprecision::number<boost::multiprecision::rational_adaptor<boost::multiprecision::tommath_int> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_arithmetic_tommath_br.cpp b/libs/multiprecision/test/test_arithmetic_tommath_br.cpp new file mode 100644 index 0000000000..cd06371d22 --- /dev/null +++ b/libs/multiprecision/test/test_arithmetic_tommath_br.cpp @@ -0,0 +1,32 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/tommath.hpp> + +#define NO_MIXED_OPS +#include "test_arithmetic.hpp" + +#include <boost/rational.hpp> + +template <class T> +struct is_boost_rational<boost::rational<T> > : public boost::mpl::true_{}; + +namespace boost{ namespace multiprecision{ + +template<> +struct number_category<rational<tom_int> > : public mpl::int_<number_kind_rational> {}; + +}} + +int main() +{ + test<boost::rational<boost::multiprecision::tom_int> >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_asin.cpp b/libs/multiprecision/test/test_asin.cpp new file mode 100644 index 0000000000..5891068421 --- /dev/null +++ b/libs/multiprecision/test/test_asin.cpp @@ -0,0 +1,143 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array<boost::array<T, 2>, 6> exact_data = + {{ + {{ 0.5, static_cast<T>("0.523598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752213717775") }}, + {{ 0.25, static_cast<T>("0.252680255142078653485657436993710972252193733096838193633923778740575060481021222411748742228014601605092602909414066566") }}, + {{0.75, static_cast<T>("0.848062078981481008052944338998418080073366213263112642860718163570200821228474234349189801731957230300995227265307531834") }}, + {{std::ldexp(1.0, -20), static_cast<T>("9.53674316406394560289664793089102218648031077292419572854816420395098616062014311172490017625353237219958438022056661501e-7") }}, + {{ 1 - std::ldexp(1.0, -20), static_cast<T>("1.56941525875313420204921285316218397515809899320201864334535204504240776023375739189119474528488143494473216475057072728") }}, + {{ 1, static_cast<T>("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064") }}, + }}; + unsigned max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = asin(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + val = asin(-exact_data[k][0]); + e = relative_error(val, T(-exact_data[k][1])); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + BOOST_TEST(asin(T(0)) == 0); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_atan.cpp b/libs/multiprecision/test/test_atan.cpp new file mode 100644 index 0000000000..49ab34dce2 --- /dev/null +++ b/libs/multiprecision/test/test_atan.cpp @@ -0,0 +1,297 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +template <class T> +T atan2_def(T y, T x) +{ + T t; + t.backend() = boost::multiprecision::default_ops::get_constant_pi<typename T::backend_type>(); + T t2; + if(x) + t2 = atan(y / x); + else + t2 = y.sign() * t / 2; + return t2 + (t / 2) * (1 - x.sign()) * T(y.sign() + 0.5).sign(); +} + +template <class T> +struct is_mpfr_type : public boost::mpl::false_ {}; + +#ifdef TEST_MPFR_50 +template <unsigned Digits10> +struct is_mpfr_type<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<Digits10> > > : public boost::mpl::true_{}; +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<const char*, 51u> data = + {{ + "9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-101", + 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"1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017312671058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730507638560496657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138", + "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412661058533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163657440030136963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138", + "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671057533991074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803963457903970195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138", + "1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671058533891074043256641153323546922304775291115862679704064240558725142051350969260552779822311474477465190982214405487832966723064237824116893391582635600954572824283461730174305227163324106696803630124570637195626836636491127420774093793814747960379191015517279628513338998598607743566594025406809304089138", + }}; + + T arg = static_cast<T>("1e-100"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = atan(arg); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + val = atan(-arg); + e = relative_error(val, T(-T(data[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + arg *= 10000; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 10); + BOOST_TEST(atan(T(0)) == 0); + + // + // And again, but test all the phases of atan2: + // + arg = static_cast<T>("1e-100"); + unsigned err; + for(unsigned k = 0; k < data.size(); k++) + { + T val = atan2(arg, 1); + T e = relative_error(val, atan2_def(arg, T(1))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = atan2(-arg, 1); + e = relative_error(val, atan2_def(T(-arg), T(1))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = atan2(arg, -1); + e = relative_error(val, atan2_def(arg, T(-1))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = atan2(-arg, -1); + e = relative_error(val, atan2_def(T(-arg), T(-1))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + arg *= 10000; + } + // + // special cases: + // + err = relative_error(T(atan2(T(0), T(1))), atan2_def(T(0), T(1))).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + if(!boost::multiprecision::is_interval_number<T>::value) + { + // We don't test this with intervals as [-0,0] leads to strange behaviour in atan2... + err = relative_error(T(atan2(T(0), T(-1))), atan2_def(T(0), T(-1))).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + + T pi; + pi.backend() = boost::multiprecision::default_ops::get_constant_pi<typename T::backend_type>(); + + err = relative_error(T(atan2(T(1), T(0))), T(pi / 2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + + err = relative_error(T(atan2(T(-1), T(0))), T(pi / -2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + + T mv = (std::numeric_limits<T>::max)(); + err = relative_error(T(atan2(mv, T(1))), T(pi / 2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + err = relative_error(T(atan2(-mv, T(1))), T(pi / -2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + + if(std::numeric_limits<T>::has_infinity) + { + mv = (std::numeric_limits<T>::infinity)(); + err = relative_error(T(atan2(mv, T(1))), T(pi / 2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + err = relative_error(T(atan2(-mv, T(1))), T(pi / -2)).template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 2000); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_checked_cpp_int.cpp b/libs/multiprecision/test/test_checked_cpp_int.cpp new file mode 100644 index 0000000000..847760d243 --- /dev/null +++ b/libs/multiprecision/test/test_checked_cpp_int.cpp @@ -0,0 +1,116 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include "test.hpp" + +template <class Number> +void test() +{ + using namespace boost::multiprecision; + typedef Number test_type; + + if(std::numeric_limits<test_type>::is_bounded) + { + test_type val = (std::numeric_limits<test_type>::max)(); + BOOST_CHECK_THROW(++val, std::overflow_error); + val = (std::numeric_limits<test_type>::max)(); + BOOST_CHECK_THROW(test_type(1 + val), std::overflow_error); + BOOST_CHECK_THROW(test_type(val + 1), std::overflow_error); + BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error); + val /= 2; + val += 1; + BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error); + + if(std::numeric_limits<test_type>::is_signed) + { + val = (std::numeric_limits<test_type>::min)(); + BOOST_CHECK_THROW(--val, std::overflow_error); + val = (std::numeric_limits<test_type>::min)(); + BOOST_CHECK_THROW(test_type(val - 1), std::overflow_error); + BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error); + val /= 2; + val -= 1; + BOOST_CHECK_THROW(test_type(2 * val), std::overflow_error); + } + else + { + val = (std::numeric_limits<test_type>::min)(); + BOOST_CHECK_THROW(--val, std::range_error); + val = (std::numeric_limits<test_type>::min)(); + BOOST_CHECK_THROW(test_type(val - 1), std::range_error); + } + } + + if(std::numeric_limits<test_type>::is_signed) + { + test_type a = -1; + test_type b = 1; + BOOST_CHECK_THROW(test_type(a | b), std::range_error); + BOOST_CHECK_THROW(test_type(a & b), std::range_error); + BOOST_CHECK_THROW(test_type(a ^ b), std::range_error); + } + else + { + // Constructing from a negative value is not allowed: + BOOST_CHECK_THROW(test_type(-2), std::range_error); + BOOST_CHECK_THROW(test_type("-2"), std::range_error); + } + if(std::numeric_limits<test_type>::digits < std::numeric_limits<long long>::digits) + { + long long llm = (std::numeric_limits<long long>::max)(); + test_type t; + BOOST_CHECK_THROW(t = llm, std::range_error); + BOOST_CHECK_THROW(t = static_cast<test_type>(llm), std::range_error); + unsigned long long ullm = (std::numeric_limits<unsigned long long>::max)(); + BOOST_CHECK_THROW(t = ullm, std::range_error); + BOOST_CHECK_THROW(t = static_cast<test_type>(ullm), std::range_error); + + static const checked_uint512_t big = (std::numeric_limits<checked_uint512_t>::max)(); + BOOST_CHECK_THROW(t = static_cast<test_type>(big), std::range_error); + } + // + // String errors: + // + BOOST_CHECK_THROW(test_type("12A"), std::runtime_error); + BOOST_CHECK_THROW(test_type("0658"), std::runtime_error); + + if(std::numeric_limits<test_type>::is_signed) + { + BOOST_CHECK_THROW(test_type(-2).str(0, std::ios_base::hex), std::runtime_error); + BOOST_CHECK_THROW(test_type(-2).str(0, std::ios_base::oct), std::runtime_error); + } +} + +int main() +{ + using namespace boost::multiprecision; + + test<number<cpp_int_backend<0, 0, signed_magnitude, checked> > >(); + test<checked_int512_t>(); + test<checked_uint512_t>(); + test<number<cpp_int_backend<32, 32, signed_magnitude, checked, void> > >(); + test<number<cpp_int_backend<32, 32, unsigned_magnitude, checked, void> > >(); + + // + // We also need to test type with "odd" bit counts in order to ensure full code coverage: + // + test<number<cpp_int_backend<528, 528, signed_magnitude, checked, void> > >(); + test<number<cpp_int_backend<528, 528, unsigned_magnitude, checked, void> > >(); + test<number<cpp_int_backend<48, 48, signed_magnitude, checked, void> > >(); + test<number<cpp_int_backend<48, 48, unsigned_magnitude, checked, void> > >(); + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_constants.cpp b/libs/multiprecision/test/test_constants.cpp new file mode 100644 index 0000000000..b7f6afe91c --- /dev/null +++ b/libs/multiprecision/test/test_constants.cpp @@ -0,0 +1,198 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50) +# define TEST_MPF_50 +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif + +#include "test.hpp" + +static const char* ln2 = +"0.693147180559945309417232121458176568075500134360255254120680009493393621969694" +"71560586332699641868754200148102057068573368552023575813055703267075163507596193" +"07275708283714351903070386238916734711233501153644979552391204751726815749320651" +"55524734139525882950453007095326366642654104239157814952043740430385500801944170" +"64167151864471283996817178454695702627163106454615025720740248163777338963855069" +"52606683411372738737229289564935470257626520988596932019650585547647033067936544" +"32547632744951250406069438147104689946506220167720424524529612687946546193165174" +"68139267250410380254625965686914419287160829380317271436778265487756648508567407" +"76484514644399404614226031930967354025744460703080960850474866385231381816767514" +"38667476647890881437141985494231519973548803751658612753529166100071053558249879" +"41472950929311389715599820565439287170007218085761025236889213244971389320378439" +"35308877482597017155910708823683627589842589185353024363421436706118923678919237" +"23146723217205340164925687274778234453534764811494186423867767744060695626573796" +"00867076257199184734022651462837904883062033061144630073719489002743643965002580" +"93651944304119115060809487930678651588709006052034684297361938412896525565396860" +"22194122924207574321757489097706752687115817051137009158942665478595964890653058" +"46025866838294002283300538207400567705304678700184162404418833232798386349001563" +"12188956065055315127219939833203075140842609147900126516824344389357247278820548" +"62715527418772430024897945401961872339808608316648114909306675193393128904316413" +"70681397776498176974868903887789991296503619270710889264105230924783917373501229" +"84242049956893599220660220465494151061391878857442455775102068370308666194808964" +"12186807790208181588580001688115973056186676199187395200766719214592236720602539" +"59543654165531129517598994005600036651356756905124592682574394648316833262490180" +"38242408242314523061409638057007025513877026817851630690255137032340538021450190" +"15374029509942262995779647427138157363801729873940704242179972266962979939312706" +"93574724049338653087975872169964512944649188377115670167859880498183889678413493" +"83140140731664727653276359192335112333893387095132090592721854713289754707978913" +"84445466676192702885533423429899321803769154973340267546758873236778342916191810" +"43011609169526554785973289176354555674286387746398710191243175425588830120677921" +"02803412068797591430812833072303008834947057924965910058600123415617574132724659" +"43068435465211135021544341539955381856522750221424566440006276183303206472725721" +"97515290827856842132079598863896727711955221881904660395700977470651261950527893" +"22960889314056254334425523920620303439417773579455921259019925591148440242390125" +"54259003129537051922061506434583787873002035414421785758013236451660709914383145" +"00498589668857722214865288216941812704886075897220321666312837832915676307498729" +"85746389282693735098407780493950049339987626475507031622161390348452994249172483" +"73406136622638349368111684167056925214751383930638455371862687797328895558871634" +"429756244755392366369488877823890174981027"; +static const char* pi = +"3.141592653589793238462643383279502884197169399375105820974944592307816406286208" +"99862803482534211706798214808651328230664709384460955058223172535940812848111745" +"02841027019385211055596446229489549303819644288109756659334461284756482337867831" +"65271201909145648566923460348610454326648213393607260249141273724587006606315588" +"17488152092096282925409171536436789259036001133053054882046652138414695194151160" +"94330572703657595919530921861173819326117931051185480744623799627495673518857527" +"24891227938183011949129833673362440656643086021394946395224737190702179860943702" +"77053921717629317675238467481846766940513200056812714526356082778577134275778960" +"91736371787214684409012249534301465495853710507922796892589235420199561121290219" +"60864034418159813629774771309960518707211349999998372978049951059731732816096318" +"59502445945534690830264252230825334468503526193118817101000313783875288658753320" +"83814206171776691473035982534904287554687311595628638823537875937519577818577805" +"32171226806613001927876611195909216420198938095257201065485863278865936153381827" +"96823030195203530185296899577362259941389124972177528347913151557485724245415069" +"59508295331168617278558890750983817546374649393192550604009277016711390098488240" +"12858361603563707660104710181942955596198946767837449448255379774726847104047534" +"64620804668425906949129331367702898915210475216205696602405803815019351125338243" +"00355876402474964732639141992726042699227967823547816360093417216412199245863150" +"30286182974555706749838505494588586926995690927210797509302955321165344987202755" +"96023648066549911988183479775356636980742654252786255181841757467289097777279380" +"00816470600161452491921732172147723501414419735685481613611573525521334757418494" +"68438523323907394143334547762416862518983569485562099219222184272550254256887671" +"79049460165346680498862723279178608578438382796797668145410095388378636095068006" +"42251252051173929848960841284886269456042419652850222106611863067442786220391949" +"45047123713786960956364371917287467764657573962413890865832645995813390478027590" +"09946576407895126946839835259570982582262052248940772671947826848260147699090264" +"01363944374553050682034962524517493996514314298091906592509372216964615157098583" +"87410597885959772975498930161753928468138268683868942774155991855925245953959431" +"04997252468084598727364469584865383673622262609912460805124388439045124413654976" +"27807977156914359977001296160894416948685558484063534220722258284886481584560285" +"06016842739452267467678895252138522549954666727823986456596116354886230577456498" +"03559363456817432411251507606947945109659609402522887971089314566913686722874894" +"05601015033086179286809208747609178249385890097149096759852613655497818931297848" +"21682998948722658804857564014270477555132379641451523746234364542858444795265867" +"82105114135473573952311342716610213596953623144295248493718711014576540359027993" +"44037420073105785390621983874478084784896833214457138687519435064302184531910484" +"81005370614680674919278191197939952061419663428754440643745123718192179998391015" +"91956181467514269123974894090718649423196"; +static const char* e = +"2.718281828459045235360287471352662497757247093699959574966967627724076630353547" +"59457138217852516642742746639193200305992181741359662904357290033429526059563073" +"81323286279434907632338298807531952510190115738341879307021540891499348841675092" +"44761460668082264800168477411853742345442437107539077744992069551702761838606261" +"33138458300075204493382656029760673711320070932870912744374704723069697720931014" +"16928368190255151086574637721112523897844250569536967707854499699679468644549059" +"87931636889230098793127736178215424999229576351482208269895193668033182528869398" +"49646510582093923982948879332036250944311730123819706841614039701983767932068328" +"23764648042953118023287825098194558153017567173613320698112509961818815930416903" +"51598888519345807273866738589422879228499892086805825749279610484198444363463244" +"96848756023362482704197862320900216099023530436994184914631409343173814364054625" +"31520961836908887070167683964243781405927145635490613031072085103837505101157477" +"04171898610687396965521267154688957035035402123407849819334321068170121005627880" 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+"72721155519486685080036853228183152196003735625279449515828418829478761085263981" +"39559900673764829224437528718462457803619298197139914756448826260390338144182326" +"25150974827987779964373089970388867782271383605772978824125611907176639465070633" +"04527954661855096666185664709711344474016070462621568071748187784437143698821855" +"96709591025968620023537185887485696522000503117343920732113908032936344797273559" +"55277349071783793421637012050054513263835440001863239914907054797780566978533580" +"48966906295119432473099587655236812859041383241160722602998330535370876138939639" +"17795745401613722361878936526053815584158718692553860616477983402543512843961294" +"60352913325942794904337299085731580290958631382683291477116396337092400316894586" +"36060645845925126994655724839186564209752685082307544254599376917041977780085362" +"73094171016343490769642372229435236612557250881477922315197477806056967253801718" +"07763603462459278778465850656050780844211529697521890874019660906651803516501792" +"50461950136658543663271254963990854914420001457476081930221206602433009641270489" +"43903971771951806990869986066365832322787"; + +template <class T> +inline bool is_mpfr(const T&) +{ + return false; +} +#if defined(TEST_MPFR_50) +template <unsigned N, boost::multiprecision::expression_template_option ET> +inline bool is_mpfr(const boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<N>, ET>&) +{ + return true; +} +#endif + +template <class T> +void test() +{ + typedef typename T::backend_type backend_type; + T num, expect; + num.backend() = boost::multiprecision::default_ops::get_constant_pi<backend_type>(); + expect = static_cast<T>(pi); + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits<T>::epsilon() * (is_mpfr(num) ? 1200 : 2)); + num.backend() = boost::multiprecision::default_ops::get_constant_ln2<backend_type>(); + expect = static_cast<T>(ln2); + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits<T>::epsilon() * (is_mpfr(num) ? 30 : 1)); + num.backend() = boost::multiprecision::default_ops::get_constant_e<backend_type>(); + expect = static_cast<T>(e); + BOOST_CHECK_CLOSE_FRACTION(num, expect, std::numeric_limits<T>::epsilon() * (is_mpfr(num) ? 2 : 1)); +} + +int main() +{ +#ifdef TEST_MPFR_50 + test<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<2000> > >(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<2000> > >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::number<boost::multiprecision::gmp_float<2000> > >(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_constexpr.cpp b/libs/multiprecision/test/test_constexpr.cpp new file mode 100644 index 0000000000..d90cfe32d3 --- /dev/null +++ b/libs/multiprecision/test/test_constexpr.cpp @@ -0,0 +1,61 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#if defined(HAVE_FLOAT128) +#include <boost/multiprecision/float128.hpp> +#endif + +#ifndef BOOST_NO_CXX11_CONSTEXPR + +template <class T> +void silence_unused(const T&){} + +template <class T> +void test1() +{ + constexpr T i1 = 2u; + constexpr T i2; + constexpr T i3 = -3; + constexpr T i4(i1); + + silence_unused(i1); + silence_unused(i2); + silence_unused(i3); + silence_unused(i4); +} +template <class T> +void test2() +{ + constexpr T i1 = 2u; + constexpr T i2; + constexpr T i3 = -3; + + silence_unused(i1); + silence_unused(i2); + silence_unused(i3); +} +template <class T> +void test3() +{ + constexpr T i1 = 2u; + constexpr T i2; + + silence_unused(i1); + silence_unused(i2); +} + +using namespace boost::multiprecision; + +template void test1<number<cpp_int_backend<64, 64, unsigned_magnitude, unchecked, void>, et_off> >(); +template void test1<number<cpp_int_backend<64, 64, signed_magnitude, unchecked, void>, et_off> >(); +template void test3<number<cpp_int_backend<2048, 2048, unsigned_magnitude, unchecked, void>, et_off> >(); +template void test2<number<cpp_int_backend<2048, 2048, signed_magnitude, unchecked, void>, et_off> >(); + +#if defined(HAVE_FLOAT128) +template void test1<float128>(); +#endif + +#endif diff --git a/libs/multiprecision/test/test_cos.cpp b/libs/multiprecision/test/test_cos.cpp new file mode 100644 index 0000000000..ee48a85cb6 --- /dev/null +++ b/libs/multiprecision/test/test_cos.cpp @@ -0,0 +1,361 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type " << typeid(T).name() << std::endl; + static const boost::array<const char*, 101u> data = + {{ + 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max_err = err; + val = cos(-euler_gamma * ((100 * k) - 5000)); + e = relative_error(val, T(data[k])); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 5000000000ULL); + + static const boost::array<const char*, 51u> near_one = + {{ + "0.001103662615143147017601393734232421549156847219973314118949247990939859507971857976111288683988415478257878902917354105871236439563170045857810738102729287303674642020538722348587741395785016549139854168605590336633274890874911975139498047488076101124170425114828336211817830671418321600962996502656221412102902998671173649312277667706874059520046508702908872747388744526457997404065469953155187340837", + 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static_cast<T>("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"); + + max_err = 0; + for(unsigned k = 0; k < near_one.size(); k++) + { + static const T euler_gamma = static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); + T val = cos(half_pi - (euler_gamma + k) / 523); + T e = relative_error(val, T(near_one[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + val = cos(-half_pi + (euler_gamma + k) / 523); + e = relative_error(val, T(near_one[k])); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; +#if defined(BOOST_INTEL) && defined(TEST_FLOAT128) + BOOST_TEST(max_err < 8000); +#else + BOOST_TEST(max_err < 750); +#endif + + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array<boost::array<T, 2>, 8> exact_data = + {{ + {{ 0.5, static_cast<T>("0.877582561890372716116281582603829651991645197109744052997610868315950763274213947405794184084682258355478400593109053993") }}, + {{ 0.25, static_cast<T>("0.968912421710644784144595449494189199804134190287442831148128124288942561184523327264655202799685025510352709626116202617") }}, + {{0.75, static_cast<T>("0.731688868873820886311838753000084543840541276050772482507683220220750082501569499540967562610201174960122884908227300721") }}, + {{std::ldexp(1.0, -20), static_cast<T>("0.99999999999954525264911357034690133684385823577463126432241468890539365027135494672267164697779879113636143901797362388") }}, + {{ 2, static_cast<T>("-0.416146836547142386997568229500762189766000771075544890755149973781964936124079169074531777860169140367366791365215728559") }}, + {{ 5, static_cast<T>("0.283662185463226264466639171513557308334422592252215944930359066586151456767382702286176981668344573238827368717546699737") }}, + {{ 10, static_cast<T>("-0.839071529076452452258863947824064834519930165133168546835953731048792586866270768400933712760422138927451054405350243624") }}, + {{ 8.5, static_cast<T>("-0.60201190268482361534842652295699870029606776360435523539636606145572515876770619546025351418378467287262574566665150299") }} + }}; + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = cos(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + val = cos(-exact_data[k][0]); + e = relative_error(val, exact_data[k][1]); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + BOOST_TEST(cos(T(0)) == 1); +#if defined(BOOST_INTEL) && defined(TEST_FLOAT128) + BOOST_TEST(fabs(cos(half_pi)) < 4 * std::numeric_limits<T>::epsilon()); +#else + BOOST_TEST(fabs(cos(half_pi)) < std::numeric_limits<T>::epsilon()); +#endif + +#include "sincos.ipp" + max_err = 0; + for(unsigned k = 0; k < sincos.size(); k++) + { + T val = cos(sincos[k][0]); + T e = relative_error(val, sincos[k][2]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cosh.cpp b/libs/multiprecision/test/test_cosh.cpp new file mode 100644 index 0000000000..97bb068a8e --- /dev/null +++ b/libs/multiprecision/test/test_cosh.cpp @@ -0,0 +1,188 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<const char*, 51u> data = + {{ + 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"3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024", + "1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067", + "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110", + }}; + + T eg = static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::cosh(x * x); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + std::cout << x * x << std::endl; + max_err = err; + } + val = boost::multiprecision::cosh(-x * x); + e = relative_error(val, T(data[k])); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + std::cout << x * x << std::endl; + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 2000); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_bin_float.cpp b/libs/multiprecision/test/test_cpp_bin_float.cpp new file mode 100644 index 0000000000..9bcae51b4a --- /dev/null +++ b/libs/multiprecision/test/test_cpp_bin_float.cpp @@ -0,0 +1,221 @@ +// Copyright John Maddock 2013. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> +#ifdef TEST_MPFR +#include <boost/multiprecision/mpfr.hpp> +#endif +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include "libs/multiprecision/test/test.hpp" +#include <iostream> +#include <iomanip> + +template <class T> +T generate_random() +{ + typedef int e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution<e_type> ui(-20, 20); + return ldexp(val, ui(gen)); +} + + +using namespace boost::multiprecision; +#ifdef TEST_MPFR +typedef number<mpfr_float_backend<35> > good_type; +#else +typedef double good_type; +#endif +typedef number<cpp_bin_float<std::numeric_limits<good_type>::digits, digit_base_2>, et_off> test_type; + +void test_special_cases() +{ + test_type max_val = (std::numeric_limits<test_type>::max)(); + test_type min_val = (std::numeric_limits<test_type>::min)(); + test_type eps = std::numeric_limits<test_type>::epsilon(); + test_type inf_val = (std::numeric_limits<test_type>::infinity)(); + test_type nan_val = (std::numeric_limits<test_type>::quiet_NaN)(); + test_type half = 0.5; + test_type one_point_5 = 1.5; + + BOOST_CHECK((boost::math::isnormal)(max_val)); + BOOST_CHECK((boost::math::isnormal)(-max_val)); + BOOST_CHECK((boost::math::isnormal)(min_val)); + BOOST_CHECK((boost::math::isnormal)(-min_val)); + BOOST_CHECK((boost::math::isinf)(inf_val)); + BOOST_CHECK((boost::math::isinf)(-inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val)); + BOOST_CHECK((boost::math::isnan)(-nan_val)); + + if(std::numeric_limits<test_type>::has_denorm) + min_val = std::numeric_limits<test_type>::denorm_min(); + + BOOST_CHECK(test_type(1) + eps != test_type(1)); + BOOST_CHECK(test_type(1) + eps / 2 == test_type(1)); + + // Overflow: + BOOST_CHECK_EQUAL(max_val + max_val * eps, inf_val); + BOOST_CHECK_EQUAL(-max_val - max_val * eps, -inf_val); + BOOST_CHECK_EQUAL(max_val * 2, inf_val); + BOOST_CHECK_EQUAL(max_val * -2, -inf_val); + BOOST_CHECK_EQUAL(max_val / half, inf_val); + BOOST_CHECK_EQUAL(max_val / -half, -inf_val); + // Underflow: + BOOST_CHECK_EQUAL(min_val * 2 - one_point_5 * min_val, 0); + BOOST_CHECK_EQUAL(-min_val * 2 + one_point_5 * min_val, 0); + BOOST_CHECK_EQUAL(min_val / 2, 0); + BOOST_CHECK_EQUAL(min_val * half, 0); + BOOST_CHECK_EQUAL(min_val - min_val, 0); + BOOST_CHECK_EQUAL(max_val - max_val, 0); + BOOST_CHECK_EQUAL(-min_val + min_val, 0); + BOOST_CHECK_EQUAL(-max_val + max_val, 0); + // Things involving zero: + BOOST_CHECK_EQUAL(max_val + 0, max_val); + BOOST_CHECK_EQUAL(max_val - 0, max_val); + BOOST_CHECK_EQUAL(0 + max_val, max_val); + BOOST_CHECK_EQUAL(0 - max_val, -max_val); + BOOST_CHECK_EQUAL(max_val * 0, 0); + BOOST_CHECK_EQUAL(0 * max_val, 0); + BOOST_CHECK_EQUAL(max_val / 0, inf_val); + BOOST_CHECK_EQUAL(0 / max_val, 0); + BOOST_CHECK_EQUAL(-max_val / 0, -inf_val); + BOOST_CHECK_EQUAL(0 / -max_val, 0); + // Things involving infinity: + BOOST_CHECK_EQUAL(inf_val + 2, inf_val); + BOOST_CHECK_EQUAL(inf_val + inf_val, inf_val); + BOOST_CHECK_EQUAL(-inf_val - 2, -inf_val); + BOOST_CHECK_EQUAL(inf_val - 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val + 2, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val - inf_val)); + BOOST_CHECK_EQUAL(inf_val * 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val * 2, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val * 0)); + BOOST_CHECK((boost::math::isnan)(-inf_val * 0)); + BOOST_CHECK_EQUAL(inf_val / 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val / 2, -inf_val); + BOOST_CHECK_EQUAL(inf_val / 0, inf_val); + BOOST_CHECK_EQUAL(-inf_val / 0, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val / inf_val)); + BOOST_CHECK((boost::math::isnan)(-inf_val / inf_val)); + // Things involving nan: + BOOST_CHECK((boost::math::isnan)(nan_val + 2)); + BOOST_CHECK((boost::math::isnan)(nan_val - 2)); + BOOST_CHECK((boost::math::isnan)(nan_val + 0)); + BOOST_CHECK((boost::math::isnan)(nan_val - 0)); + BOOST_CHECK((boost::math::isnan)(nan_val + inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val - inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val + nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val - nan_val)); + BOOST_CHECK((boost::math::isnan)(2 + nan_val)); + BOOST_CHECK((boost::math::isnan)(2 - nan_val)); + BOOST_CHECK((boost::math::isnan)(0 - nan_val)); + BOOST_CHECK((boost::math::isnan)(0 - nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val + nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val - nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val * 2)); + BOOST_CHECK((boost::math::isnan)(nan_val / 2)); + BOOST_CHECK((boost::math::isnan)(nan_val * 0)); + BOOST_CHECK((boost::math::isnan)(nan_val / 0)); + BOOST_CHECK((boost::math::isnan)(nan_val * inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val / inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val * nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val / nan_val)); + BOOST_CHECK((boost::math::isnan)(2 * nan_val)); + BOOST_CHECK((boost::math::isnan)(2 / nan_val)); + BOOST_CHECK((boost::math::isnan)(0 / nan_val)); + BOOST_CHECK((boost::math::isnan)(0 / nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val * nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val / nan_val)); +} + +int main() +{ + test_special_cases(); + unsigned error_count = 0; + for(unsigned i = 0; i < 100000; ++i) + { + good_type a = generate_random<good_type>(); + good_type b = generate_random<good_type>(); + test_type ta(a); + test_type tb(b); + + BOOST_CHECK_EQUAL(test_type(a * b), ta * tb); + BOOST_CHECK_EQUAL(test_type(-a * b), -ta * tb); + BOOST_CHECK_EQUAL(test_type(a * -b), ta * -tb); + BOOST_CHECK_EQUAL(test_type(-a * -b), -ta * -tb); + + BOOST_CHECK_EQUAL(test_type(a + b), ta + tb); + BOOST_CHECK_EQUAL(test_type(-a + b), -ta + tb); + BOOST_CHECK_EQUAL(test_type(a + -b), ta + -tb); + BOOST_CHECK_EQUAL(test_type(-a + -b), -ta + -tb); + + BOOST_CHECK_EQUAL(test_type(a - b), ta - tb); + BOOST_CHECK_EQUAL(test_type(-a - b), -ta - tb); + BOOST_CHECK_EQUAL(test_type(a - -b), ta - -tb); + BOOST_CHECK_EQUAL(test_type(-a - -b), -ta - -tb); + + BOOST_CHECK_EQUAL(test_type(a / b), ta / tb); + BOOST_CHECK_EQUAL(test_type(-a / b), -ta / tb); + BOOST_CHECK_EQUAL(test_type(a / -b), ta / -tb); + BOOST_CHECK_EQUAL(test_type(-a / -b), -ta / -tb); + + BOOST_CHECK_EQUAL(test_type(sqrt(a)), sqrt(ta)); + BOOST_CHECK_EQUAL(test_type(floor(a)), floor(ta)); + BOOST_CHECK_EQUAL(test_type(floor(-a)), floor(-ta)); + BOOST_CHECK_EQUAL(test_type(ceil(a)), ceil(ta)); + BOOST_CHECK_EQUAL(test_type(ceil(-a)), ceil(-ta)); + + static boost::random::mt19937 i_gen; + + int si = i_gen(); + BOOST_CHECK_EQUAL(test_type(a * si), ta * si); + BOOST_CHECK_EQUAL(test_type(-a * si), -ta * si); + BOOST_CHECK_EQUAL(test_type(-a * -si), -ta * -si); + BOOST_CHECK_EQUAL(test_type(a * -si), ta * -si); + unsigned ui = std::abs(si); + BOOST_CHECK_EQUAL(test_type(a * ui), ta * ui); + BOOST_CHECK_EQUAL(test_type(-a * ui), -ta * ui); + + // Divide: + BOOST_CHECK_EQUAL(test_type(a / si), ta / si); + BOOST_CHECK_EQUAL(test_type(-a / si), -ta / si); + BOOST_CHECK_EQUAL(test_type(-a / -si), -ta / -si); + BOOST_CHECK_EQUAL(test_type(a / -si), ta / -si); + BOOST_CHECK_EQUAL(test_type(a / ui), ta / ui); + BOOST_CHECK_EQUAL(test_type(-a / ui), -ta / ui); + // Error reporting: + if(boost::detail::test_errors() != error_count) + { + error_count = boost::detail::test_errors(); + std::cout << std::setprecision(std::numeric_limits<test_type>::max_digits10) << std::scientific; + std::cout << "a (mpfr) = " << a << std::endl; + std::cout << "a (test) = " << ta << std::endl; + std::cout << "b (mpfr) = " << b << std::endl; + std::cout << "b (test) = " << tb << std::endl; + std::cout << "si = " << si << std::endl; + std::cout << "ui = " << ui << std::endl; + } + } + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_cpp_bin_float_io.cpp b/libs/multiprecision/test/test_cpp_bin_float_io.cpp new file mode 100644 index 0000000000..9fe628e94a --- /dev/null +++ b/libs/multiprecision/test/test_cpp_bin_float_io.cpp @@ -0,0 +1,271 @@ +// Copyright John Maddock 2013. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> + +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/chrono.hpp> +#include "test.hpp" +#include <boost/array.hpp> +#include <iostream> +#include <iomanip> + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + + +void print_flags(std::ios_base::fmtflags f) +{ + std::cout << "Formatting flags were: "; + if(f & std::ios_base::scientific) + std::cout << "scientific "; + if(f & std::ios_base::fixed) + std::cout << "fixed "; + if(f & std::ios_base::showpoint) + std::cout << "showpoint "; + if(f & std::ios_base::showpos) + std::cout << "showpos "; + std::cout << std::endl; +} + + +template <class T> +void test() +{ + typedef T mp_t; + boost::array<std::ios_base::fmtflags, 9> f = + {{ + std::ios_base::fmtflags(0), std::ios_base::showpoint, std::ios_base::showpos, std::ios_base::scientific, std::ios_base::scientific|std::ios_base::showpos, + std::ios_base::scientific|std::ios_base::showpoint, std::ios_base::fixed, std::ios_base::fixed|std::ios_base::showpoint, + std::ios_base::fixed|std::ios_base::showpos + }}; + + boost::array<boost::array<const char*, 13 * 9>, 40> string_data = {{ +#include "libs/multiprecision/test/string_data.ipp" + }}; + + double num = 123456789.0; + double denom = 1; + double val = num; + for(unsigned j = 0; j < 40; ++j) + { + unsigned col = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = string_data[j][col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + num = -num; + if(j & 1) + denom *= 8; + val = num / denom; + } + + boost::array<const char*, 13 * 9> zeros = + {{ "0", "0.", "+0", "0.0e+00", "+0.0e+00", "0.0e+00", "0.0", "0.0", "+0.0", "0", "0.0", "+0", "0.00e+00", "+0.00e+00", "0.00e+00", "0.00", "0.00", "+0.00", "0", "0.00", "+0", "0.000e+00", "+0.000e+00", "0.000e+00", "0.000", "0.000", "+0.000", "0", "0.000", "+0", "0.0000e+00", "+0.0000e+00", "0.0000e+00", "0.0000", "0.0000", "+0.0000", "0", "0.0000", "+0", "0.00000e+00", "+0.00000e+00", "0.00000e+00", "0.00000", "0.00000", "+0.00000", "0", "0.00000", "+0", "0.000000e+00", "+0.000000e+00", "0.000000e+00", "0.000000", "0.000000", "+0.000000", "0", "0.000000", "+0", "0.0000000e+00", "+0.0000000e+00", "0.0000000e+00", "0.0000000", "0.0000000", "+0.0000000", "0", "0.0000000", "+0", "0.00000000e+00", "+0.00000000e+00", "0.00000000e+00", "0.00000000", "0.00000000", "+0.00000000", "0", "0.00000000", "+0", "0.000000000e+00", "+0.000000000e+00", "0.000000000e+00", "0.000000000", "0.000000000", "+0.000000000", "0", "0.000000000", "+0", "0.0000000000e+00", "+0.0000000000e+00", "0.0000000000e+00", "0.0000000000", "0.0000000000", "+0.0000000000", "0", "0.0000000000", "+0", "0.00000000000e+00", "+0.00000000000e+00", "0.00000000000e+00", "0.00000000000", "0.00000000000", "+0.00000000000", "0", "0.00000000000", "+0", "0.000000000000e+00", "+0.000000000000e+00", "0.000000000000e+00", "0.000000000000", "0.000000000000", "+0.000000000000", "0", "0.000000000000", "+0", "0.0000000000000e+00", "+0.0000000000000e+00", "0.0000000000000e+00", "0.0000000000000", "0.0000000000000", "+0.0000000000000" }}; + + unsigned col = 0; + val = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = zeros[col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + + if(std::numeric_limits<mp_t>::has_infinity) + { + T val = std::numeric_limits<T>::infinity(); + BOOST_CHECK_EQUAL(val.str(), "inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "+inf"); + val = -val; + BOOST_CHECK_EQUAL(val.str(), "-inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "-inf"); + + val = static_cast<T>("inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits<T>::infinity()); + val = static_cast<T>("+inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits<T>::infinity()); + val = static_cast<T>("-inf"); + BOOST_CHECK_EQUAL(val, -std::numeric_limits<T>::infinity()); + } + if(std::numeric_limits<mp_t>::has_quiet_NaN) + { + T val = std::numeric_limits<T>::quiet_NaN(); + BOOST_CHECK_EQUAL(val.str(), "nan"); + val = static_cast<T>("nan"); + BOOST_CHECK((boost::math::isnan)(val)); + } + // + // Min and max values: + // + T t((std::numeric_limits<T>::max)().str(std::numeric_limits<T>::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits<T>::max)()); + t = T((std::numeric_limits<T>::min)().str(std::numeric_limits<T>::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits<T>::min)()); + t = T((std::numeric_limits<T>::lowest)().str(std::numeric_limits<T>::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits<T>::lowest)()); +} + +template <class T> +T generate_random() +{ + typedef typename T::backend_type::exponent_type e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution<e_type> ui(0, std::numeric_limits<T>::max_exponent); + return ldexp(val, ui(gen)); +} + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + ss << std::setprecision(std::numeric_limits<T>::max_digits10); +#else + ss << std::setprecision(std::numeric_limits<T>::digits10 + 2); +#endif + ss.flags(f); + ss << val; + T new_val = static_cast<T>(ss.str()); + BOOST_CHECK_EQUAL(new_val, val); + new_val = static_cast<T>(val.str(0, f)); + BOOST_CHECK_EQUAL(new_val, val); +} + +template <class T> +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::scientific)); + if((fabs(val) > 1) && (fabs(val) < 1e100)) + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::fixed)); + + static int error_count = 0; + + if(error_count != boost::detail::test_errors()) + { + error_count = boost::detail::test_errors(); + std::cout << "Errors occured while testing value...."; + if(val.backend().sign()) + std::cout << "-"; + std::cout << boost::multiprecision::cpp_int(val.backend().bits()) << "e" << val.backend().exponent() << std::endl; + } +} + +template <class T> +void test_round_trip() +{ + std::cout << "Testing type " << typeid(T).name() << std::endl; + std::cout << "digits = " << std::numeric_limits<T>::digits << std::endl; + std::cout << "digits10 = " << std::numeric_limits<T>::digits10 << std::endl; + std::cout << "max_digits10 = " << std::numeric_limits<T>::max_digits10 << std::endl; + + stopwatch<boost::chrono::high_resolution_clock> w; + + while(boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() < 200) + { + T val = generate_random<T>(); + do_round_trip(val); + do_round_trip(T(-val)); + do_round_trip(T(1/val)); + do_round_trip(T(-1/val)); + + if(boost::detail::test_errors() > 200) break; // escape if there are too many errors. + } + + std::cout << "Execution time = " << boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() << "s" << std::endl; +} + +#if !defined(TEST1) && !defined(TEST2) +# define TEST1 +# define TEST2 +#endif + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + test<number<cpp_bin_float<113, digit_base_2> > >(); + test_round_trip<number<cpp_bin_float<113, digit_base_2> > >(); +#endif +#ifdef TEST2 + test<number<cpp_bin_float<53, digit_base_2> > >(); + test_round_trip<number<cpp_bin_float<53, digit_base_2> > >(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_cpp_bin_float_serial.cpp b/libs/multiprecision/test/test_cpp_bin_float_serial.cpp new file mode 100644 index 0000000000..361692ba07 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_bin_float_serial.cpp @@ -0,0 +1,36 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_bin_float.hpp> +#include "test_float_serial.hpp" + +#if !defined(TEST1) && !defined(TEST2) +# define TEST1 +# define TEST2 +#endif + + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + test<cpp_bin_float_50>(); +#endif +#ifdef TEST2 + test<cpp_bin_float_quad>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_dec_float_conv.cpp b/libs/multiprecision/test/test_cpp_dec_float_conv.cpp new file mode 100644 index 0000000000..d1c7306497 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_dec_float_conv.cpp @@ -0,0 +1,42 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#include <boost/multiprecision/cpp_dec_float.hpp> + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between different precisions: + // + cpp_dec_float_50 f1(2); + cpp_dec_float_100 f2(3); + + cpp_dec_float_100 f3 = f1; // implicit conversion OK + BOOST_TEST(f3 == 2); + cpp_dec_float_50 f4(f2); // explicit conversion OK + BOOST_TEST(f4 == 3); + + f2 = f1; + BOOST_TEST(f2 == 2); + f2 = 4; + f1 = static_cast<cpp_dec_float_50>(f2); + BOOST_TEST(f1 == 4); + + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_dec_float_round.cpp b/libs/multiprecision/test/test_cpp_dec_float_round.cpp new file mode 100644 index 0000000000..4d70719aac --- /dev/null +++ b/libs/multiprecision/test/test_cpp_dec_float_round.cpp @@ -0,0 +1,67 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 Christopher Kormanyos. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +// Test case for ticket: +// #8065: Multiprecision rounding issue + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include "test.hpp" +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/math/special_functions/round.hpp> + +template<int N> +static bool round_test_imp() +{ + typedef boost::multiprecision::cpp_dec_float<N> mp_backend_type; + typedef boost::multiprecision::number<mp_backend_type, boost::multiprecision::et_off> mp_type; + + const mp_type original_digits(1.0F); + + const mp_type scale = pow(mp_type(10), N); + + mp_type these_digits = original_digits * scale; + + these_digits = boost::math::round(these_digits); + these_digits /= scale; + + const std::string result = these_digits.str(); + + return (result == original_digits.str()); +} + +template<int N> +struct round_test +{ + static bool test() + { + return (round_test_imp<N>() && round_test<N - 1>::test()); + } +}; + +template<> +struct round_test<0> +{ + static bool test() + { + return round_test_imp<0>(); + } +}; + +int main() +{ + // + // Test cpp_dec_float rounding with boost::math::round() at various precisions: + // + const bool round_test_result = round_test<40>::test(); + + BOOST_CHECK_EQUAL(round_test_result, true); + + return boost::report_errors(); +} diff --git a/libs/multiprecision/test/test_cpp_dec_float_serial.cpp b/libs/multiprecision/test/test_cpp_dec_float_serial.cpp new file mode 100644 index 0000000000..166cfa3b82 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_dec_float_serial.cpp @@ -0,0 +1,36 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> +#include "test_float_serial.hpp" + +#if !defined(TEST1) && !defined(TEST2) +# define TEST1 +# define TEST2 +#endif + + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + test<cpp_dec_float_50>(); +#endif +#ifdef TEST2 + test<number<cpp_dec_float<100, boost::int64_t, std::allocator<void> > > >(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_int.cpp b/libs/multiprecision/test/test_cpp_int.cpp new file mode 100644 index 0000000000..70c5f7b4bb --- /dev/null +++ b/libs/multiprecision/test/test_cpp_int.cpp @@ -0,0 +1,593 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/timer.hpp> +#include "test.hpp" + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +template <class T> +struct is_checked_cpp_int : public boost::mpl::false_ {}; +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, class Allocator, boost::multiprecision::expression_template_option ET> +struct is_checked_cpp_int<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::checked, Allocator>, ET> > : public boost::mpl::true_ {}; + +template <class Number> +struct tester +{ + typedef Number test_type; + typedef typename test_type::backend_type::checked_type checked; + + unsigned last_error_count; + boost::timer tim; + + boost::multiprecision::mpz_int a, b, c, d; + int si; + unsigned ui; + test_type a1, b1, c1, d1; + + + void t1() + { + using namespace boost::multiprecision; + BOOST_CHECK_EQUAL(a.str(), a1.str()); + BOOST_CHECK_EQUAL(b.str(), b1.str()); + BOOST_CHECK_EQUAL(c.str(), c1.str()); + BOOST_CHECK_EQUAL(d.str(), d1.str()); + BOOST_CHECK_EQUAL(mpz_int(a+b).str(), test_type(a1 + b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=b).str(), (test_type(a1) += b1).str()); + BOOST_CHECK_EQUAL((mpz_int(b)+=a).str(), (test_type(b1) += a1).str()); + BOOST_CHECK_EQUAL(mpz_int(a-b).str(), test_type(a1 - b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=b).str(), (test_type(a1) -= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), test_type(test_type(-a1) + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), test_type(test_type(-a1) - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * d).str(), test_type(c1 * d1).str()); + BOOST_CHECK_EQUAL((mpz_int(c)*=d).str(), (test_type(c1) *= d1).str()); + BOOST_CHECK_EQUAL((mpz_int(d)*=c).str(), (test_type(d1) *= c1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), test_type(c1 * -d1).str()); + BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), test_type(-c1 * d1).str()); + BOOST_CHECK_EQUAL((mpz_int(c)*=-d).str(), (test_type(c1) *= -d1).str()); + BOOST_CHECK_EQUAL((mpz_int(-d)*=c).str(), (test_type(-d1) *= c1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * c).str(), test_type(b1 * c1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / b).str(), test_type(a1 / b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=b).str(), (test_type(a1) /= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), test_type(a1 / -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), test_type(-a1 / b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=-b).str(), (test_type(a1) /= -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=b).str(), (test_type(-a1) /= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / d).str(), test_type(a1 / d1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % b).str(), test_type(a1 % b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=b).str(), (test_type(a1) %= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), test_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=-b).str(), (test_type(a1) %= -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), test_type(-a1 % b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=b).str(), (test_type(-a1) %= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % d).str(), test_type(a1 % d1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=d).str(), (test_type(a1) %= d1).str()); + + if(!std::numeric_limits<test_type>::is_bounded) + { + test_type p = a1 * b1; + test_type r; + divide_qr(p, b1, p, r); + BOOST_CHECK_EQUAL(p, a1); + BOOST_CHECK_EQUAL(r, test_type(0)); + + p = a1 * d1; + divide_qr(p, d1, p, r); + BOOST_CHECK_EQUAL(p, a1); + BOOST_CHECK_EQUAL(r, test_type(0)); + + divide_qr(p, test_type(1), p, r); + BOOST_CHECK_EQUAL(p, a1); + BOOST_CHECK_EQUAL(r, test_type(0)); + } + } + + void t2() + { + using namespace boost::multiprecision; + // bitwise ops: + BOOST_CHECK_EQUAL(mpz_int(a|b).str(), test_type(a1 | b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=b).str(), (test_type(a1) |= b1).str()); + if(!is_checked_cpp_int<test_type>::value) + { + BOOST_CHECK_EQUAL(mpz_int(-a|b).str(), test_type(-a1 | b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)|=b).str(), (test_type(-a1) |= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a|-b).str(), test_type(a1 | -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=-b).str(), (test_type(a1) |= -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a|-b).str(), test_type(-a1 | -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)|=-b).str(), (test_type(-a1) |= -b1).str()); + } + BOOST_CHECK_EQUAL(mpz_int(a&b).str(), test_type(a1 & b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=b).str(), (test_type(a1) &= b1).str()); + if(!is_checked_cpp_int<test_type>::value) + { + BOOST_CHECK_EQUAL(mpz_int(-a&b).str(), test_type(-a1 & b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)&=b).str(), (test_type(-a1) &= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&-b).str(), test_type(a1 & -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=-b).str(), (test_type(a1) &= -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a&-b).str(), test_type(-a1 & -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)&=-b).str(), (test_type(-a1) &= -b1).str()); + } + BOOST_CHECK_EQUAL(mpz_int(a^b).str(), test_type(a1 ^ b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=b).str(), (test_type(a1) ^= b1).str()); + if(!is_checked_cpp_int<test_type>::value) + { + BOOST_CHECK_EQUAL(mpz_int(-a^b).str(), test_type(-a1 ^ b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)^=b).str(), (test_type(-a1) ^= b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^-b).str(), test_type(a1 ^ -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=-b).str(), (test_type(a1) ^= -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a^-b).str(), test_type(-a1 ^ -b1).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)^=-b).str(), (test_type(-a1) ^= -b1).str()); + } + // Shift ops: + for(unsigned i = 0; i < 128; ++i) + { + if(!std::numeric_limits<test_type>::is_bounded) + { + BOOST_CHECK_EQUAL(mpz_int(a << i).str(), test_type(a1 << i).str()); + } + else if(!is_checked_cpp_int<test_type>::value) + { + test_type t1(mpz_int(a << i).str()); + test_type t2 = a1 << i; + BOOST_CHECK_EQUAL(t1, t2); + } + BOOST_CHECK_EQUAL(mpz_int(a >> i).str(), test_type(a1 >> i).str()); + } + // gcd/lcm + BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), test_type(gcd(a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), test_type(lcm(c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, b)).str(), test_type(gcd(-a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, d)).str(), test_type(lcm(-c1, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -b)).str(), test_type(gcd(-a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -d)).str(), test_type(lcm(-c1, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, -b)).str(), test_type(gcd(a1, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, -d)).str(), test_type(lcm(c1, -d1)).str()); + // Integer sqrt: + mpz_int r; + test_type r1; + BOOST_CHECK_EQUAL(sqrt(a, r).str(), sqrt(a1, r1).str()); + BOOST_CHECK_EQUAL(r.str(), r1.str()); + } + + void t3() + { + using namespace boost::multiprecision; + // Now check operations involving signed integers: + BOOST_CHECK_EQUAL(mpz_int(a + si).str(), test_type(a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), test_type(a1 + -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), test_type(-a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(si + a).str(), test_type(si + a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=si).str(), (test_type(a1) += si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=-si).str(), (test_type(a1) += -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=si).str(), (test_type(-a1) += si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=-si).str(), (test_type(-a1) += -si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - si).str(), test_type(a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), test_type(a1 - -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), test_type(-a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(si - a).str(), test_type(si - a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=si).str(), (test_type(a1) -= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=-si).str(), (test_type(a1) -= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=si).str(), (test_type(-a1) -= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=-si).str(), (test_type(-a1) -= -si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * si).str(), test_type(b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), test_type(b1 * -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), test_type(-b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(si * b).str(), test_type(si * b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=si).str(), (test_type(a1) *= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=-si).str(), (test_type(a1) *= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=si).str(), (test_type(-a1) *= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=-si).str(), (test_type(-a1) *= -si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / si).str(), test_type(a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), test_type(a1 / -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), test_type(-a1 / si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=si).str(), (test_type(a1) /= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=-si).str(), (test_type(a1) /= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=si).str(), (test_type(-a1) /= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=-si).str(), (test_type(-a1) /= -si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % si).str(), test_type(a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), test_type(a1 % -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), test_type(-a1 % si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=si).str(), (test_type(a1) %= si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=-si).str(), (test_type(a1) %= -si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=si).str(), (test_type(-a1) %= si).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=-si).str(), (test_type(-a1) %= -si).str()); + if((si > 0) || !is_checked_cpp_int<test_type>::value) + { + BOOST_CHECK_EQUAL(mpz_int(a|si).str(), test_type(a1 | si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=si).str(), (test_type(a1) |= si).str()); + BOOST_CHECK_EQUAL(mpz_int(a&si).str(), test_type(a1 & si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=si).str(), (test_type(a1) &= si).str()); + BOOST_CHECK_EQUAL(mpz_int(a^si).str(), test_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=si).str(), (test_type(a1) ^= si).str()); + BOOST_CHECK_EQUAL(mpz_int(si|a).str(), test_type(si|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si&a).str(), test_type(si&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si^a).str(), test_type(si^a1).str()); + } + BOOST_CHECK_EQUAL(mpz_int(gcd(a, si)).str(), test_type(gcd(a1, si)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(si, b)).str(), test_type(gcd(si, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, si)).str(), test_type(lcm(c1, si)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(si, d)).str(), test_type(lcm(si, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, si)).str(), test_type(gcd(-a1, si)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-si, b)).str(), test_type(gcd(-si, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, si)).str(), test_type(lcm(-c1, si)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-si, d)).str(), test_type(lcm(-si, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, -si)).str(), test_type(gcd(-a1, -si)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-si, -b)).str(), test_type(gcd(-si, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, -si)).str(), test_type(lcm(-c1, -si)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-si, -d)).str(), test_type(lcm(-si, -d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, -si)).str(), test_type(gcd(a1, -si)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(si, -b)).str(), test_type(gcd(si, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, -si)).str(), test_type(lcm(c1, -si)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(si, -d)).str(), test_type(lcm(si, -d1)).str()); + } + + void t4() + { + using namespace boost::multiprecision; + // Now check operations involving unsigned integers: + BOOST_CHECK_EQUAL(mpz_int(a + ui).str(), test_type(a1 + ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + ui).str(), test_type(-a1 + ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui + a).str(), test_type(ui + a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)+=ui).str(), (test_type(a1) += ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)+=ui).str(), (test_type(-a1) += ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a - ui).str(), test_type(a1 - ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - ui).str(), test_type(-a1 - ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui - a).str(), test_type(ui - a1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)-=ui).str(), (test_type(a1) -= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)-=ui).str(), (test_type(-a1) -= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(b * ui).str(), test_type(b1 * ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * ui).str(), test_type(-b1 * ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui * b).str(), test_type(ui * b1).str()); + BOOST_CHECK_EQUAL((mpz_int(a)*=ui).str(), (test_type(a1) *= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)*=ui).str(), (test_type(-a1) *= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a / ui).str(), test_type(a1 / ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / ui).str(), test_type(-a1 / ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)/=ui).str(), (test_type(a1) /= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)/=ui).str(), (test_type(-a1) /= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a % ui).str(), test_type(a1 % ui).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % ui).str(), test_type(-a1 % ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)%=ui).str(), (test_type(a1) %= ui).str()); + BOOST_CHECK_EQUAL((mpz_int(-a)%=ui).str(), (test_type(-a1) %= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a|ui).str(), test_type(a1 | ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)|=ui).str(), (test_type(a1) |= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a&ui).str(), test_type(a1 & ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)&=ui).str(), (test_type(a1) &= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(a^ui).str(), test_type(a1 ^ ui).str()); + BOOST_CHECK_EQUAL((mpz_int(a)^=ui).str(), (test_type(a1) ^= ui).str()); + BOOST_CHECK_EQUAL(mpz_int(ui|a).str(), test_type(ui|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(ui&a).str(), test_type(ui&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(ui^a).str(), test_type(ui^a1).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, ui)).str(), test_type(gcd(a1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(ui, b)).str(), test_type(gcd(ui, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, ui)).str(), test_type(lcm(c1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(ui, d)).str(), test_type(lcm(ui, d1)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(-a, ui)).str(), test_type(gcd(-a1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(-c, ui)).str(), test_type(lcm(-c1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(ui, -b)).str(), test_type(gcd(ui, -b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(ui, -d)).str(), test_type(lcm(ui, -d1)).str()); + + if(std::numeric_limits<test_type>::is_modulo && checked::value) + { + static mpz_int m = mpz_int(1) << std::numeric_limits<test_type>::digits; + mpz_int t(a); + test_type t1(a1); + for(unsigned i = 0; i < 10; ++i) + { + t *= a; + t %= m; + t += a; + t %= m; + t1 *= a1; + t1 += a1; + } + BOOST_CHECK_EQUAL(t.str(), t1.str()); + } + } + + void t5() + { + using namespace boost::multiprecision; + // + // Now integer functions: + // + mpz_int z1, z2; + test_type t1, t2; + divide_qr(a, b, z1, z2); + divide_qr(a1, b1, t1, t2); + BOOST_CHECK_EQUAL(z1.str(), t1.str()); + BOOST_CHECK_EQUAL(z2.str(), t2.str()); + BOOST_CHECK_EQUAL(integer_modulus(a, si), integer_modulus(a1, si)); + BOOST_CHECK_EQUAL(lsb(a), lsb(a1)); + BOOST_CHECK_EQUAL(msb(a), msb(a1)); + + for(unsigned i = 0; i < 1000; i += 13) + { + BOOST_CHECK_EQUAL(bit_test(a, i), bit_test(a1, i)); + } + if(!std::numeric_limits<test_type>::is_modulo) + { + // We have to take care that our powers don't grow too large, otherwise this takes "forever", + // also don't test for modulo types, as these may give a different result from arbitrary + // precision types: + BOOST_CHECK_EQUAL(mpz_int(pow(d, ui % 19)).str(), test_type(pow(d1, ui % 19)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, c)).str(), test_type(powm(a1, b1, c1)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, b, ui)).str(), test_type(powm(a1, b1, ui)).str()); + BOOST_CHECK_EQUAL(mpz_int(powm(a, ui, c)).str(), test_type(powm(a1, ui, c1)).str()); + } + BOOST_CHECK_EQUAL(lsb(a), lsb(a1)); + BOOST_CHECK_EQUAL(msb(a), msb(a1)); + } + + void test_bug_cases() + { + if(!std::numeric_limits<test_type>::is_bounded) + { + // https://svn.boost.org/trac/boost/ticket/7878 + test_type a("0x1000000000000000000000000000000000000000000000000000000000000000"); + test_type b = 0xFFFFFFFF; + test_type c = a * b + b; // quotient has 1 in the final place + test_type q, r; + divide_qr(c, b, q, r); + BOOST_CHECK_EQUAL(a + 1, q); + BOOST_CHECK_EQUAL(r, 0); + + b = static_cast<test_type>("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + c = a * b + b; // quotient has 1 in the final place + divide_qr(c, b, q, r); + BOOST_CHECK_EQUAL(a + 1, q); + BOOST_CHECK_EQUAL(r, 0); + // + // Not a bug, but test some other special cases that don't otherwise occur through + // random testing: + // + c = a * b; // quotient has zero in the final place + divide_qr(c, b, q, r); + BOOST_CHECK_EQUAL(q, a); + BOOST_CHECK_EQUAL(r, 0); + divide_qr(c, a, q, r); + BOOST_CHECK_EQUAL(q, b); + BOOST_CHECK_EQUAL(r, 0); + ++c; + divide_qr(c, b, q, r); + BOOST_CHECK_EQUAL(q, a); + BOOST_CHECK_EQUAL(r, 1); + } + // Bug https://svn.boost.org/trac/boost/ticket/8126: + test_type a("-4294967296"); + test_type b("4294967296"); + test_type c("-1"); + a = (a / b); + BOOST_CHECK_EQUAL(a, -1); + a = -4294967296; + a = (a / b) * c; + BOOST_CHECK_EQUAL(a, 1); + a = -23; + b = 23; + a = (a / b) * c; + BOOST_CHECK_EQUAL(a, 1); + a = -23; + a = (a / b) / c; + BOOST_CHECK_EQUAL(a, 1); + a = test_type("-26607734784073568386365259775"); + b = test_type("8589934592"); + a = a / b; + BOOST_CHECK_EQUAL(a, test_type("-3097548007973652377")); + // Bug https://svn.boost.org/trac/boost/ticket/8133: + a = test_type("0x12345600012434ffffffffffffffffffffffff"); + unsigned ui = 0xffffffff; + a = a - ui; + BOOST_CHECK_EQUAL(a, test_type("0x12345600012434ffffffffffffffff00000000")); + a = test_type("0x12345600012434ffffffffffffffffffffffff"); +#ifndef BOOST_NO_LONG_LONG + unsigned long long ull = 0xffffffffffffffffuLL; + a = a - ull; + BOOST_CHECK_EQUAL(a, test_type("0x12345600012434ffffffff0000000000000000")); +#endif + // + // Now check that things which should be zero really are + // https://svn.boost.org/trac/boost/ticket/8145: + // + a = -1; + a += 1; + BOOST_CHECK_EQUAL(a, 0); + a = 1; + a += -1; + BOOST_CHECK_EQUAL(a, 0); + a = -1; + a += test_type(1); + BOOST_CHECK_EQUAL(a, 0); + a = 1; + a += test_type(-1); + BOOST_CHECK_EQUAL(a, 0); + a = test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + a -= test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + BOOST_CHECK_EQUAL(a, 0); + a = -test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + a += test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + BOOST_CHECK_EQUAL(a, 0); + a = 2; + a *= 0; + BOOST_CHECK_EQUAL(a, 0); + a = -2; + a *= 0; + BOOST_CHECK_EQUAL(a, 0); + a = 2; + a *= test_type(0); + BOOST_CHECK_EQUAL(a, 0); + a = -2; + a *= test_type(0); + BOOST_CHECK_EQUAL(a, 0); + a = -2; + a /= 50; + BOOST_CHECK_EQUAL(a, 0); + a = -test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + a /= (1 + test_type("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF")); + BOOST_CHECK_EQUAL(a, 0); + // https://svn.boost.org/trac/boost/ticket/8160 + a = 1; + a = 0 / test_type(1); + BOOST_CHECK_EQUAL(a, 0); + a = 1; + a = 0 % test_type(25); + BOOST_CHECK_EQUAL(a, 0); + } + + void test() + { + using namespace boost::multiprecision; + + test_bug_cases(); + + last_error_count = 0; + + BOOST_CHECK_EQUAL(Number(), 0); + + for(int i = 0; i < 10000; ++i) + { + a = generate_random<mpz_int>(1000); + b = generate_random<mpz_int>(512); + c = generate_random<mpz_int>(256); + d = generate_random<mpz_int>(32); + + si = d.convert_to<int>(); + ui = si; + + a1 = static_cast<test_type>(a.str()); + b1 = static_cast<test_type>(b.str()); + c1 = static_cast<test_type>(c.str()); + d1 = static_cast<test_type>(d.str()); + + t1(); + t2(); +#ifndef SLOW_COMPILER + t3(); + t4(); + t5(); +#endif + + if(last_error_count != (unsigned)boost::detail::test_errors()) + { + last_error_count = boost::detail::test_errors(); + std::cout << std::hex << std::showbase; + + std::cout << "a = " << a << std::endl; + std::cout << "a1 = " << a1 << std::endl; + std::cout << "b = " << b << std::endl; + std::cout << "b1 = " << b1 << std::endl; + std::cout << "c = " << c << std::endl; + std::cout << "c1 = " << c1 << std::endl; + std::cout << "d = " << d << std::endl; + std::cout << "d1 = " << d1 << std::endl; + std::cout << "a + b = " << a+b << std::endl; + std::cout << "a1 + b1 = " << a1+b1 << std::endl; + std::cout << std::dec; + std::cout << "a - b = " << a-b << std::endl; + std::cout << "a1 - b1 = " << a1-b1 << std::endl; + std::cout << "-a + b = " << mpz_int(-a)+b << std::endl; + std::cout << "-a1 + b1 = " << test_type(-a1)+b1 << std::endl; + std::cout << "-a - b = " << mpz_int(-a)-b << std::endl; + std::cout << "-a1 - b1 = " << test_type(-a1)-b1 << std::endl; + std::cout << "c*d = " << c*d << std::endl; + std::cout << "c1*d1 = " << c1*d1 << std::endl; + std::cout << "b*c = " << b*c << std::endl; + std::cout << "b1*c1 = " << b1*c1 << std::endl; + std::cout << "a/b = " << a/b << std::endl; + std::cout << "a1/b1 = " << a1/b1 << std::endl; + std::cout << "a/d = " << a/d << std::endl; + std::cout << "a1/d1 = " << a1/d1 << std::endl; + std::cout << "a%b = " << a%b << std::endl; + std::cout << "a1%b1 = " << a1%b1 << std::endl; + std::cout << "a%d = " << a%d << std::endl; + std::cout << "a1%d1 = " << a1%d1 << std::endl; + } + + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 200) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + + } + } +}; + +#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3) +#define TEST1 +#define TEST2 +#define TEST3 +#endif + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + tester<cpp_int> t1; + t1.test(); +#endif +#ifdef TEST2 + tester<number<cpp_int_backend<2048, 2048, signed_magnitude, checked, void> > > t2; + t2.test(); +#endif +#ifdef TEST3 + // Unchecked test verifies modulo arithmetic: + tester<number<cpp_int_backend<2048, 2048, signed_magnitude, unchecked, void> > > t3; + t3.test(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_int_conv.cpp b/libs/multiprecision/test/test_cpp_int_conv.cpp new file mode 100644 index 0000000000..d5a8e2a333 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_int_conv.cpp @@ -0,0 +1,77 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#include <boost/multiprecision/cpp_int.hpp> + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between different precisions: + // + cpp_int i1(2); + int128_t i2(3); + int256_t i3(4); + number<cpp_int_backend<32, 32, signed_magnitude, checked, void> > i4(5); + + i1 = i3; + BOOST_TEST(i1 == 4); + i1 = i4; + BOOST_TEST(i1 == 5); + + i3 = -1234567; + i4 = -5677334; + i1 = i3; + BOOST_TEST(i1 == -1234567); + i1 = i4; + BOOST_TEST(i1 == -5677334); + + i3 = i2; + BOOST_TEST(i3 == 3); + + i3 = -1234567; + + uint128_t i5(i3); + BOOST_TEST(i5 == -1234567); + + int128_t i6(i4); + BOOST_TEST(i6 == -5677334); + + number<cpp_int_backend<32, 32, signed_magnitude, unchecked, void>, et_off> i7(i3); + BOOST_TEST(i7 == -1234567); + + int256_t i8(i6); + BOOST_TEST(i8 == -5677334); + + i7.assign(4.0); + BOOST_TEST(i7 == 4); + + number<cpp_int_backend<30, 30, signed_magnitude, checked, void>, et_off> i9(-5677334); + i7 = i9; + BOOST_TEST(i7 == -5677334); + i7 = number<cpp_int_backend<32, 32, signed_magnitude, checked, void>, et_off>(i9); + BOOST_TEST(i7 == -5677334); + + i9 = static_cast<number<cpp_int_backend<30, 30, signed_magnitude, checked, void>, et_off> >(i7); + BOOST_TEST(i9 == -5677334); + + ++i9; + i7 = i9; + BOOST_TEST(i7 == 1 - 5677334); + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_int_deserial.cpp b/libs/multiprecision/test/test_cpp_int_deserial.cpp new file mode 100644 index 0000000000..6b5d888c37 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_int_deserial.cpp @@ -0,0 +1,3197 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include "test.hpp" + +#include <iostream> +#include <iomanip> +#include <fstream> +#include <boost/archive/text_iarchive.hpp> +#include <boost/archive/text_oarchive.hpp> +#include <boost/archive/binary_iarchive.hpp> +#include <boost/archive/binary_oarchive.hpp> +#include <boost/exception/all.hpp> +#include <boost/filesystem.hpp> +#include <boost/filesystem/fstream.hpp> + +boost::filesystem::path root; + +template <class T> +void test64() +{ + using namespace boost::multiprecision; + + const char* text_array[] = { + "4991075498124186", + "-4991075498124186", + "750", + "-750", + "415210192158791091", + "-415210192158791091", + "2172493004228646", + "-2172493004228646", + "993", + "-993", + "801484291299519218", + "-801484291299519218", + "294605502329193119", + "-294605502329193119", + "52506", + "-52506", + "1509449075377", + "-1509449075377", + "2042599", + "-2042599", + "228", + "-228", + "38666759073", + "-38666759073", + "611489", + "-611489", + "5393", + "-5393", + "12930071684", + "-12930071684", + "3606852234541437552", + "-3606852234541437552", + "3764404188985662264", + "-3764404188985662264", + "13300301596736993408", + "-13300301596736993408", + "3519758520509816019", + "-3519758520509816019", + "811951798554103911", + "-811951798554103911", + "2440", + "-2440", + "175149377023342", + "-175149377023342", + "5347169560611466452", + "-5347169560611466452", + "187134495165780485", + "-187134495165780485", + "761263991097466327", + "-761263991097466327", + "205", + "-205", + "7437277938", + "-7437277938", + "2530448830165700", + "-2530448830165700", + "3771546153060183", + "-3771546153060183", + "1238034", + "-1238034", + "1470", + "-1470", + "7", + "-7", + "203065689", + "-203065689", + "130", + "-130", + "74717518653749632", + "-74717518653749632", + "3028698162338", + "-3028698162338", + "3471587482356581", + "-3471587482356581", + "34698219712863216", + "-34698219712863216", + "941191493582057728", + "-941191493582057728", + "14803251323", + "-14803251323", + "552076672455", + "-552076672455", + "410481316632532", + "-410481316632532", + "6", + "-6", + "3851011", + "-3851011", + "12895806074024545", + "-12895806074024545", + "59538", + "-59538", + "944776298737546117", + "-944776298737546117", + "25010240662345", + "-25010240662345", + "29657097213970", + "-29657097213970", + "88000252", + "-88000252", + "545263458410825", + "-545263458410825", + "216600129907865", + "-216600129907865", + "262741237793873", + "-262741237793873", + "226964744", + "-226964744", + "111776857", + "-111776857", + "346922769", + "-346922769", + "7324307011273", + "-7324307011273", + "182", + "-182", + "4204", + "-4204", + "60455", + "-60455", + "35250836865461", + "-35250836865461", + "4100298085120029", + "-4100298085120029", + "6", + "-6", + "3262369", + "-3262369", + "103928", + "-103928", + "82055266594432948", + "-82055266594432948", + "8", + "-8", + "1731", + "-1731", + "338", + "-338", + "13202690186510006305", + "-13202690186510006305", + "3916209444926814", + "-3916209444926814", + "1801701990484582", + "-1801701990484582", + "54042343363098", + "-54042343363098", + "86", + "-86", + "1346703", + "-1346703", + "34499847353417", + "-34499847353417", + "870972860051498248", + "-870972860051498248", + "2676223213", + "-2676223213", + "10", + "-10", + "2207730666882", + "-2207730666882", + "256557933", + "-256557933", + "742", + "-742", + "17809514", + "-17809514", + "41738", + "-41738", + "937490350973899", + "-937490350973899", + "10", + "-10", + "2153955175933399", + "-2153955175933399", + "21", + "-21", + "9767", + "-9767", + "160991545", + "-160991545", + "5537202949", + "-5537202949", + "1729222816", + "-1729222816", + "880543773", + "-880543773", + "4994415770", + "-4994415770", + "5667270210124", + "-5667270210124", + "1789552738407096", + "-1789552738407096", + "52084908492459", + "-52084908492459", + "419923376385918098", + "-419923376385918098", + "193184120308428", + "-193184120308428", + "3716593161704457", + "-3716593161704457", + "835313", + "-835313", + "47794728416344", + "-47794728416344", + "32162267350660", + "-32162267350660", + "1", + "-1", + "6746653265049", + "-6746653265049", + "72924075986572", + "-72924075986572", + "4061", + "-4061", + "1776612112178", + "-1776612112178", + "798", + "-798", + "266401037", + "-266401037", + "6773927626", + "-6773927626", + "935572859041371", + "-935572859041371", + "2667878767142547263", + "-2667878767142547263", + "107694081993", + "-107694081993", + "2478862", + "-2478862", + "75439252494463178", + "-75439252494463178", + "502732137506", + "-502732137506", + "1345285828338743", + "-1345285828338743", + "15181", + "-15181", + "6", + "-6", + "503497089658971", + "-503497089658971", + "3925896855680859", + "-3925896855680859", + "259231", + "-259231", + "7499637741115431", + "-7499637741115431", + "16282283214", + "-16282283214", + "1664259700668569315", + "-1664259700668569315", + "63205423227654", + "-63205423227654", + "122839112", + "-122839112", + "254133246000861645", + "-254133246000861645", + "324448699", + "-324448699", + "2634830651678498499", + "-2634830651678498499", + "65612160397", + "-65612160397", + "7064926544", + "-7064926544", + "3816", + "-3816", + "1964", + "-1964", + "208639360759781", + "-208639360759781", + "3910", + "-3910", + "95080", + "-95080", + "175945", + "-175945", + "5880392757177227", + "-5880392757177227", + "17254376508100660", + "-17254376508100660", + "16568677462108662019", + "-16568677462108662019", + "193490", + "-193490", + "6055816", + "-6055816", + "4421583059373970", + "-4421583059373970", + "34879", + "-34879", + "52778", + "-52778", + "0", + "0", + "935000170463558922", + "-935000170463558922", + "173", + "-173", + "10327678", + "-10327678", + "45810516546119519", + "-45810516546119519", + "8712", + "-8712", + "1932876094515139", + "-1932876094515139", + "84388", + "-84388", + "2050813773845403160", + "-2050813773845403160", + "1542848238524", + "-1542848238524", + "1555584758215827", + "-1555584758215827", + "3571489748", + "-3571489748", + "18291705113053112226", + "-18291705113053112226", + "5713248", + "-5713248", + "43", + "-43", + "7537188724850197", + "-7537188724850197", + "3450872745386207", + "-3450872745386207", + "335595262120", + "-335595262120", + "481778267224", + "-481778267224", + "86277827129", + "-86277827129", + "132147177032651", + "-132147177032651", + "222305704702019735", + "-222305704702019735", + "15454425372201", + "-15454425372201", + "37444", + "-37444", + "14915074751748", + "-14915074751748", + "322332143987563", + "-322332143987563", + "126997604", + "-126997604", + "484901511158709", + "-484901511158709", + "7452547923", + "-7452547923", + "43400437", + "-43400437", + "950", + "-950", + "133435748899", + "-133435748899", + "13225323986", + "-13225323986", + "113", + "-113", + "31298263", + "-31298263", + "33", + "-33", + "11093233", + "-11093233", + "13921728621", + "-13921728621", + "256811828405", + "-256811828405", + "568533463853249", + "-568533463853249", + "384553", + "-384553", + "1046793359495877872", + "-1046793359495877872", + "3513488911471240501", + "-3513488911471240501", + "999", + "-999", + "3257", + "-3257", + "141868737283", + "-141868737283", + "97723548", + "-97723548", + "380232796", + "-380232796", + "11615871", + "-11615871", + "2", + "-2", + "516935083428", + "-516935083428", + "2767393", + "-2767393", + "74918721", + "-74918721", + "7083", + "-7083", + "497484184665289623", + "-497484184665289623", + "3309660146889781", + "-3309660146889781", + "795624163", + "-795624163", + "1739075", + "-1739075", + "38737391516580422", + "-38737391516580422", + "33363484068", + "-33363484068", + "453947517553", + "-453947517553", + "7206", + "-7206", + "912", + "-912", + "1070565937975", + "-1070565937975", + "3607679046", + "-3607679046", + "503313", + "-503313", + "5384337", + "-5384337", + "7913554120377", + "-7913554120377", + "4112847188", + "-4112847188", + "8191226371802", + "-8191226371802", + "41268527630506", + "-41268527630506", + "446828884957609", + "-446828884957609", + "17378379828995102574", + "-17378379828995102574", + "802194395", + "-802194395", + "6459076776036", + "-6459076776036", + "189", + "-189", + "456272745323742742", + "-456272745323742742", + "35245", + "-35245", + "4142317167", + "-4142317167", + "240455833189507891", + "-240455833189507891", + "32426861928", + "-32426861928", + "3464", + "-3464", + "15152220677", + "-15152220677", + "8550134950160679", + "-8550134950160679", + "226598734", + "-226598734", + "35686909663", + "-35686909663", + "59277903563", + "-59277903563", + "6946537179316043375", + "-6946537179316043375", + "516198226", + "-516198226", + "54", + "-54", + "27406574726722597", + "-27406574726722597", + "717765982", + "-717765982", + "540734180837", + "-540734180837", + "381", + "-381", + "2883798342", + "-2883798342", + "2454889904722697593", + "-2454889904722697593", + "5324758776781459411", + "-5324758776781459411", + "0", + "0", + "3", + "-3", + "758016775051877", + "-758016775051877", + "6368641396491647651", + "-6368641396491647651", + "2409862725919775", + "-2409862725919775", + "19831125", + "-19831125", + "19839578195623645", + "-19839578195623645", + "19556929453271", + "-19556929453271", + "245", + "-245", + "83382", + "-83382", + "30044944", + "-30044944", + "10307835790108389", + "-10307835790108389", + "266904", + "-266904", + "29", + "-29", + "1691697088175268", + "-1691697088175268", + "6361142035143", + "-6361142035143", + "440939789", + "-440939789", + "19836890767598", + "-19836890767598", + "78676472953102968", + "-78676472953102968", + "1663", + "-1663", + "7103", + "-7103", + "2602952185917450011", + 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"2190428804113181503", + "-2190428804113181503", + "5182131", + "-5182131", + "35710270", + "-35710270", + "30830418043327", + "-30830418043327", + "157", + "-157", + "56976290639537", + "-56976290639537", + "429094", + "-429094", + "8166", + "-8166", + "259284720", + "-259284720", + "1974", + "-1974", + "414549061889", + "-414549061889", + "12126192", + "-12126192", + "477683", + "-477683", + "26", + "-26", + "200991115623", + "-200991115623", + "105657935189602", + "-105657935189602", + "137401581416017", + "-137401581416017", + "3133", + "-3133", + "41301", + "-41301", + "9120545960887397", + "-9120545960887397", + "615", + "-615", + "1677628", + "-1677628", + "487311", + "-487311", + "6467819698256", + "-6467819698256", + "2721454", + "-2721454", + "356423793", + "-356423793", + "525408497", + "-525408497", + "1791793366931794", + "-1791793366931794", + "16267730984", + "-16267730984", + "787", + "-787", + "82", + "-82", + "8594582631777749056", + "-8594582631777749056", + "494351", + "-494351", + "5138", + "-5138", + "404787056092544", + "-404787056092544", + "235074602368269", + "-235074602368269", + "14", + "-14", + "364870", + "-364870", + "592299531695979194", + "-592299531695979194", + "243533", + "-243533", + "228268671797977", + "-228268671797977", + "150", + "-150", + "2109092292", + "-2109092292", + "10814341", + "-10814341", + "229344736512", + "-229344736512", + "506659", + "-506659", + "15065", + "-15065", + "73012461469893725", + "-73012461469893725", + "183623698", + "-183623698", + "30820", + "-30820" + }; + + boost::filesystem::ifstream is(root / "cpp_int64_serial64.txt"); + std::cout << "Testing cpp_int64_serial64.txt with T=" << typeid(T).name() << std::endl; + is.peek(); + BOOST_CHECK(is.good()); + boost::archive::text_iarchive ia(is); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + T val; + ia >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } + + boost::filesystem::ifstream is2(root / "cpp_int64_serial32.txt"); + std::cout << "Testing cpp_int64_serial32.txt with T=" << typeid(T).name() << std::endl; + is2.peek(); + BOOST_CHECK(is2.good()); + boost::archive::text_iarchive ia2(is2); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + T val; + ia2 >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } +} + +template <class T> +void test128() +{ + using namespace boost::multiprecision; + + const char* text_array[] = { + "27388486965920179246162874599461", + "-27388486965920179246162874599461", + "144684", + "-144684", + "40075268927703813213972787292005375", + "-40075268927703813213972787292005375", + "185882978840350932616815972016599", + "-185882978840350932616815972016599", + "118042", + "-118042", + "18836407318976510834104635573348923563", + "-18836407318976510834104635573348923563", + "305594372610563985628870243265194313", + "-305594372610563985628870243265194313", + "992608567", + "-992608567", + "1079802217950896854831728", + "-1079802217950896854831728", + "382261429251", + "-382261429251", + "7995", + "-7995", + "1691954012304306190464", + "-1691954012304306190464", + "252558125876", + "-252558125876", + "63408135", + "-63408135", + "1923885021482774859879", + "-1923885021482774859879", + "218151618018868077912122028563473880039", + "-218151618018868077912122028563473880039", + "1830482607233486577967554117978261568", + "-1830482607233486577967554117978261568", + "232684363792492642717810801641182199046", + "-232684363792492642717810801641182199046", + "18951107105103656564987041230801322761", + "-18951107105103656564987041230801322761", + "18602001100058210837668227206289280804", + "-18602001100058210837668227206289280804", + "619312", + "-619312", + "3300635207581175104869860370", + "-3300635207581175104869860370", + "35913874076527213864347472731883210240", + "-35913874076527213864347472731883210240", + "22584003535744275158325315387889625225", + "-22584003535744275158325315387889625225", + "1087569784912004503372385117646999025", + "-1087569784912004503372385117646999025", + "53419", + "-53419", + "6365946347248672643", + "-6365946347248672643", + "923074766928095495451885549346", + "-923074766928095495451885549346", + "791386027675064089452885112122", + "-791386027675064089452885112122", + "1095850863769", + "-1095850863769", + "585462", + "-585462", + "7", + "-7", + "14396352646034696", + "-14396352646034696", + "103513", + "-103513", + "236879494739813627852695329647307484", + "-236879494739813627852695329647307484", + "833105528657041028703317", + "-833105528657041028703317", + "403987552870100762517310706932", + "-403987552870100762517310706932", + "9241069445104304081394313010837003", + "-9241069445104304081394313010837003", + "7747462702643357490732429745555870341", + "-7747462702643357490732429745555870341", + "24325940392988231200", + "-24325940392988231200", + "3169332595628505508931977", + "-3169332595628505508931977", + "2956433455556566120076606972499", + "-2956433455556566120076606972499", + "97", + "-97", + "162358208806282", + "-162358208806282", + "450940116154946927404473774882465", + "-450940116154946927404473774882465", + "451641858", + "-451641858", + "1225696755823790187144596188382442861", + "-1225696755823790187144596188382442861", + "29784146626131423063590613", + "-29784146626131423063590613", + "234254347872215512272431905", + "-234254347872215512272431905", + "1188109449997714", + "-1188109449997714", + "67931289973154010244863599404", + "-67931289973154010244863599404", + "15985550526478899202524298413", + "-15985550526478899202524298413", + "44969358144856504665069077764", + "-44969358144856504665069077764", + "2433869372731414379", + "-2433869372731414379", + "389948478409995", + "-389948478409995", + "42980455782580666", + "-42980455782580666", + "32377741714896213765436617", + "-32377741714896213765436617", + "14147536", + "-14147536", + "7281984", + "-7281984", + "1940499846845", + "-1940499846845", + "431464371512114469628917178", + "-431464371512114469628917178", + "7407337220313553496076208494128", + "-7407337220313553496076208494128", + "30", + "-30", + "1327411295501", + "-1327411295501", + "66903469770", + "-66903469770", + "1681234517540805320612830262883456", + "-1681234517540805320612830262883456", + "100", + "-100", + "1619033", + "-1619033", + "31778", + "-31778", + "157454929543174151967897543014505981946", + "-157454929543174151967897543014505981946", + "71577966086399886868276034834304", + "-71577966086399886868276034834304", + "39053861540146327519720396203958", + "-39053861540146327519720396203958", + "744644565611021440442223814", + "-744644565611021440442223814", + "141620", + "-141620", + "2207944969567", + "-2207944969567", + "203426602629118177589459157758", + "-203426602629118177589459157758", + "4687930831049614526662210561259545215", + "-4687930831049614526662210561259545215", + "13741620425001328569", + "-13741620425001328569", + "28", + "-28", + "19919840763987597711639960", + "-19919840763987597711639960", + "58845502926990870", + "-58845502926990870", + "46503", + "-46503", + "227899590091810", + "-227899590091810", + "520269641", + "-520269641", + "533635134464326491653819104191", + "-533635134464326491653819104191", + "32", + "-32", + "2311765742988497575052179436185", + "-2311765742988497575052179436185", + "104", + "-104", + "13174010", + "-13174010", + "9157004287034859", + "-9157004287034859", + "13439929054075798978", + "-13439929054075798978", + "1005710832260650449", + "-1005710832260650449", + "45810516546119519", + "-45810516546119519", + "10111031832823515595", + "-10111031832823515595", + "1556666498630726306813245", + "-1556666498630726306813245", + "3776079563026301615061583892830", + "-3776079563026301615061583892830", + "3554220000452135447940601650", + "-3554220000452135447940601650", + "342914370059615129601458555955512766", + "-342914370059615129601458555955512766", + "37211915143242116097464702285", + 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"6609227084602664174553003642710", + "-6609227084602664174553003642710", + "37231518369001507", + "-37231518369001507", + "4301528568595403190", + "-4301528568595403190", + "2333077100212", + "-2333077100212", + "11565", + "-11565", + "255726621336514413017008354182674709", + "-255726621336514413017008354182674709", + "17395422733913073065750181", + "-17395422733913073065750181", + "125019234224449492", + "-125019234224449492", + "4740360722276299853297125", + "-4740360722276299853297125", + "7568347", + "-7568347", + "17122026961016863428287", + "-17122026961016863428287", + "112577394987931131505768113032531171", + "-112577394987931131505768113032531171", + "7046212555452856822490707564", + "-7046212555452856822490707564", + "33256103762317100748101545285090311772", + "-33256103762317100748101545285090311772", + "104639691131091", + "-104639691131091", + "74043463548796243", + "-74043463548796243", + "49942702457067622169669481", + "-49942702457067622169669481", + "12806", + "-12806", + "4194227136755752775246633399", + "-4194227136755752775246633399", + "22363149786", + "-22363149786", + "53844", + "-53844", + "6204108132585699", + "-6204108132585699", + "133987", + "-133987", + "47357030709179941308475", + "-47357030709179941308475", + "167735124254221045", + "-167735124254221045", + "58394613871", + "-58394613871", + "214", + "-214", + "97085709128533841718123", + "-97085709128533841718123", + "9049249133086876221572990732831", + "-9049249133086876221572990732831", + "1860834869623152381150863486", + "-1860834869623152381150863486", + "3868776", + "-3868776", + "714752211", + "-714752211", + "117044601375672047600456567336894", + "-117044601375672047600456567336894", + "38202", + "-38202", + "1706135867048", + "-1706135867048", + "568201454130", + "-568201454130", + "10071543790040355676774628", + "-10071543790040355676774628", + "3955606956905", + "-3955606956905", + "1710822834542941", + "-1710822834542941", + "28185453895207483", + "-28185453895207483", + "2241403707806732425937134125743", + "-2241403707806732425937134125743", + "24424908461669836348", + "-24424908461669836348", + "39965", + "-39965", + "5776", + "-5776", + "161984235115107451958835599550261843326", + "-161984235115107451958835599550261843326", + "29821471341", + "-29821471341", + "3087720", + "-3087720", + "234408055908870511236228564329", + "-234408055908870511236228564329", + "367687929171771055426419375659", + "-367687929171771055426419375659", + "31", + "-31", + "14038375921", + "-14038375921", + "1272562766857183500104765994611086188", + "-1272562766857183500104765994611086188", + "5395131009", + "-5395131009", + "34630426722601695384252351222", + "-34630426722601695384252351222", + "16553", + "-16553", + "11084856402443484655", + "-11084856402443484655", + "4497048086787", + "-4497048086787", + "32568631422747274845485", + "-32568631422747274845485", + "262201867566", + "-262201867566", + "3603196342", + "-3603196342", + "32228667062769096924274427075075163477", + "-32228667062769096924274427075075163477", + "693196875773858622", + "-693196875773858622", + "375838207", + "-375838207", + }; + + boost::filesystem::ifstream is(root / "cpp_int128_serial64.txt"); + std::cout << "Testing cpp_int128_serial64.txt with T=" << typeid(T).name() << std::endl; + is.peek(); + BOOST_CHECK(is.good()); + boost::archive::text_iarchive ia(is); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + try + { + T val; + ia >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + } + + boost::filesystem::ifstream is2(root / "cpp_int128_serial32.txt"); + std::cout << "Testing cpp_int128_serial32.txt with T=" << typeid(T).name() << std::endl; + is2.peek(); + BOOST_CHECK(is2.good()); + boost::archive::text_iarchive ia2(is2); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + try + { + T val; + ia2 >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + } +} + +template <class T> +void test1024() +{ + using namespace boost::multiprecision; + + const char* text_array[] = { + "199116592524695642085302184291534972104821103496846288349049702743455488423756865233534697793799569802866670981662356904270988544309072648691983459024063468708849163858558300444260495432655880504371186304007206097685833870163932928823469130199562442992", + "-199116592524695642085302184291534972104821103496846288349049702743455488423756865233534697793799569802866670981662356904270988544309072648691983459024063468708849163858558300444260495432655880504371186304007206097685833870163932928823469130199562442992", + "900593985907599133309438051698408853499625", + "-900593985907599133309438051698408853499625", + "1999874529133918706984995533406759076286565612920872635155416162504047196283513226624804224664215451103787410646351770677862238993331622942206185777454355265435238628326337253875004975201674224657309748975788962678417182798452737039836018579998386385843839364431684621083773420995", + "-1999874529133918706984995533406759076286565612920872635155416162504047196283513226624804224664215451103787410646351770677862238993331622942206185777454355265435238628326337253875004975201674224657309748975788962678417182798452737039836018579998386385843839364431684621083773420995", + 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"-1604105217156493424796219158328988017738562338480346273566670218046", + }; + + boost::filesystem::ifstream is(root / "cpp_int1024_serial64.txt"); + std::cout << "Testing cpp_int1024_serial64.txt with T=" << typeid(T).name() << std::endl; + is.peek(); + BOOST_CHECK(is.good()); + boost::archive::text_iarchive ia(is); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + try + { + T val; + ia >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + } + + boost::filesystem::ifstream is2(root / "cpp_int1024_serial32.txt"); + std::cout << "Testing cpp_int1024_serial32.txt with T=" << typeid(T).name() << std::endl; + is2.peek(); + BOOST_CHECK(is2.good()); + boost::archive::text_iarchive ia2(is2); + for(unsigned i = 0; i < sizeof(text_array) / sizeof(text_array[0]); ++i) + { + try + { + T val; + ia2 >> val; + BOOST_CHECK_EQUAL(val, T(text_array[i])); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + } +} + +int main(int argc, char const* argv[]) +{ + if(argc == 2) + { + root = argv[1]; + std::cout << "Setting root directory to " << argv[1] << std::endl; + } + using namespace boost::multiprecision; + test64<cpp_int>(); + test64<number<cpp_int_backend<64, 64> > >(); + test128<cpp_int>(); + test128<number<cpp_int_backend<128, 128> > >(); + test1024<cpp_int>(); + test1024<number<cpp_int_backend<1024, 1024> > >(); + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_cpp_int_lit.cpp b/libs/multiprecision/test/test_cpp_int_lit.cpp new file mode 100644 index 0000000000..366309d0f3 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_int_lit.cpp @@ -0,0 +1,57 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/multiprecision/cpp_int.hpp> +#include "test.hpp" + + +#ifdef BOOST_MP_USER_DEFINED_LITERALS + + +using namespace boost::multiprecision; + +template <class T> +void test_literal(T val, const char* p) +{ + BOOST_CHECK_EQUAL(val, cpp_int(p)); +} + +#define TEST_LITERAL(x)\ +{\ + constexpr auto val1 = BOOST_JOIN(x, _cppi);\ + constexpr int1024_t val2 = BOOST_JOIN(x, _cppi1024);\ + constexpr auto val3 = BOOST_JOIN(x, _cppui);\ + constexpr uint1024_t val4 = BOOST_JOIN(x, _cppui1024);\ + test_literal(val1, BOOST_STRINGIZE(x));\ + test_literal(val2, BOOST_STRINGIZE(x));\ + test_literal(val3, BOOST_STRINGIZE(x));\ + test_literal(val4, BOOST_STRINGIZE(x));\ + /* Negative values: */\ + constexpr auto val5 = -BOOST_JOIN(x, _cppi);\ + constexpr int1024_t val6 = -BOOST_JOIN(x, _cppi1024);\ + constexpr auto val7 = -val1;\ + constexpr int1024_t val8 = -val2;\ + BOOST_CHECK_EQUAL(val5, -cpp_int(val1));\ + BOOST_CHECK_EQUAL(val6, -cpp_int(val1));\ + BOOST_CHECK_EQUAL(val7, -cpp_int(val1));\ + BOOST_CHECK_EQUAL(val8, -cpp_int(val1));\ +}\ + +int main() +{ + using namespace boost::multiprecision::literals; + TEST_LITERAL(0x0); + TEST_LITERAL(0x00000); + TEST_LITERAL(0x10000000); + TEST_LITERAL(0x1234500000000123450000000123345000678000000456000000567000000fefabc00000000000000); + return boost::report_errors(); +} + +#else + +int main() { return 0; } + + +#endif diff --git a/libs/multiprecision/test/test_cpp_int_serial.cpp b/libs/multiprecision/test/test_cpp_int_serial.cpp new file mode 100644 index 0000000000..915b68f897 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_int_serial.cpp @@ -0,0 +1,177 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/timer.hpp> +#include "test.hpp" + +#include <iostream> +#include <iomanip> +#include <sstream> +#include <boost/archive/text_iarchive.hpp> +#include <boost/archive/text_oarchive.hpp> +#include <boost/archive/binary_iarchive.hpp> +#include <boost/archive/binary_oarchive.hpp> +#include <boost/exception/all.hpp> + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +template <class T> +void test_neg(const T& x, const boost::mpl::true_&) +{ + T val = -x; + try{ + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } +} +template <class T> +void test_neg(const T& , const boost::mpl::false_&){} + +template <class T> +void test() +{ + using namespace boost::multiprecision; + + boost::random::mt19937 gen; + boost::uniform_int<> d(3, std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits : 3000); + boost::timer tim; + + while(true) + { + T val = generate_random<T>(d(gen)); + try + { + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + + test_neg(val, boost::mpl::bool_<std::numeric_limits<T>::is_signed>()); + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 150) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + } +} + +#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3) && !defined(TEST4) +# define TEST1 +# define TEST2 +# define TEST3 +# define TEST4 +#endif + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + test<cpp_int>(); +#endif +#ifdef TEST2 + test<number<cpp_int_backend<61, 61, unsigned_magnitude, unchecked, void> > >(); +#endif +#ifdef TEST3 + test<number<cpp_int_backend<120, 120, signed_magnitude, unchecked, void> > >(); +#endif +#ifdef TEST4 + test<int1024_t>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_cpp_rat_serial.cpp b/libs/multiprecision/test/test_cpp_rat_serial.cpp new file mode 100644 index 0000000000..6f4537be90 --- /dev/null +++ b/libs/multiprecision/test/test_cpp_rat_serial.cpp @@ -0,0 +1,163 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/timer.hpp> +#include "test.hpp" + +#include <iostream> +#include <iomanip> +#include <sstream> +#include <boost/archive/text_iarchive.hpp> +#include <boost/archive/text_oarchive.hpp> +#include <boost/archive/binary_iarchive.hpp> +#include <boost/archive/binary_oarchive.hpp> +#include <boost/exception/all.hpp> + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == (unsigned)std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + if(!val) + val = 1; + return val; +} + +template <class T> +void test_neg(const T& x, const boost::mpl::true_&) +{ + T val = -x; + try + { + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } +} +template <class T> +void test_neg(const T& , const boost::mpl::false_&){} + +template <class T> +void test() +{ + using namespace boost::multiprecision; + + boost::random::mt19937 gen; + boost::uniform_int<> d(3, std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits : 3000); + boost::timer tim; + + while(true) + { + T val(generate_random<typename component_type<T>::type>(d(gen)), generate_random<typename component_type<T>::type>(d(gen))); + try + { + std::stringstream ss; + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + + ss.clear(); + boost::archive::binary_oarchive ob(ss); + ob << static_cast<const T&>(val); + boost::archive::binary_iarchive ib(ss); + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + } + + test_neg(val, boost::mpl::bool_<std::numeric_limits<T>::is_signed>()); + + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 150) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + } +} + +int main() +{ + using namespace boost::multiprecision; + test<cpp_rational>(); + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_exp.cpp b/libs/multiprecision/test/test_exp.cpp new file mode 100644 index 0000000000..f3eae923f4 --- /dev/null +++ b/libs/multiprecision/test/test_exp.cpp @@ -0,0 +1,233 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) \ + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) \ + && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type " << typeid(T).name() << std::endl; + static const boost::array<const char*, 51u> data = + {{ + "1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "9.47747587596218770242116751705184563668845029215054154915126374673142219159548534317576897266130328412495991561490384353e76", + "8.98225489794452370997623936390755615068333094834545092387689795875746440121970819499035111276893290879203289092353747850e153", + "8.51291041070124257524798251795398355552294928156627848633073113916721592074889256105483993631579761345100284245144410506e230", + "8.06809030516483860484254925989129017112482132468761563276276594763374886826841745433660192438855214332469192411759402790e307", + "7.64651312322841630493169711336894888932951818957138997327518186691187347879142222644283389432604713409023263917264358401e384", + "7.24696436606255985380192585665173794455118215150711210905481870053193336336731228464367470327868286988180495111406609690e461", + "6.86829299533155197480610865771404565313986987801060270120621935139741577246731459024227828759564450034267891072352816870e538", + "6.50940811722948585242669672360741252715012399316164518226061001845519670701239429603657927628755169479689062519606799624e615", + "6.16927583978348964454665652571294215251327375137123272041877979478545511090085756858225302357977159539777447847855503405e692", + "5.84691629437043896753869572004324228849833391140408095171257918435296982661233664069534601413835876272500275725690968474e769", + "5.54140081286660645835370762406928689330724181979654545550204201113926269281603301564114980528619942840737770415885783439e846", + "5.25184925229805200184933663459660562493261505058724212670923083643709964294855282715531768162298567379648573804433968486e923", + "4.97742745928448409225535325233998957076879979440190164347796593390995994951755710667491911026476108957070504003155645761e1000", + "4.71734486697204622371883518659702954552385115723942808636490157561056417525827884479573988899517566587636669779645610803e1077", + "4.47085221753216236037602345430121605512330975424643767098987010800161616413051148037751552110081034066081309007796182114e1154", + "4.23723940366531198300986713567588008777043812458400705569721660157434941774066620870256745107265536124077734836797938268e1231", + "4.01583342289144005397455901781647949754375366066998182220342540048111140676724909947493787596336610499122085983712119281e1308", + "3.80599643873362813900306284477369187319506389058898599816705625750135796510808933786432614186155972485637939057212164098e1385", + "3.60712394320959592074309301816510372687695286650188776957291994751966018917404878612237961367128638199290387601511358836e1462", + "3.41864301533745457066062991907289263038319874930395315315257927161138360206596116102724713069518697248463965164712972907e1539", + "3.24001067063873569456703204286462007769933831045558617578289414699244767403736057931834775727420762410328297596596814910e1616", + "3.07071229688386868087623659761166306563170839771162347830514606977592027644137144160294469813988158463967740978461420862e1693", + "2.91026017157373047094077218552378456052150304677863670611408570458991015300131731261787644801415538043027268185097710615e1770", + "2.75819205688636078700279174380111581147323147951670302427494196210176478494486073721584055059489736040565979466551070179e1847", + "2.61406986804110104534167739704643351039975992759905579635058824027507742375380077276380178376470686987855503581867681046e1924", + "2.47747841124391945459619002346303925269640785743990333362087223895627681769816204236257960940497519376881830373722711456e2001", + "2.34802418757813746316913800667907927718925648696508255347624141597281474683823345136640610924639820192825966082309575303e2078", + "2.22533425939475124828943430510333464605535146852848680647615867629953075390889821397228584866395924176189346073006180260e2155", + "2.10905517593659363154553947631071808925462553114068144748077359132255993441363479041540672158497404660986163617828972963e2232", + "1.99885195510122536266653916064141606295420554580140619900425370702471778604391774578696867899999534265169574306808906810e2309", + "1.89440711840917173277691572886942144916664047407963356271198286654087884646102070148271284410118233470318337745546895603e2386", + "1.79541977639739687088375911648976940254141946934175300605485966288703931992861387257771264702798405630917098672594899744e2463", + "1.70160476180317540861346545791118106171203487587101437710693054174454895160403997508137760007058856854991413121389834429e2540", + "1.61269180804119796097157014527479883521656118500417752963675677684343588976915851637637232001139108420659882326614772004e2617", + "1.52842477060722969066998464046690349841548269556677423378408183476489015878816585045578141383463708674469365281537792914e2694", + "1.44856088916530600122626623629347336702026699647293500058111037526381692645547938577338582002157148103479049071921438452e2771", + "1.37287008819265239873777879432333192404914357037749380145412895230166352318128978403808382142784030558123748263528360645e2848", + "1.30113431416759441771790128053911040907207490879890145597562380328956450092799014856149474809345424672958343296615764490e2925", + "1.23314690739099822369963411660419632130352733806319401863570442920347696015409870236230656305563674376063778482449716744e3002", + "1.16871200663155636468514484039368694043851858077879103221831997264419096417014996945143145495038265243932745953706526253e3079", + "1.10764398487979357804590117089134596938734185016144401218934115168561552640448889215089150481162977776214124397487013110e3156", + "1.04976691458528698318220729857405616816444374000182094405930946710168752954926612218474430081526312018810817657409158490e3233", + "9.94914060836531582868347569174220216007647278536863127198023584205669825317884219144692385409156165042162234017403353704e3309", + "9.42927401023380446961314339401657458785389811652244742482194123119943160577946366372207045050095290781679375214307398844e3386", + "8.93657169598281164656322298275337750103095739790107943666668184304335665562867744740310577868880098719252549186849812451e3463", + "8.46961426624835911826517103631490619655296714141872141145089865045804196205328364155921945616925875458926717336478525196e3540", + "8.02705648870740089929294815816002943860908317454595055392168733404583122074223427054310572378841634984243492063192095337e3617", + "7.60762342267101369970765191988545810374824800500875923752736467467657167098026707905341603949108433696304383346239333297e3694", + "7.21010674617694221027190468649359000420209460539838589305387835463807416706224777302997789297329446308541513638035437482e3771", + "6.83336127500041943234365059231968669406267422759442985746460610830503287734479988530512309065240678799786759250323660701e3848", + }}; + + T pi = static_cast<T>("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = exp(sqrt((pi * (100 * k)) * (100 * k))); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = exp(-sqrt((pi * (100 * k)) * (100 * k))); + e = relative_error(val, T(1/T(data[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; +#if defined(BOOST_INTEL) && defined(TEST_FLOAT128) + BOOST_TEST(max_err < 40000); +#elif defined(TEST_CPP_BIN_FLOAT) + BOOST_TEST(max_err < 6000); +#else + BOOST_TEST(max_err < 5000); +#endif + + static const boost::array<boost::array<T, 2>, 10> exact_data = + {{ + {{ std::ldexp(1.0, -50), static_cast<T>("1.00000000000000088817841970012562676935794497867573073630970950828771105957980924149923657574337470594698012676100224953") }}, + {{ std::ldexp(1.0, -20), static_cast<T>("1.00000095367477115374544678824955687428365188553281789775169686343569285229334215539516690752571791280462887427635269562") }}, + {{ std::ldexp(1.0, -10), static_cast<T>("1.00097703949241653524284529261160650646585162918174419940186408264916250428896869173656853690882467186075613761065459261") }}, + {{ 0.25, static_cast<T>("1.28402541668774148407342056806243645833628086528146308921750729687220776586723800275330641943955356890166283174967968731") }}, + {{ 0.5, static_cast<T>("1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663775630779700") }}, + {{ 0.75, static_cast<T>("2.11700001661267466854536981983709561013449158470240342177913303081098453336401282000279156026661579821888590471901551426") }}, + {{ 10, static_cast<T>("22026.4657948067165169579006452842443663535126185567810742354263552252028185707925751991209681645258954515555010924578367") }}, + {{ 10.5, static_cast<T>("36315.5026742466377389120269013166179689315579671275857607480190550842856628099187749764427758174866310742771977376827512") }}, + {{ 25, static_cast<T>("7.20048993373858725241613514661261579152235338133952787362213864472320593107782569745000325654258093194727871848859163684e10") }}, + {{ 31.25, static_cast<T>("3.72994612957188849046766396046821396700589012875701157893019118883826370993674081486706667149871508642909416337810227575e13") }}, + }}; + + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = exp(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = exp(-exact_data[k][0]); + e = relative_error(val, T(1/exact_data[k][1])); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + BOOST_TEST(exp(T(0)) == 1); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPILER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_fixed_int.cpp b/libs/multiprecision/test/test_fixed_int.cpp new file mode 100644 index 0000000000..87a7239984 --- /dev/null +++ b/libs/multiprecision/test/test_fixed_int.cpp @@ -0,0 +1,165 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/fixed_int.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include "test.hpp" + +template <class T> +T generate_random(unsigned bits_wanted) +{ + static boost::random::mt19937 gen; + typedef boost::random::mt19937::result_type random_type; + + T max_val; + unsigned digits; + if(std::numeric_limits<T>::is_bounded && (bits_wanted == std::numeric_limits<T>::digits)) + { + max_val = (std::numeric_limits<T>::max)(); + digits = std::numeric_limits<T>::digits; + } + else + { + max_val = T(1) << bits_wanted; + digits = bits_wanted; + } + + unsigned bits_per_r_val = std::numeric_limits<random_type>::digits - 1; + while((random_type(1) << bits_per_r_val) > (gen.max)()) --bits_per_r_val; + + unsigned terms_needed = digits / bits_per_r_val + 1; + + T val = 0; + for(unsigned i = 0; i < terms_needed; ++i) + { + val *= (gen.max)(); + val += gen(); + } + val %= max_val; + return val; +} + +int main() +{ + using namespace boost::multiprecision; + typedef number<fixed_int<1024, true> > packed_type; + unsigned last_error_count = 0; + for(int i = 0; i < 1000; ++i) + { + mpz_int a = generate_random<mpz_int>(1000); + mpz_int b = generate_random<mpz_int>(512); + mpz_int c = generate_random<mpz_int>(256); + mpz_int d = generate_random<mpz_int>(32); + + int si = d.convert_to<int>(); + + packed_type a1 = a.str(); + packed_type b1 = b.str(); + packed_type c1 = c.str(); + packed_type d1 = d.str(); + + BOOST_CHECK_EQUAL(a.str(), a1.str()); + BOOST_CHECK_EQUAL(b.str(), b1.str()); + BOOST_CHECK_EQUAL(c.str(), c1.str()); + BOOST_CHECK_EQUAL(d.str(), d1.str()); + BOOST_CHECK_EQUAL(mpz_int(a+b).str(), packed_type(a1 + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a-b).str(), packed_type(a1 - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)+b).str(), packed_type(packed_type(-a1) + b1).str()); + BOOST_CHECK_EQUAL(mpz_int(mpz_int(-a)-b).str(), packed_type(packed_type(-a1) - b1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * d).str(), packed_type(c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(c * -d).str(), packed_type(c1 * -d1).str()); + BOOST_CHECK_EQUAL(mpz_int(-c * d).str(), packed_type(-c1 * d1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * c).str(), packed_type(b1 * c1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / b).str(), packed_type(a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -b).str(), packed_type(a1 / -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / b).str(), packed_type(-a1 / b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / d).str(), packed_type(a1 / d1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % b).str(), packed_type(a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -b).str(), packed_type(a1 % -b1).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % b).str(), packed_type(-a1 % b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a % d).str(), packed_type(a1 % d1).str()); + // bitwise ops: + BOOST_CHECK_EQUAL(mpz_int(a|b).str(), packed_type(a1 | b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a&b).str(), packed_type(a1 & b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a^b).str(), packed_type(a1 ^ b1).str()); + // Now check operations involving integers: + BOOST_CHECK_EQUAL(mpz_int(a + si).str(), packed_type(a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(a + -si).str(), packed_type(a1 + -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a + si).str(), packed_type(-a1 + si).str()); + BOOST_CHECK_EQUAL(mpz_int(si + a).str(), packed_type(si + a1).str()); + BOOST_CHECK_EQUAL(mpz_int(a - si).str(), packed_type(a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(a - -si).str(), packed_type(a1 - -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a - si).str(), packed_type(-a1 - si).str()); + BOOST_CHECK_EQUAL(mpz_int(si - a).str(), packed_type(si - a1).str()); + BOOST_CHECK_EQUAL(mpz_int(b * si).str(), packed_type(b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(b * -si).str(), packed_type(b1 * -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-b * si).str(), packed_type(-b1 * si).str()); + BOOST_CHECK_EQUAL(mpz_int(si * b).str(), packed_type(si * b1).str()); + BOOST_CHECK_EQUAL(mpz_int(a / si).str(), packed_type(a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a / -si).str(), packed_type(a1 / -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a / si).str(), packed_type(-a1 / si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % si).str(), packed_type(a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a % -si).str(), packed_type(a1 % -si).str()); + BOOST_CHECK_EQUAL(mpz_int(-a % si).str(), packed_type(-a1 % si).str()); + BOOST_CHECK_EQUAL(mpz_int(a|si).str(), packed_type(a1 | si).str()); + BOOST_CHECK_EQUAL(mpz_int(a&si).str(), packed_type(a1 & si).str()); + BOOST_CHECK_EQUAL(mpz_int(a^si).str(), packed_type(a1 ^ si).str()); + BOOST_CHECK_EQUAL(mpz_int(si|a).str(), packed_type(si|a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si&a).str(), packed_type(si&a1).str()); + BOOST_CHECK_EQUAL(mpz_int(si^a).str(), packed_type(si^a1).str()); + BOOST_CHECK_EQUAL(mpz_int(gcd(a, b)).str(), packed_type(gcd(a1, b1)).str()); + BOOST_CHECK_EQUAL(mpz_int(lcm(c, d)).str(), packed_type(lcm(c1, d1)).str()); + + if(last_error_count != boost::detail::test_errors()) + { + last_error_count = boost::detail::test_errors(); + std::cout << std::hex << std::showbase; + + std::cout << "a = " << a << std::endl; + std::cout << "a1 = " << a1 << std::endl; + std::cout << "b = " << b << std::endl; + std::cout << "b1 = " << b1 << std::endl; + std::cout << "c = " << c << std::endl; + std::cout << "c1 = " << c1 << std::endl; + std::cout << "d = " << d << std::endl; + std::cout << "d1 = " << d1 << std::endl; + std::cout << "a + b = " << a+b << std::endl; + std::cout << "a1 + b1 = " << a1+b1 << std::endl; + std::cout << std::dec; + std::cout << "a - b = " << a-b << std::endl; + std::cout << "a1 - b1 = " << a1-b1 << std::endl; + std::cout << "-a + b = " << mpz_int(-a)+b << std::endl; + std::cout << "-a1 + b1 = " << packed_type(-a1)+b1 << std::endl; + std::cout << "-a - b = " << mpz_int(-a)-b << std::endl; + std::cout << "-a1 - b1 = " << packed_type(-a1)-b1 << std::endl; + std::cout << "c*d = " << c*d << std::endl; + std::cout << "c1*d1 = " << c1*d1 << std::endl; + std::cout << "b*c = " << b*c << std::endl; + std::cout << "b1*c1 = " << b1*c1 << std::endl; + std::cout << "a/b = " << a/b << std::endl; + std::cout << "a1/b1 = " << a1/b1 << std::endl; + std::cout << "a/d = " << a/d << std::endl; + std::cout << "a1/d1 = " << a1/d1 << std::endl; + std::cout << "a%b = " << a%b << std::endl; + std::cout << "a1%b1 = " << a1%b1 << std::endl; + std::cout << "a%d = " << a%d << std::endl; + std::cout << "a1%d1 = " << a1%d1 << std::endl; + } + } + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_float128_serial.cpp b/libs/multiprecision/test/test_float128_serial.cpp new file mode 100644 index 0000000000..8966969fb2 --- /dev/null +++ b/libs/multiprecision/test/test_float128_serial.cpp @@ -0,0 +1,26 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/float128.hpp> +#include "test_float_serial.hpp" + + +int main() +{ + using namespace boost::multiprecision; + test<float128>(); + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_float_io.cpp b/libs/multiprecision/test/test_float_io.cpp new file mode 100644 index 0000000000..8ed9e9d4ba --- /dev/null +++ b/libs/multiprecision/test/test_float_io.cpp @@ -0,0 +1,336 @@ +// Copyright John Maddock 2011. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPF_50) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50) \ + && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +# define TEST_MPF_50 +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_FLOAT128 + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif + +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include "test.hpp" +#include <boost/array.hpp> +#include <iostream> +#include <iomanip> + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +#if defined(TEST_MPF_50) +template <unsigned N, boost::multiprecision::expression_template_option ET> +bool has_bad_bankers_rounding(const boost::multiprecision::number<boost::multiprecision::gmp_float<N>, ET>&) +{ return true; } +#endif +#if defined(TEST_FLOAT128) && defined(BOOST_INTEL) +bool has_bad_bankers_rounding(const boost::multiprecision::float128&) +{ return true; } +#endif +template <class T> +bool has_bad_bankers_rounding(const T&) { return false; } + +bool is_bankers_rounding_error(const std::string& s, const char* expect) +{ + // This check isn't foolproof: that would require *much* more sophisticated code!!! + std::string::size_type l = std::strlen(expect); + if(l != s.size()) + return false; + std::string::size_type len = s.find('e'); + if(len == std::string::npos) + len = l - 1; + else + --len; + if(s.compare(0, len, expect, len)) + return false; + if(s[len] != expect[len] + 1) + return false; + return true; +} + +void print_flags(std::ios_base::fmtflags f) +{ + std::cout << "Formatting flags were: "; + if(f & std::ios_base::scientific) + std::cout << "scientific "; + if(f & std::ios_base::fixed) + std::cout << "fixed "; + if(f & std::ios_base::showpoint) + std::cout << "showpoint "; + if(f & std::ios_base::showpos) + std::cout << "showpos "; + std::cout << std::endl; +} + + +template <class T> +void test() +{ + typedef T mp_t; + boost::array<std::ios_base::fmtflags, 9> f = + {{ + std::ios_base::fmtflags(0), std::ios_base::showpoint, std::ios_base::showpos, std::ios_base::scientific, std::ios_base::scientific|std::ios_base::showpos, + std::ios_base::scientific|std::ios_base::showpoint, std::ios_base::fixed, std::ios_base::fixed|std::ios_base::showpoint, + std::ios_base::fixed|std::ios_base::showpos + }}; + + boost::array<boost::array<const char*, 13 * 9>, 40> string_data = {{ +#include "libs/multiprecision/test/string_data.ipp" + }}; + + double num = 123456789.0; + double denom = 1; + double val = num; + for(unsigned j = 0; j < 40; ++j) + { + unsigned col = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = string_data[j][col]; + if(ss.str() != expect) + { + if(has_bad_bankers_rounding(mp_t()) && is_bankers_rounding_error(ss.str(), expect)) + { + std::cout << "Ignoring bankers-rounding error with GMP mp_f.\n"; + } + else + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + } + num = -num; + if(j & 1) + denom *= 8; + val = num / denom; + } + + boost::array<const char*, 13 * 9> zeros = + {{ "0", "0.", "+0", "0.0e+00", "+0.0e+00", "0.0e+00", "0.0", "0.0", "+0.0", "0", "0.0", "+0", "0.00e+00", "+0.00e+00", "0.00e+00", "0.00", "0.00", "+0.00", "0", "0.00", "+0", "0.000e+00", "+0.000e+00", "0.000e+00", "0.000", "0.000", "+0.000", "0", "0.000", "+0", "0.0000e+00", "+0.0000e+00", "0.0000e+00", "0.0000", "0.0000", "+0.0000", "0", "0.0000", "+0", "0.00000e+00", "+0.00000e+00", "0.00000e+00", "0.00000", "0.00000", "+0.00000", "0", "0.00000", "+0", "0.000000e+00", "+0.000000e+00", "0.000000e+00", "0.000000", "0.000000", "+0.000000", "0", "0.000000", "+0", "0.0000000e+00", "+0.0000000e+00", "0.0000000e+00", "0.0000000", "0.0000000", "+0.0000000", "0", "0.0000000", "+0", "0.00000000e+00", "+0.00000000e+00", "0.00000000e+00", "0.00000000", "0.00000000", "+0.00000000", "0", "0.00000000", "+0", "0.000000000e+00", "+0.000000000e+00", "0.000000000e+00", "0.000000000", "0.000000000", "+0.000000000", "0", "0.000000000", "+0", "0.0000000000e+00", "+0.0000000000e+00", "0.0000000000e+00", "0.0000000000", "0.0000000000", "+0.0000000000", "0", "0.0000000000", "+0", "0.00000000000e+00", "+0.00000000000e+00", "0.00000000000e+00", "0.00000000000", "0.00000000000", "+0.00000000000", "0", "0.00000000000", "+0", "0.000000000000e+00", "+0.000000000000e+00", "0.000000000000e+00", "0.000000000000", "0.000000000000", "+0.000000000000", "0", "0.000000000000", "+0", "0.0000000000000e+00", "+0.0000000000000e+00", "0.0000000000000e+00", "0.0000000000000", "0.0000000000000", "+0.0000000000000" }}; + + unsigned col = 0; + val = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = zeros[col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + + if(std::numeric_limits<mp_t>::has_infinity) + { + T val = std::numeric_limits<T>::infinity(); + BOOST_CHECK_EQUAL(val.str(), "inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "+inf"); + val = -val; + BOOST_CHECK_EQUAL(val.str(), "-inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "-inf"); + + val = static_cast<T>("inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits<T>::infinity()); + val = static_cast<T>("+inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits<T>::infinity()); + val = static_cast<T>("-inf"); + BOOST_CHECK_EQUAL(val, -std::numeric_limits<T>::infinity()); + } + if(std::numeric_limits<mp_t>::has_quiet_NaN) + { + T val = std::numeric_limits<T>::quiet_NaN(); + BOOST_CHECK_EQUAL(val.str(), "nan"); + val = static_cast<T>("nan"); + BOOST_CHECK((boost::math::isnan)(val)); + } +} + +template <class T> +T generate_random() +{ + typedef typename T::backend_type::exponent_type e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution<e_type> ui(0, std::numeric_limits<T>::max_exponent - 10); + return ldexp(val, ui(gen)); +} + +template <class T> +struct max_digits10_proxy +{ + static const unsigned value = std::numeric_limits<T>::digits10 + 5; +}; +#ifdef TEST_CPP_DEC_FLOAT +template <unsigned D, boost::multiprecision::expression_template_option ET> +struct max_digits10_proxy<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<D>, ET> > +{ + static const unsigned value = std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<D>, ET> >::max_digits10; +}; +#endif +#ifdef TEST_MPF_50 +template <unsigned D, boost::multiprecision::expression_template_option ET> +struct max_digits10_proxy<boost::multiprecision::number<boost::multiprecision::gmp_float<D>, ET> > +{ + static const unsigned value = std::numeric_limits<boost::multiprecision::number<boost::multiprecision::gmp_float<D>, ET> >::max_digits10; +}; +#endif +#ifdef TEST_MPFR_50 +template <unsigned D, boost::multiprecision::expression_template_option ET> +struct max_digits10_proxy<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<D>, ET> > +{ + static const unsigned value = std::numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<D>, ET> >::max_digits10; +}; +#endif + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + ss << std::setprecision(std::numeric_limits<T>::max_digits10); +#else + ss << std::setprecision(max_digits10_proxy<T>::value); +#endif + ss.flags(f); + ss << val; + T new_val = static_cast<T>(ss.str()); + BOOST_CHECK_EQUAL(new_val, val); + new_val = static_cast<T>(val.str(0, f)); + BOOST_CHECK_EQUAL(new_val, val); +} + +template <class T> +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::scientific)); + if((fabs(val) > 1) && (fabs(val) < 1e100)) + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::fixed)); +} + +template <class T> +void test_round_trip() +{ + for(unsigned i = 0; i < 1000; ++i) + { + T val = generate_random<T>(); + do_round_trip(val); + do_round_trip(T(-val)); + do_round_trip(T(1/val)); + do_round_trip(T(-1/val)); + } +} + +int main() +{ +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); + + test_round_trip<boost::multiprecision::mpfr_float_50>(); + test_round_trip<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); + + test_round_trip<boost::multiprecision::mpfr_float_50>(); + test_round_trip<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); + + // cpp_dec_float has extra guard digits that messes this up: + test_round_trip<boost::multiprecision::cpp_dec_float_50>(); + test_round_trip<boost::multiprecision::cpp_dec_float_100>(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); + /* + // I can't get this to work with mpf_t - mpf_str appears + // not to actually print enough decimal digits: + test_round_trip<boost::multiprecision::mpf_float_50>(); + test_round_trip<boost::multiprecision::mpf_float_100>(); + */ +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#ifndef BOOST_INTEL + test_round_trip<boost::multiprecision::float128>(); +#endif +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_float_serial.hpp b/libs/multiprecision/test/test_float_serial.hpp new file mode 100644 index 0000000000..cc560b256f --- /dev/null +++ b/libs/multiprecision/test/test_float_serial.hpp @@ -0,0 +1,132 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/timer.hpp> +#include "test.hpp" + +#include <iostream> +#include <iomanip> +#include <sstream> +#include <boost/archive/text_iarchive.hpp> +#include <boost/archive/text_oarchive.hpp> +#include <boost/archive/binary_iarchive.hpp> +#include <boost/archive/binary_oarchive.hpp> +#include <boost/exception/all.hpp> + + +#ifndef BOOST_MP_TEST_FLOAT_SERIAL_HPP +#define BOOST_MP_TEST_FLOAT_SERIAL_HPP + +template <class T> +T generate_random(unsigned bits_wanted) +{ + typedef typename T::backend_type::exponent_type e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution<e_type> ui(std::numeric_limits<T>::min_exponent + 1, std::numeric_limits<T>::max_exponent - 1); + return ldexp(val, ui(gen)); +} + +template <class T> +void test() +{ + boost::timer tim; + + while(true) + { + T val = generate_random<T>(boost::math::tools::digits<T>()); + int test_id = 0; + std::string stream_contents; + try{ + test_id = 0; + { + std::stringstream ss(std::ios_base::in | std::ios_base::out | std::ios_base::binary); + boost::archive::text_oarchive oa(ss); + oa << static_cast<const T&>(val); + stream_contents = ss.str(); + boost::archive::text_iarchive ia(ss); + T val2; + ia >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + { + std::stringstream ss(std::ios_base::in | std::ios_base::out | std::ios_base::binary); + ++test_id; + boost::archive::binary_oarchive ba(ss); + ba << static_cast<const T&>(val); + stream_contents = ss.str(); + boost::archive::binary_iarchive ib(ss); + T val2; + ib >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + { + std::stringstream ss(std::ios_base::in | std::ios_base::out | std::ios_base::binary); + val = -val; + ++test_id; + boost::archive::text_oarchive oa2(ss); + oa2 << static_cast<const T&>(val); + stream_contents = ss.str(); + boost::archive::text_iarchive ia2(ss); + T val2; + ia2 >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + { + std::stringstream ss(std::ios_base::in | std::ios_base::out | std::ios_base::binary); + ++test_id; + boost::archive::binary_oarchive ba2(ss); + ba2 << static_cast<const T&>(val); + stream_contents = ss.str(); + boost::archive::binary_iarchive ib2(ss); + T val2; + ib2 >> val2; + BOOST_CHECK_EQUAL(val, val2); + } + } + catch(const boost::exception& e) + { + std::cout << "Caught boost::exception with:\n"; + std::cout << diagnostic_information(e); + std::cout << "Failed test ID = " << test_id << std::endl; + std::cout << "Stream contents were: \n" << stream_contents << std::endl; + ++boost::detail::test_errors(); + break; + } + catch(const std::exception& e) + { + std::cout << "Caught std::exception with:\n"; + std::cout << e.what() << std::endl; + std::cout << "Failed test ID = " << test_id << std::endl; + std::cout << "Stream contents were: \n" << stream_contents << std::endl; + ++boost::detail::test_errors(); + break; + } + // + // Check to see if test is taking too long. + // Tests run on the compiler farm time out after 300 seconds, + // so don't get too close to that: + // + if(tim.elapsed() > 150) + { + std::cout << "Timeout reached, aborting tests now....\n"; + break; + } + } +} + +#endif diff --git a/libs/multiprecision/test/test_fpclassify.cpp b/libs/multiprecision/test/test_fpclassify.cpp new file mode 100644 index 0000000000..dd5221cfc8 --- /dev/null +++ b/libs/multiprecision/test/test_fpclassify.cpp @@ -0,0 +1,342 @@ +// Copyright John Maddock 2006. +// Copyright Paul A. Bristow 2007 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <cmath> +#include <math.h> +#include <boost/limits.hpp> +#include <boost/math/special_functions/fpclassify.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_MPFR_50 +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_MPFI_50 +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +#ifdef _MSC_VER +#pragma warning(disable: 4127) // conditional expression is constant +#endif + +const char* method_name(const boost::math::detail::native_tag&) +{ + return "Native"; +} + +const char* method_name(const boost::math::detail::generic_tag<true>&) +{ + return "Generic (with numeric limits)"; +} + +const char* method_name(const boost::math::detail::generic_tag<false>&) +{ + return "Generic (without numeric limits)"; +} + +const char* method_name(const boost::math::detail::ieee_tag&) +{ + return "IEEE std"; +} + +const char* method_name(const boost::math::detail::ieee_copy_all_bits_tag&) +{ + return "IEEE std, copy all bits"; +} + +const char* method_name(const boost::math::detail::ieee_copy_leading_bits_tag&) +{ + return "IEEE std, copy leading bits"; +} + +template <class T> +void test() +{ + typedef typename boost::math::detail::fp_traits<T>::type traits; + + T t = 2; + T u = 2; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + if(std::numeric_limits<T>::is_specialized) + { + t = (std::numeric_limits<T>::max)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t = (std::numeric_limits<T>::min)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + if(std::numeric_limits<T>::has_denorm) + { + t = (std::numeric_limits<T>::min)(); + t /= 2; + if(t != 0) + { + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + t = std::numeric_limits<T>::denorm_min(); + if((t != 0) && (t < (std::numeric_limits<T>::min)())) + { + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_SUBNORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + } + } + else + { + std::cout << "Denormalised forms not tested" << std::endl; + } + t = 0; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t /= -u; // create minus zero if it exists + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_ZERO); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + // infinity: + if(std::numeric_limits<T>::has_infinity) + { + // At least one std::numeric_limits<T>::infinity)() returns zero + // (Compaq true64 cxx), hence the check. + t = (std::numeric_limits<T>::infinity)(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); +#if !defined(__BORLANDC__) && !(defined(__DECCXX) && !defined(_IEEE_FP)) + // divide by zero on Borland triggers a C++ exception :-( + // divide by zero on Compaq CXX triggers a C style signal :-( + t = 2; + u = 0; + t /= u; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); + t = -2; + t /= u; + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_INFINITE); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (::boost::math::fpclassify)(t + 0)); +#else + std::cout << "Infinities from divide by zero not tested" << std::endl; +#endif + } + else + { + std::cout << "Infinity not tested" << std::endl; + } +#ifndef __BORLANDC__ + // NaN's: + // Note that Borland throws an exception if we even try to obtain a Nan + // by calling std::numeric_limits<T>::quiet_NaN() !!!!!!! + if(std::numeric_limits<T>::has_quiet_NaN) + { + t = std::numeric_limits<T>::quiet_NaN(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + } + else + { + std::cout << "Quiet NaN's not tested" << std::endl; + } + if(std::numeric_limits<T>::has_signaling_NaN) + { + t = std::numeric_limits<T>::signaling_NaN(); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NAN); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), false); + } + else + { + std::cout << "Signaling NaN's not tested" << std::endl; + } +#endif +} + +int main() +{ + BOOST_MATH_CONTROL_FP; + // start by printing some information: +#ifdef isnan + std::cout << "Platform has isnan macro." << std::endl; +#endif +#ifdef fpclassify + std::cout << "Platform has fpclassify macro." << std::endl; +#endif +#ifdef BOOST_HAS_FPCLASSIFY + std::cout << "Platform has FP_NORMAL macro." << std::endl; +#endif + std::cout << "FP_ZERO: " << (int)FP_ZERO << std::endl; + std::cout << "FP_NORMAL: " << (int)FP_NORMAL << std::endl; + std::cout << "FP_INFINITE: " << (int)FP_INFINITE << std::endl; + std::cout << "FP_NAN: " << (int)FP_NAN << std::endl; + std::cout << "FP_SUBNORMAL: " << (int)FP_SUBNORMAL << std::endl; + +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#endif +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_generic_conv.cpp b/libs/multiprecision/test/test_generic_conv.cpp new file mode 100644 index 0000000000..f23aa39c5d --- /dev/null +++ b/libs/multiprecision/test/test_generic_conv.cpp @@ -0,0 +1,207 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#include <boost/multiprecision/cpp_bin_float.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/random.hpp> + +#ifdef TEST_GMP +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_TOMMATH +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_MPFR +#include <boost/multiprecision/mpfr.hpp> +#endif + +int main() +{ + using namespace boost::multiprecision; + using namespace boost::random; + + independent_bits_engine<mt11213b, 1024, cpp_int> gen; + mt11213b small_gen; + + for(unsigned i = 0; i < 100; ++i) + { + cpp_int c = gen(); + // + // Integer to integer conversions first: + // +#ifdef TEST_GMP + mpz_int z(c); + cpp_int t(z); + BOOST_CHECK_EQUAL(t, c); + z.assign(-c); + t.assign(-z); + BOOST_CHECK_EQUAL(t, c); +#endif +#ifdef TEST_TOMMATH + tom_int tom(c); + cpp_int t2(tom); + BOOST_CHECK_EQUAL(t2, c); + tom.assign(-c); + t2.assign(-tom); + BOOST_CHECK_EQUAL(t2, c); +#endif + // + // Now integer to float: + // + typedef number<cpp_dec_float<500> > dec_float_500; + dec_float_500 df(c); + dec_float_500 df2(c.str()); + BOOST_CHECK_EQUAL(df, df2); + df.assign(-c); + df2 = -df2; + BOOST_CHECK_EQUAL(df, df2); +#ifdef TEST_GMP + typedef number<gmp_float<500> > mpf_type; + mpf_type mpf(c); + mpf_type mpf2(c.str()); + BOOST_CHECK_EQUAL(mpf, mpf2); + mpf.assign(-c); + mpf2 = -mpf2; + BOOST_CHECK_EQUAL(mpf, mpf2); +#endif +#ifdef TEST_MPFR + typedef number<mpfr_float_backend<500> > mpfr_type; + mpfr_type mpfr(c); + mpfr_type mpfr2(c.str()); + BOOST_CHECK_EQUAL(mpfr, mpfr2); + mpfr.assign(-c); + mpfr2 = -mpfr2; + BOOST_CHECK_EQUAL(mpfr, mpfr2); +#endif + // + // Now float to float: + // + df.assign(c); + df /= dec_float_500(gen()); + dec_float_500 tol("1e-500"); +#ifdef TEST_GMP + mpf.assign(df); + mpf2 = static_cast<mpf_type>(df.str()); + BOOST_CHECK_EQUAL(mpf, mpf2); + df.assign(mpf); + df2 = static_cast<dec_float_500>(mpf.str()); + BOOST_CHECK(fabs((df - df2) / df) < tol); +#endif +#ifdef TEST_MPFR + mpfr.assign(df); + mpfr2 = static_cast<mpfr_type>(df.str()); + BOOST_CHECK_EQUAL(mpfr, mpfr2); + df.assign(mpfr); + df2 = static_cast<dec_float_500>(mpfr.str()); + BOOST_CHECK(fabs((df - df2) / df) < tol); +#endif + // + // Rational to rational conversions: + // + cpp_rational cppr(c, gen()), cppr2, cppr3; +#ifdef TEST_GMP + mpq_rational mpq(cppr); + cppr2.assign(mpq); + BOOST_CHECK_EQUAL(cppr, cppr2); +#endif +#ifdef TEST_TOMMATH + tom_rational tr(cppr); + cppr3.assign(tr); + BOOST_CHECK_EQUAL(cppr, cppr3); +#endif + // + // Integer to rational conversions: + // +#ifdef TEST_GMP + mpq.assign(c); + mpq_rational mpq2 = static_cast<mpq_rational>(c.str()); + BOOST_CHECK_EQUAL(mpq, mpq2); +#endif +#ifdef TEST_TOMMATH + tr.assign(c); + tom_rational tr2 = static_cast<tom_rational>(c.str()); + BOOST_CHECK_EQUAL(tr, tr2); +#endif + // + // Rational to float: + // + df.assign(cppr); + df2.assign(numerator(cppr)); + df2 /= dec_float_500(denominator(cppr)); + BOOST_CHECK(fabs(df - df2) / df2 < tol); + // + // Float to rational: + // + static const int max_range = std::numeric_limits<double>::digits >= std::numeric_limits<int>::digits ? std::numeric_limits<int>::max() : (1 << (std::numeric_limits<double>::digits - 1)) - 1; + static const int min_range = std::numeric_limits<double>::digits >= std::numeric_limits<int>::digits ? std::numeric_limits<int>::min() : -(1 << (std::numeric_limits<double>::digits - 1)) + 1; + static const boost::random::uniform_int_distribution<> i_val_dist(min_range, max_range); + static const boost::random::uniform_int_distribution<> i_exp_dist(std::numeric_limits<double>::min_exponent, std::numeric_limits<double>::max_exponent - 2 - std::numeric_limits<int>::digits); + int iv = i_val_dist(small_gen); + int eval = i_exp_dist(small_gen); + double dv = iv; + dv = ldexp(dv, eval); + cppr = dv; + cppr2 = iv; + cpp_int cppi = 1; + cppi <<= abs(eval); + if(eval < 0) + cppr2 /= cppi; + else + cppr2 *= cppi; + BOOST_CHECK_EQUAL(cppr, cppr2); + // + // Again but with bigger numbers: + // + cpp_int cppi2 = gen(); + number<cpp_bin_float<1030> > cppbf(cppi2); + cppbf = ldexp(cppbf, eval); + cppr.assign(cppbf); + cppr2 = cppi2; + if(eval < 0) + cppr2 /= cppi; + else + cppr2 *= cppi; + BOOST_CHECK_EQUAL(cppr, cppr2); + // + // MSVC will compile either the code above, or + // the code below, but not both in the same file. + // Other compilers including Intel in msvc-compatibity + // mode have no such difficulty. Indeed the fact that + // the presence of the code below causes the code above to + // fail to compile strongly suggests a compiler bug. + // +#if !defined(BOOST_MSVC) + // + // Again but with bigger base 10 numbers: + // + number<cpp_dec_float<std::numeric_limits<int1024_t>::digits10 + 2> > cppdec2(cppi2); + cppdec2 = scalbn(cppdec2, eval); + cppr.assign(cppdec2); + cppr2 = cppi2; + cppi = 10; + cppi = pow(cppi, abs(eval)); + if(eval < 0) + cppr2 /= cppi; + else + cppr2 *= cppi; + BOOST_CHECK_EQUAL(cppr, cppr2); +#endif + } + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_gmp_conversions.cpp b/libs/multiprecision/test/test_gmp_conversions.cpp new file mode 100644 index 0000000000..3309b8a568 --- /dev/null +++ b/libs/multiprecision/test/test_gmp_conversions.cpp @@ -0,0 +1,158 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#include <boost/multiprecision/gmp.hpp> + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between GMP supported backends: + // + mpf_t mpf; + mpz_t mpz; + mpq_t mpq; + mpf_init2(mpf, 100); + mpf_set_ui(mpf, 2u); + mpz_init(mpz); + mpz_set_ui(mpz, 2u); + mpq_init(mpq); + mpq_set_ui(mpq, 2u, 1u); + + BOOST_TEST(mpf_float(mpf) == 2); + BOOST_TEST(mpf_float_50(mpf) == 2); + BOOST_TEST(mpf_float(mpz) == 2); + BOOST_TEST(mpf_float_50(mpz) == 2); + BOOST_TEST(mpf_float(mpq) == 2); + BOOST_TEST(mpf_float_50(mpq) == 2); + + mpf_float f0; + mpf_float_50 f50; + f0 = mpf; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpz; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpq; + BOOST_TEST(f0 == 2); + + f50 = mpf; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpz; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpq; + BOOST_TEST(f50 == 2); + + f50 = 4; + f0 = f50; + BOOST_TEST(f0 == 4); + f0 = 3; + f50 = f0; + BOOST_TEST(f50 == 3); + f50 = 4; + BOOST_TEST(mpf_float(f50) == 4); + BOOST_TEST(mpf_float_50(f0) == 3); + + mpz_int iz(2); + mpq_rational rat(2); + f50 = iz; + BOOST_TEST(f50 == 2); + f0 = iz; + BOOST_TEST(f0 == 2); + BOOST_TEST(mpf_float(iz) == 2); + BOOST_TEST(mpf_float_50(iz) == 2); + BOOST_TEST(mpf_float(rat) == 2); + BOOST_TEST(mpf_float_50(rat) == 2); + + BOOST_TEST(mpz_int(mpf) == 2); + BOOST_TEST(mpz_int(mpz) == 2); + BOOST_TEST(mpz_int(mpq) == 2); + iz = 3; + iz = mpz_int(mpf); // explicit conversion only + BOOST_TEST(iz == 2); + iz = 3; + iz = mpz; + BOOST_TEST(iz == 2); + iz = 4; + iz = mpz_int(mpq); // explicit conversion only + BOOST_TEST(iz == 2); + f0 = 2; + f50 = 2; + + BOOST_TEST(mpz_int(f0) == 2); + BOOST_TEST(mpz_int(f50) == 2); + rat = 2; + BOOST_TEST(mpz_int(rat) == 2); + iz = 3; + iz = static_cast<mpz_int>(f0); + BOOST_TEST(iz == 2); + iz = 3; + iz = static_cast<mpz_int>(f50); + BOOST_TEST(iz == 2); + iz = 3; + iz = static_cast<mpz_int>(rat); + BOOST_TEST(iz == 2); + + BOOST_TEST(mpq_rational(mpz) == 2); + BOOST_TEST(mpq_rational(mpq) == 2); + BOOST_TEST(mpq_rational(iz) == 2); + rat = 3; + rat = mpz; + BOOST_TEST(rat == 2); + rat = 3; + rat = mpq; + BOOST_TEST(rat == 2); + rat = 3; + rat = iz; + BOOST_TEST(rat == 2); + + iz = numerator(rat); + BOOST_TEST(iz == 2); + iz = denominator(rat); + BOOST_TEST(iz == 1); + + // + // Conversions involving precision only, + // note that mpf_t precisions are only approximate: + // + mpf_float::default_precision(30); + f50 = 2; + mpf_float_100 f100(3); + mpf_float f0a(4); + mpf_float f0b(f100); + BOOST_TEST(f0a.precision() >= 30); + BOOST_TEST(f0b.precision() >= 100); + f0a = f100; + BOOST_TEST(f0a == 3); + BOOST_TEST(f0a.precision() >= 100); + + f100 = f50; + BOOST_TEST(f100 == 2); + + mpf_clear(mpf); + mpz_clear(mpz); + mpq_clear(mpq); + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_int_io.cpp b/libs/multiprecision/test/test_int_io.cpp new file mode 100644 index 0000000000..a1f01a3512 --- /dev/null +++ b/libs/multiprecision/test/test_int_io.cpp @@ -0,0 +1,169 @@ +// Copyright John Maddock 2011. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPZ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_TOMMATH +# define TEST_MPZ +# define TEST_CPP_INT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPZ) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_TOMMATH) +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_CPP_INT +#include <boost/multiprecision/cpp_int.hpp> +#endif + +#include <boost/algorithm/string/case_conv.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include "test.hpp" +#include <iostream> +#include <iomanip> + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +template <class T> +struct unchecked_type{ typedef T type; }; + +#ifdef TEST_CPP_INT +template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +struct unchecked_type<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> > +{ + typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, boost::multiprecision::unchecked, Allocator>, ExpressionTemplates> type; +}; +#endif + +template <class T> +T generate_random() +{ + typedef typename unchecked_type<T>::type unchecked_T; + + static const unsigned limbs = std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_bounded ? std::numeric_limits<T>::digits / std::numeric_limits<unsigned>::digits + 3 : 20; + + static boost::random::uniform_int_distribution<unsigned> ui(0, limbs); + static boost::random::mt19937 gen; + unchecked_T val = gen(); + unsigned lim = ui(gen); + for(unsigned i = 0; i < lim; ++i) + { + val *= (gen.max)(); + val += gen(); + } + return val; +} + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + ss << std::setprecision(std::numeric_limits<T>::max_digits10); +#else + ss << std::setprecision(std::numeric_limits<T>::digits10 + 5); +#endif + ss.flags(f); + ss << val; + T new_val = static_cast<T>(ss.str()); + BOOST_CHECK_EQUAL(new_val, val); + new_val = static_cast<T>(val.str(0, f)); + BOOST_CHECK_EQUAL(new_val, val); +} + +template <class T> +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + if(val >= 0) + { + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::hex)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::oct)); + } +} + +template <class T> +void negative_round_trip(T val, const boost::mpl::true_&) +{ + do_round_trip(T(-val)); +} +template <class T> +void negative_round_trip(T, const boost::mpl::false_&) +{ +} + +template <class T> +void negative_spots(const boost::mpl::true_&) +{ + BOOST_CHECK_EQUAL(T(-1002).str(), "-1002"); + if(!std::numeric_limits<T>::is_modulo) + { + BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::oct), std::runtime_error); + BOOST_CHECK_THROW(T(-2).str(0, std::ios_base::hex), std::runtime_error); + } +} +template <class T> +void negative_spots(const boost::mpl::false_&) +{ +} + +template <class T> +void test_round_trip() +{ + for(unsigned i = 0; i < 1000; ++i) + { + T val = generate_random<T>(); + do_round_trip(val); + negative_round_trip(val, boost::mpl::bool_<std::numeric_limits<T>::is_signed>()); + } + + BOOST_CHECK_EQUAL(T(1002).str(), "1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::showpos), "+1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct), "1752"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::oct|std::ios_base::showbase), "01752"); + BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex)), "3ea"); + BOOST_CHECK_EQUAL(boost::to_lower_copy(T(1002).str(0, std::ios_base::hex|std::ios_base::showbase)), "0x3ea"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec), "1002"); + BOOST_CHECK_EQUAL(T(1002).str(0, std::ios_base::dec|std::ios_base::showbase), "1002"); + + negative_spots<T>(boost::mpl::bool_<std::numeric_limits<T>::is_signed>()); +} + +int main() +{ +#ifdef TEST_MPZ + test_round_trip<boost::multiprecision::mpz_int>(); +#endif +#ifdef TEST_TOMMATH + test_round_trip<boost::multiprecision::tom_int>(); +#endif +#ifdef TEST_CPP_INT + test_round_trip<boost::multiprecision::cpp_int>(); + test_round_trip<boost::multiprecision::checked_int1024_t>(); + test_round_trip<boost::multiprecision::checked_uint512_t >(); + test_round_trip<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<32, 32, boost::multiprecision::signed_magnitude, boost::multiprecision::checked, void> > >(); + test_round_trip<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<32, 32, boost::multiprecision::unsigned_magnitude, boost::multiprecision::checked, void> > >(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_log.cpp b/libs/multiprecision/test/test_log.cpp new file mode 100644 index 0000000000..669deb1e81 --- /dev/null +++ b/libs/multiprecision/test/test_log.cpp @@ -0,0 +1,264 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_MPFR_50 +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_MPFI_50 +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type " << typeid(T).name() << std::endl; + static const boost::array<const char*, 101> data = + {{ + 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"19.565410630120075532420489068555321524954362381908007338302983473268528473151341321768804731192210840056455228388636731122203200610869021021871133154865620432257415783302175345843898977949742849569372169004904667621738405749986270376895267386643049526766451459390277406632576412790748533372863644721976845168460840162066672290292749672668879524315410824251032084115058493720402881895485689493165441193", + }}; + + T pi = static_cast<T>("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609"); + T tenth = 1; + tenth /= 10; + T logten = log(T(10)); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = boost::multiprecision::log(tenth + pi * (100 * k) * (100 * k)); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + + val = boost::multiprecision::log(1 / (tenth + pi * (100 * k) * (100 * k))); + e = relative_error(val, T(-T(data[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + + val = boost::multiprecision::log10(tenth + pi * (100 * k) * (100 * k)); + e = relative_error(val, T(T(data[k]) / logten)); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + + val = boost::multiprecision::log10(1 / (tenth + pi * (100 * k) * (100 * k))); + e = relative_error(val, T(-T(data[k]) / logten)); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; +#if defined(BOOST_INTEL) && defined(TEST_FLOAT128) + BOOST_TEST(max_err < 20); +#else + BOOST_TEST(max_err < 10); +#endif + BOOST_TEST(log(T(1)) == 0); + // + // Some tricky special cases: + // + BOOST_CHECK((boost::math::isfinite)(log((std::numeric_limits<T>::max)()))); + BOOST_CHECK((boost::math::isfinite)(log((std::numeric_limits<T>::min)()))); + BOOST_CHECK((boost::math::isfinite)(log10((std::numeric_limits<T>::max)()))); + BOOST_CHECK((boost::math::isfinite)(log10((std::numeric_limits<T>::min)()))); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_miller_rabin.cpp b/libs/multiprecision/test/test_miller_rabin.cpp new file mode 100644 index 0000000000..ec12ab8bd0 --- /dev/null +++ b/libs/multiprecision/test/test_miller_rabin.cpp @@ -0,0 +1,90 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/gmp.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#include <boost/multiprecision/miller_rabin.hpp> +#include <boost/math/special_functions/prime.hpp> +#include <iostream> +#include <iomanip> +#include "test.hpp" + + +template <class I> +void test() +{ + // + // Very simple test program to verify that the GMP's Miller-Rabin + // implementation and this one agree on whether some random numbers + // are prime or not. Of course these are probabilistic tests so there's + // no reason why they should actually agree - except the probability of + // disagreement for 25 trials is almost infinitely small. + // + using namespace boost::random; + using namespace boost::multiprecision; + + typedef I test_type; + + static const unsigned test_bits = + std::numeric_limits<test_type>::digits && (std::numeric_limits<test_type>::digits <= 256) + ? std::numeric_limits<test_type>::digits + : 128; + + independent_bits_engine<mt11213b, test_bits, test_type> gen; + // + // We must use a different generator for the tests and number generation, otherwise + // we get false positives. Further we use the same random number engine for the + // Miller Rabin test as GMP uses internally: + // + mt19937 gen2; + + // + // Begin by testing the primes in our table as all these should return true: + // + for(unsigned i = 1; i < boost::math::max_prime; ++i) + { + BOOST_TEST(miller_rabin_test(test_type(boost::math::prime(i)), 25, gen)); + BOOST_TEST(mpz_probab_prime_p(mpz_int(boost::math::prime(i)).backend().data(), 25)); + } + // + // Now test some random values and compare GMP's native routine with ours. + // + for(unsigned i = 0; i < 10000; ++i) + { + test_type n = gen(); + bool is_prime_boost = miller_rabin_test(n, 25, gen2); + bool is_gmp_prime = mpz_probab_prime_p(mpz_int(n).backend().data(), 25) ? true : false; + if(is_prime_boost && is_gmp_prime) + { + std::cout << "We have a prime: " << std::hex << std::showbase << n << std::endl; + } + if(is_prime_boost != is_gmp_prime) + std::cout << std::hex << std::showbase << "n = " << n << std::endl; + BOOST_CHECK_EQUAL(is_prime_boost, is_gmp_prime); + } +} + +int main() +{ + using namespace boost::multiprecision; + + test<mpz_int>(); + test<number<gmp_int, et_off> >(); + test<boost::uint64_t>(); + test<boost::uint32_t>(); + + test<cpp_int>(); + test<number<cpp_int_backend<64, 64, unsigned_magnitude, checked, void>, et_off> >(); + test<checked_uint128_t>(); + test<checked_uint1024_t>(); + + return boost::report_errors(); +} + + diff --git a/libs/multiprecision/test/test_mixed_cpp_int.cpp b/libs/multiprecision/test/test_mixed_cpp_int.cpp new file mode 100644 index 0000000000..b098e00be6 --- /dev/null +++ b/libs/multiprecision/test/test_mixed_cpp_int.cpp @@ -0,0 +1,119 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/cpp_int.hpp> +#include "test.hpp" + +template <class Number, class BigNumber> +void test() +{ + using namespace boost::multiprecision; + typedef Number test_type; + + test_type h = (std::numeric_limits<test_type>::max)(); + test_type l = (std::numeric_limits<test_type>::max)(); + BigNumber r; + + add(r, h, h); + BOOST_CHECK_EQUAL(r, cpp_int(h) + cpp_int(h)); + + multiply(r, h, h); + BOOST_CHECK_EQUAL(r, cpp_int(h) * cpp_int(h)); + + if(std::numeric_limits<test_type>::is_signed) + { + subtract(r, l, h); + BOOST_CHECK_EQUAL(r, cpp_int(l) - cpp_int(h)); + subtract(r, h, l); + BOOST_CHECK_EQUAL(r, cpp_int(h) - cpp_int(l)); + multiply(r, l, l); + BOOST_CHECK_EQUAL(r, cpp_int(l) * cpp_int(l)); + } + + // + // Try again with integer types as the source: + // + enum{ max_digits = std::numeric_limits<test_type>::is_signed ? std::numeric_limits<long long>::digits : std::numeric_limits<unsigned long long>::digits }; + enum{ require_digits = std::numeric_limits<test_type>::digits <= 2 * max_digits ? std::numeric_limits<test_type>::digits / 2 : max_digits }; + typedef typename boost::uint_t<require_digits>::least uint_least; + typedef typename boost::int_t<require_digits>::least int_least; + typedef typename boost::mpl::if_c<std::numeric_limits<test_type>::is_signed, int_least, uint_least>::type i_type; + + i_type ih = (std::numeric_limits<i_type>::max)(); + i_type il = (std::numeric_limits<i_type>::max)(); + + add(r, ih, ih); + BOOST_CHECK_EQUAL(r, cpp_int(ih) + cpp_int(ih)); + + multiply(r, ih, ih); + BOOST_CHECK_EQUAL(r, cpp_int(ih) * cpp_int(ih)); + + if(std::numeric_limits<test_type>::is_signed) + { + subtract(r, il, ih); + BOOST_CHECK_EQUAL(r, cpp_int(il) - cpp_int(ih)); + subtract(r, ih, il); + BOOST_CHECK_EQUAL(r, cpp_int(ih) - cpp_int(il)); + multiply(r, il, il); + BOOST_CHECK_EQUAL(r, cpp_int(il) * cpp_int(il)); + } +} + +void test_rational_mixed() +{ + using namespace boost::multiprecision; + cpp_int a(2); + cpp_rational r(10); + + BOOST_CHECK_EQUAL(a + -r, -8); + BOOST_CHECK_EQUAL(-r + a, -8); + BOOST_CHECK_EQUAL(-a + r, 8); + BOOST_CHECK_EQUAL(r + -a, 8); + + BOOST_CHECK_EQUAL(a - -r, 12); + BOOST_CHECK_EQUAL(-r - a, -12); + BOOST_CHECK_EQUAL(-a - r, -12); + BOOST_CHECK_EQUAL(r - -a, 12); + + BOOST_CHECK_EQUAL(a * -r, -20); + BOOST_CHECK_EQUAL(-r * a, -20); + BOOST_CHECK_EQUAL(-a * r, -20); + BOOST_CHECK_EQUAL(r * -a, -20); + + BOOST_CHECK_EQUAL(a / -r, cpp_rational(-2, 10)); + BOOST_CHECK_EQUAL(-r / a, -5); + BOOST_CHECK_EQUAL(cpp_rational(-a / r), cpp_rational(-2, 10)); + BOOST_CHECK_EQUAL(r / -a, -5); +} + +int main() +{ + using namespace boost::multiprecision; + + test_rational_mixed(); + + test<checked_int512_t, checked_int1024_t>(); + test<checked_int256_t, checked_int512_t>(); + test<number<cpp_int_backend<64, 64, signed_magnitude, checked, void>, et_off>, checked_int128_t>(); + test<boost::int64_t, checked_int128_t>(); + + test<checked_uint512_t, checked_uint1024_t>(); + test<checked_uint256_t, checked_uint512_t>(); + test<number<cpp_int_backend<64, 64, unsigned_magnitude, checked, void>, et_off>, checked_uint128_t>(); + test<boost::uint64_t, checked_int128_t>(); + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_mixed_float.cpp b/libs/multiprecision/test/test_mixed_float.cpp new file mode 100644 index 0000000000..2b5aa6ffb2 --- /dev/null +++ b/libs/multiprecision/test/test_mixed_float.cpp @@ -0,0 +1,57 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#ifdef TEST_GMP +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_MPFR +#include <boost/multiprecision/mpfr.hpp> +#endif +#include <boost/multiprecision/cpp_dec_float.hpp> +#include "test.hpp" + +template <class Number, class BigNumber> +void test() +{ + using namespace boost::multiprecision; + typedef Number test_type; + + test_type a = 1; + a /= 3; + test_type b = -a; + + BigNumber r; + BOOST_CHECK_EQUAL(add(r, a, a), BigNumber(a) + BigNumber(a)); + BOOST_CHECK_EQUAL(subtract(r, a, b), BigNumber(a) - BigNumber(b)); + BOOST_CHECK_EQUAL(subtract(r, b, a), BigNumber(b) - BigNumber(a)); + BOOST_CHECK_EQUAL(multiply(r, a, a), BigNumber(a) * BigNumber(a)); +} + +int main() +{ + using namespace boost::multiprecision; + + test<cpp_dec_float_50, cpp_dec_float_100>(); + +#ifdef TEST_GMP + test<mpf_float_50, mpf_float_100>(); +#endif +#ifdef TEST_MPFR + test<mpfr_float_50, mpfr_float_100>(); +#endif + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_move.cpp b/libs/multiprecision/test/test_move.cpp new file mode 100644 index 0000000000..c5c5ab3b9f --- /dev/null +++ b/libs/multiprecision/test/test_move.cpp @@ -0,0 +1,336 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/config.hpp> + +#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES + +#if !defined(TEST_GMP) && !defined(TEST_MPFR) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_GMP +# define TEST_MPFR +# define TEST_TOMMATH +# define TEST_CPP_INT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_GMP) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR) +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_TOMMATH +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_CPP_INT +#include <boost/multiprecision/cpp_int.hpp> +#endif + +#include "test.hpp" + +unsigned allocation_count = 0; + +void *(*alloc_func_ptr) (size_t); +void *(*realloc_func_ptr) (void *, size_t, size_t); +void (*free_func_ptr) (void *, size_t); + +void *alloc_func(size_t n) +{ + ++allocation_count; + return (*alloc_func_ptr)(n); +} + +void free_func(void * p, size_t n) +{ + (*free_func_ptr)(p, n); +} + +void * realloc_func(void * p, size_t old, size_t n) +{ + ++allocation_count; + return (*realloc_func_ptr)(p, old, n); +} + +template <class T> +void do_something(const T&) +{ +} + +template <class T> +void test_std_lib() +{ + std::vector<T> v; + for(unsigned i = 0; i < 100; ++i) + v.insert(v.begin(), i); + + T a(2), b(3); + std::swap(a, b); + BOOST_TEST(a == 3); + BOOST_TEST(b == 2); +} + +template <class T, class A> +void test_move_and_assign(T x, A val) +{ + // move away from x, then assign val to x. + T z(x); + T y(std::move(x)); + x.assign(val); + BOOST_CHECK_EQUAL(x, T(val)); + BOOST_CHECK_EQUAL(z, y); +} + +template <class T> +void test_move_and_assign() +{ + T x(23); + test_move_and_assign(x, static_cast<short>(2)); + test_move_and_assign(x, static_cast<int>(2)); + test_move_and_assign(x, static_cast<long>(2)); + test_move_and_assign(x, static_cast<long long>(2)); + test_move_and_assign(x, static_cast<unsigned short>(2)); + test_move_and_assign(x, static_cast<unsigned int>(2)); + test_move_and_assign(x, static_cast<unsigned long>(2)); + test_move_and_assign(x, static_cast<unsigned long long>(2)); + test_move_and_assign(x, static_cast<float>(2)); + test_move_and_assign(x, static_cast<double>(2)); + test_move_and_assign(x, static_cast<long double>(2)); + test_move_and_assign(x, x); + test_move_and_assign(x, "23"); +} + + +int main() +{ +#if defined(TEST_MPFR) || defined(TEST_GMP) + mp_get_memory_functions(&alloc_func_ptr, &realloc_func_ptr, &free_func_ptr); + mp_set_memory_functions(&alloc_func, &realloc_func, &free_func); +#endif + + using namespace boost::multiprecision; + +#ifdef TEST_MPFR + { + test_std_lib<mpfr_float_50>(); + mpfr_float_50 a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpfr_float_50 b = std::move(a); + BOOST_TEST(allocation_count == 0); + // + // Move assign - we rely on knowledge of the internals to make this test work!! + // + mpfr_float_50 c(3); + do_something(b); + do_something(c); + const void* p = b.backend().data()[0]._mpfr_d; + BOOST_TEST(c.backend().data()[0]._mpfr_d != p); + c = std::move(b); + BOOST_TEST(c.backend().data()[0]._mpfr_d == p); + BOOST_TEST(b.backend().data()[0]._mpfr_d != p); + // + // Again with variable precision, this we can test more easily: + // + mpfr_float d, e; + d.precision(100); + e.precision(1000); + d = 2; + e = 3; + allocation_count = 0; + BOOST_TEST(d == 2); + d = std::move(e); + BOOST_TEST(allocation_count == 0); + BOOST_TEST(d == 3); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<mpfr_float>(); + test_move_and_assign<mpfr_float_50>(); + } +#endif +#ifdef TEST_GMP + { + test_std_lib<mpf_float_50>(); + mpf_float_50 a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpf_float_50 b = std::move(a); + BOOST_TEST(allocation_count == 0); + // + // Move assign: this requires knowledge of the internals to test!! + // + mpf_float_50 c(3); + do_something(b); + do_something(c); + const void* p = b.backend().data()[0]._mp_d; + BOOST_TEST(c.backend().data()[0]._mp_d != p); + c = std::move(b); + BOOST_TEST(c.backend().data()[0]._mp_d == p); + BOOST_TEST(b.backend().data()[0]._mp_d != p); + // + // Again with variable precision, this we can test more easily: + // + mpf_float d, e; + d.precision(100); + e.precision(1000); + d = 2; + e = 3; + allocation_count = 0; + BOOST_TEST(d == 2); + d = std::move(e); + BOOST_TEST(allocation_count == 0); + BOOST_TEST(d == 3); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<mpf_float>(); + test_move_and_assign<mpf_float_50>(); + } + { + test_std_lib<mpz_int>(); + mpz_int a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpz_int b = std::move(a); + BOOST_TEST(allocation_count == 0); + + // + // Move assign: + // + mpz_int d, e; + d = 2; + d <<= 1000; + e = 3; + allocation_count = 0; + e = std::move(d); + BOOST_TEST(allocation_count == 0); + e = 2; + BOOST_TEST(e == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<mpz_int>(); + } + { + test_std_lib<mpq_rational>(); + mpq_rational a = 2; + BOOST_TEST(allocation_count); // sanity check that we are tracking allocations + allocation_count = 0; + mpq_rational b = std::move(a); + BOOST_TEST(allocation_count == 0); + + // + // Move assign: + // + mpq_rational d, e; + d = mpz_int(2) << 1000; + e = 3; + allocation_count = 0; + e = std::move(d); + BOOST_TEST(allocation_count == 0); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<mpq_rational>(); + } +#endif +#ifdef TEST_TOMMATH + { + test_std_lib<tom_int>(); + tom_int a = 2; + void const* p = a.backend().data().dp; + tom_int b = std::move(a); + BOOST_TEST(b.backend().data().dp == p); + // We can't test this, as it will assert inside data(): + //BOOST_TEST(a.backend().data().dp == 0); + + // + // Move assign: + // + tom_int d, e; + d = 2; + d <<= 1000; + e = 3; + p = d.backend().data().dp; + BOOST_TEST(p != e.backend().data().dp); + e = std::move(d); + BOOST_TEST(e.backend().data().dp == p); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<tom_int>(); + } +#endif +#ifdef TEST_CPP_INT + { + test_std_lib<cpp_int>(); + cpp_int a = 2; + a <<= 1000; // Force dynamic allocation. + void const* p = a.backend().limbs(); + cpp_int b = std::move(a); + BOOST_TEST(b.backend().limbs() == p); + + // + // Move assign: + // + cpp_int d, e; + d = 2; + d <<= 1000; + e = 3; + e <<= 1000; + p = d.backend().limbs(); + BOOST_TEST(p != e.backend().limbs()); + e = std::move(d); + BOOST_TEST(e.backend().limbs() == p); + d = 2; + BOOST_TEST(d == 2); + d = std::move(e); + e = d; + BOOST_TEST(e == d); + + test_move_and_assign<cpp_int>(); + test_move_and_assign<int512_t>(); + } +#endif + return boost::report_errors(); +} + +#else +// +// No rvalue refs, nothing to test: +// +int main() +{ + return 0; +} + +#endif + diff --git a/libs/multiprecision/test/test_mpfi.cpp b/libs/multiprecision/test/test_mpfi.cpp new file mode 100644 index 0000000000..ed1084724b --- /dev/null +++ b/libs/multiprecision/test/test_mpfi.cpp @@ -0,0 +1,284 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include "test.hpp" +#include <boost/multiprecision/mpfi.hpp> +#include <boost/multiprecision/random.hpp> + +using namespace boost::multiprecision; +using namespace boost::random; + +void test_exp() +{ + std::cout << "Testing exp\n"; + + mpfr_float_50 val = 1.25; + + for(unsigned i = 0; i < 2000; ++i) + { + mpfr_float_100 a(val); + mpfr_float_100 b = exp(a); + mpfi_float_50 in = val; + in = exp(in); + BOOST_CHECK((boost::math::isfinite)(in)); + BOOST_CHECK(lower(in) <= b); + BOOST_CHECK(upper(in) >= b); + b = log(a); + in = val; + in = log(in); + BOOST_CHECK((boost::math::isfinite)(in)); + BOOST_CHECK(lower(in) <= b); + BOOST_CHECK(upper(in) >= b); + val *= 1.01; + } + val = 1; + for(unsigned i = 0; i < 2000; ++i) + { + mpfr_float_100 a(val); + mpfr_float_100 b = exp(a); + mpfi_float_50 in = val; + in = exp(in); + BOOST_CHECK((boost::math::isfinite)(in)); + BOOST_CHECK(lower(in) <= b); + BOOST_CHECK(upper(in) >= b); + b = log(a); + in = val; + in = log(in); + BOOST_CHECK((boost::math::isfinite)(in)); + BOOST_CHECK(lower(in) <= b); + BOOST_CHECK(upper(in) >= b); + val /= 1.01; + } +} + +void test_pow() +{ + std::cout << "Testing pow function\n"; + + mt19937 gen; + uniform_real_distribution<mpfr_float_50> dist1(0, 400); + + for(unsigned i = 0; i < 5000; ++i) + { + mpfr_float_50 base, p; + base = dist1(gen); + p = dist1(gen); + mpfr_float_100 a, b, r; + a = base; + b = p; + r = pow(a, b); + mpfi_float_50 ai, bi, ri; + ai = base; + bi = p; + ri = pow(ai, bi); + BOOST_CHECK((boost::math::isfinite)(ri)); + BOOST_CHECK(lower(ri) <= r); + BOOST_CHECK(upper(ri) >= r); + } +} + +void test_trig() +{ + std::cout << "Testing trig functions\n"; + + mt19937 gen; + uniform_real_distribution<mpfr_float_50> dist1(-1.57079632679, 1.57079632679); + uniform_real_distribution<mpfr_float_50> dist2(-1, 1); + + for(unsigned i = 0; i < 5000; ++i) + { + mpfr_float_50 val; + val = dist1(gen); + mpfr_float_100 a = val; + mpfr_float_100 b = sin(a); + mpfi_float_50 a2 = val; + mpfi_float_50 b2 = sin(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = cos(a); + b2 = cos(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = tan(a); + b2 = tan(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + } + for(unsigned i = 0; i < 5000; ++i) + { + mpfr_float_50 val; + val = dist2(gen); + mpfr_float_100 a = val; + mpfr_float_100 b = asin(a); + mpfi_float_50 a2 = val; + mpfi_float_50 b2 = asin(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = acos(a); + b2 = acos(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = atan(a); + b2 = atan(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + } +} + +void test_hyp() +{ + std::cout << "Testing hyperbolic trig functions\n"; + + mt19937 gen; + uniform_real_distribution<mpfr_float_50> dist1(-10, 10); + uniform_real_distribution<mpfr_float_50> dist2(-1, 1); + + for(unsigned i = 0; i < 5000; ++i) + { + mpfr_float_50 val; + val = dist1(gen); + mpfr_float_100 a = val; + mpfr_float_100 b = sinh(a); + mpfi_float_50 a2 = val; + mpfi_float_50 b2 = sinh(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = cosh(a); + b2 = cosh(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + b = tanh(a); + b2 = tanh(a2); + BOOST_CHECK((boost::math::isfinite)(b2)); + BOOST_CHECK(lower(b2) <= b); + BOOST_CHECK(upper(b2) >= b); + } +} + +void test_intervals() +{ + mpfi_float_50 a(1, 2); + mpfi_float_50 b(1.5, 2.5); + BOOST_CHECK_EQUAL(lower(a), 1); + BOOST_CHECK_EQUAL(upper(a), 2); + BOOST_CHECK_EQUAL(median(a), 1.5); + BOOST_CHECK_EQUAL(width(a), 1); + mpfi_float_50 r = intersect(a, b); + BOOST_CHECK_EQUAL(lower(r), 1.5); + BOOST_CHECK_EQUAL(upper(r), 2); + r = hull(a, b); + BOOST_CHECK_EQUAL(lower(r), 1); + BOOST_CHECK_EQUAL(upper(r), 2.5); + BOOST_CHECK(overlap(a, b)); + BOOST_CHECK(in(mpfr_float_50(1.5), a)); + BOOST_CHECK(in(mpfr_float_50(1), a)); + BOOST_CHECK(in(mpfr_float_50(2), a)); + BOOST_CHECK(!zero_in(a)); + b = mpfi_float_50(1.5, 1.75); + BOOST_CHECK(subset(b, a)); + BOOST_CHECK(proper_subset(b, a)); + BOOST_CHECK(!empty(a)); + BOOST_CHECK(!singleton(a)); + b = mpfi_float_50(5, 6); + r = intersect(a, b); + BOOST_CHECK(empty(r)); +} + +#ifdef TEST_SPECIAL +#include "math/table_type.hpp" +#include <boost/math/special_functions.hpp> + +#define T mpfi_float_50 + +typedef number<mpfi_float_backend<25> > mpfi_float_25; + +void test_log1p_expm1() +{ +# include "../../math/test/log1p_expm1_data.ipp" + + std::cout << std::setprecision(std::numeric_limits<mpfi_float_25>::max_digits10); + std::cout << "Testing log1p and expm1\n"; + + for(unsigned i = 0; i < log1p_expm1_data.size(); ++i) + { + mpfi_float_25 in(log1p_expm1_data[i][0]); + mpfi_float_25 out = boost::math::log1p(in); + mpfi_float_25 expected(log1p_expm1_data[i][1]); + if(!subset(expected, out)) + { + std::cout << in << std::endl; + std::cout << out << std::endl; + std::cout << expected << std::endl; + BOOST_CHECK(lower(out) <= lower(expected)); + BOOST_CHECK(upper(out) >= upper(expected)); + } + out = boost::math::expm1(in); + expected = mpfi_float_25(log1p_expm1_data[i][2]); + if(!subset(expected, out)) + { + std::cout << in << std::endl; + std::cout << out << std::endl; + std::cout << expected << std::endl; + BOOST_CHECK(lower(out) <= lower(expected)); + BOOST_CHECK(upper(out) >= upper(expected)); + } + } +} + +void test_bessel() +{ +#include "../../math/test/bessel_i_int_data.ipp" +#include "../../math/test/bessel_i_data.ipp" + + std::cout << std::setprecision(std::numeric_limits<mpfi_float_25>::max_digits10); + std::cout << "Testing Bessel Functions\n"; + + for(unsigned i = 0; i < bessel_i_int_data.size(); ++i) + { + int v = boost::lexical_cast<int>(static_cast<const char*>(bessel_i_int_data[i][0])); + mpfi_float_25 in(bessel_i_int_data[i][1]); + mpfi_float_25 out = boost::math::cyl_bessel_i(v, in); + mpfi_float_25 expected(bessel_i_int_data[i][2]); + if(!subset(expected, out)) + { + std::cout << in << std::endl; + std::cout << out << std::endl; + std::cout << expected << std::endl; + BOOST_CHECK(lower(out) <= lower(expected)); + BOOST_CHECK(upper(out) >= upper(expected)); + } + } +} + +#endif + +int main() +{ +#ifdef TEST_SPECIAL + test_log1p_expm1(); + test_bessel(); +#endif + test_intervals(); + test_exp(); + test_pow(); + test_trig(); + test_hyp(); + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_mpfr_conversions.cpp b/libs/multiprecision/test/test_mpfr_conversions.cpp new file mode 100644 index 0000000000..c7b878e4e0 --- /dev/null +++ b/libs/multiprecision/test/test_mpfr_conversions.cpp @@ -0,0 +1,131 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#include <boost/multiprecision/mpfr.hpp> +#include <boost/multiprecision/gmp.hpp> + +int main() +{ + using namespace boost::multiprecision; + // + // Test interconversions between GMP supported backends: + // + mpf_t mpf; + mpz_t mpz; + mpq_t mpq; + mpfr_t mpfr; + mpf_init2(mpf, 100); + mpf_set_ui(mpf, 2u); + mpz_init(mpz); + mpz_set_ui(mpz, 2u); + mpq_init(mpq); + mpq_set_ui(mpq, 2u, 1u); + mpfr_init(mpfr); + mpfr_set_ui(mpfr, 2u, GMP_RNDN); + + BOOST_TEST(mpfr_float(mpf) == 2); + BOOST_TEST(mpfr_float_50(mpf) == 2); + BOOST_TEST(mpfr_float(mpz) == 2); + BOOST_TEST(mpfr_float_50(mpz) == 2); + BOOST_TEST(mpfr_float(mpq) == 2); + BOOST_TEST(mpfr_float_50(mpq) == 2); + BOOST_TEST(mpfr_float(mpfr) == 2); + BOOST_TEST(mpfr_float_50(mpfr) == 2); + + mpfr_float f0; + mpfr_float_50 f50; + f0 = mpf; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpz; + BOOST_TEST(f0 == 2); + f0 = 0; + f0 = mpq; + BOOST_TEST(f0 == 2); + f0 = mpfr; + BOOST_TEST(f0 == 2); + + f50 = mpf; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpz; + BOOST_TEST(f50 == 2); + f50 = 0; + f50 = mpq; + BOOST_TEST(f50 == 2); + f50 = mpfr; + BOOST_TEST(f50 == 2); + + f50 = 4; + f0 = f50; + BOOST_TEST(f0 == 4); + f0 = 3; + f50 = f0; + BOOST_TEST(f50 == 3); + f50 = 4; + BOOST_TEST(mpfr_float(f50) == 4); + BOOST_TEST(mpfr_float_50(f0) == 3); + + mpz_int iz(2); + mpq_rational rat(2); + mpf_float gf(2); + f50 = 3; + f50 = iz; + BOOST_TEST(f50 == 2); + f50 = 3; + f0 = iz; + BOOST_TEST(f0 == 2); + f50 = 3; + f0 = gf; + BOOST_TEST(f0 == 2); + BOOST_TEST(mpfr_float(iz) == 2); + BOOST_TEST(mpfr_float_50(iz) == 2); + BOOST_TEST(mpfr_float(rat) == 2); + BOOST_TEST(mpfr_float_50(rat) == 2); + BOOST_TEST(mpfr_float(gf) == 2); + BOOST_TEST(mpfr_float_50(gf) == 2); + + // + // Conversions involving precision only: + // + mpfr_float::default_precision(30); + f50 = 2; + mpfr_float_100 f100(3); + mpfr_float f0a(4); + mpfr_float f0b(f100); + BOOST_TEST(f0a.precision() == 30); + BOOST_TEST(f0b.precision() == 100); + f0a = f100; + BOOST_TEST(f0a == 3); + BOOST_TEST(f0a.precision() == 100); + + f100 = f50; + BOOST_TEST(f100 == 2); + + f50 = static_cast<mpfr_float_50>(f100); + + mpf_clear(mpf); + mpz_clear(mpz); + mpq_clear(mpq); + mpfr_clear(mpfr); + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_native_integer.cpp b/libs/multiprecision/test/test_native_integer.cpp new file mode 100644 index 0000000000..24ae85a553 --- /dev/null +++ b/libs/multiprecision/test/test_native_integer.cpp @@ -0,0 +1,101 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +// +// Compare arithmetic results using fixed_int to GMP results. +// + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/multiprecision/integer.hpp> +#include "test.hpp" + +#ifdef BOOST_MSVC +#pragma warning(disable:4146) +#endif + +template <class I, class H> +void test() +{ + using namespace boost::multiprecision; + + I i(0); + + BOOST_CHECK_THROW(lsb(i), std::range_error); + BOOST_CHECK(bit_test(bit_set(i, 0), 0)); + BOOST_CHECK_EQUAL(bit_set(i, 0), 1); + BOOST_CHECK_EQUAL(bit_unset(i, 0), 0); + BOOST_CHECK_EQUAL(bit_flip(bit_set(i, 0), 0), 0); + + unsigned max_index = (std::numeric_limits<I>::digits) - 1; + BOOST_CHECK(bit_test(bit_set(i, max_index), max_index)); + BOOST_CHECK_EQUAL(bit_unset(i, max_index), 0); + BOOST_CHECK_EQUAL(bit_flip(bit_set(i, max_index), max_index), 0); + i = 0; + bit_set(i, max_index); + BOOST_CHECK_EQUAL(lsb(i), max_index); + BOOST_CHECK_EQUAL(msb(i), max_index); + bit_set(i, max_index / 2); + BOOST_CHECK_EQUAL(lsb(i), max_index / 2); + BOOST_CHECK_EQUAL(msb(i), max_index); + + if(std::numeric_limits<I>::is_signed) + { + i = static_cast<I>(-1); + BOOST_CHECK_THROW(lsb(i), std::range_error); + } + + H mx = (std::numeric_limits<H>::max)(); + + BOOST_CHECK_EQUAL(multiply(i, mx, mx), static_cast<I>(mx) * static_cast<I>(mx)); + BOOST_CHECK_EQUAL(add(i, mx, mx), static_cast<I>(mx) + static_cast<I>(mx)); + if(std::numeric_limits<I>::is_signed) + { + BOOST_CHECK_EQUAL(subtract(i, mx, static_cast<H>(-mx)), static_cast<I>(mx) - static_cast<I>(-mx)); + BOOST_CHECK_EQUAL(add(i, static_cast<H>(-mx), static_cast<H>(-mx)), static_cast<I>(-mx) + static_cast<I>(-mx)); + } + + i = (std::numeric_limits<I>::max)(); + I j = 12345; + I r, q; + divide_qr(i, j, q, r); + BOOST_CHECK_EQUAL(q, i / j); + BOOST_CHECK_EQUAL(r, i % j); + BOOST_CHECK_EQUAL(integer_modulus(i, j), i % j); + I p = 456; + BOOST_CHECK_EQUAL(powm(i, p, j), pow(cpp_int(i), static_cast<unsigned>(p)) % j); + + for(I i = 0; i < (2 < 8) - 1; ++i) + { + I j = i * i; + I s, r; + s = sqrt(j, r); + BOOST_CHECK_EQUAL(s, i); + BOOST_CHECK(r == 0); + j += 3; + s = sqrt(i, r); + BOOST_CHECK_EQUAL(s, i); + BOOST_CHECK(r == 3); + } +} + +int main() +{ + using namespace boost::multiprecision; + + test<boost::int16_t, boost::int8_t>(); + test<boost::int32_t, boost::int16_t>(); + test<boost::int64_t, boost::int32_t>(); + test<boost::uint16_t, boost::uint8_t>(); + test<boost::uint32_t, boost::uint16_t>(); + test<boost::uint64_t, boost::uint32_t>(); + + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_numeric_limits.cpp b/libs/multiprecision/test/test_numeric_limits.cpp new file mode 100644 index 0000000000..8b759dbc4b --- /dev/null +++ b/libs/multiprecision/test/test_numeric_limits.cpp @@ -0,0 +1,288 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ + !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && \ + !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) && !defined(TEST_MPFI_50) &&!defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPF +# define TEST_BACKEND +# define TEST_MPZ +# define TEST_MPFR +# define TEST_MPFR_50 +# define TEST_CPP_DEC_FLOAT +# define TEST_MPQ +# define TEST_TOMMATH +# define TEST_CPP_INT +# define TEST_MPFI_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) || defined(TEST_MPF) || defined(TEST_MPZ) || defined(TEST_MPQ) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#if defined(TEST_MPFR) || defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_TOMMATH +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_CPP_INT +#include <boost/multiprecision/cpp_int.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +#define PRINT(x)\ + std::cout << BOOST_STRINGIZE(x) << " = " << std::numeric_limits<Number>::x << std::endl; + +template <class Number> +void test_specific(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&) +{ + Number minv, maxv; + minv = (std::numeric_limits<Number>::min)(); + maxv = (std::numeric_limits<Number>::max)(); + BOOST_CHECK((boost::math::isnormal)(minv)); + BOOST_CHECK((boost::math::isnormal)(maxv)); + BOOST_CHECK((boost::math::isnormal)(log(minv))); + BOOST_CHECK((boost::math::isnormal)(log(maxv))); + BOOST_CHECK((boost::math::isnormal)(sqrt(minv))); + BOOST_CHECK((boost::math::isnormal)(sqrt(maxv))); + + if(std::numeric_limits<Number>::is_specialized) + { + if(std::numeric_limits<Number>::has_quiet_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits<Number>::quiet_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits<Number>::quiet_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits<Number>::quiet_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits<Number>::quiet_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits<Number>::quiet_NaN())); + } + if(std::numeric_limits<Number>::has_signaling_NaN) + { + BOOST_TEST((boost::math::isnan)(std::numeric_limits<Number>::signaling_NaN())); + BOOST_TEST(FP_NAN == (boost::math::fpclassify)(std::numeric_limits<Number>::signaling_NaN())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits<Number>::signaling_NaN())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits<Number>::signaling_NaN())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits<Number>::signaling_NaN())); + } + if(std::numeric_limits<Number>::has_infinity) + { + BOOST_TEST((boost::math::isinf)(std::numeric_limits<Number>::infinity())); + BOOST_TEST(FP_INFINITE == (boost::math::fpclassify)(std::numeric_limits<Number>::infinity())); + BOOST_TEST(!(boost::math::isfinite)(std::numeric_limits<Number>::infinity())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits<Number>::infinity())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits<Number>::infinity())); + } + if(std::numeric_limits<Number>::has_denorm) + { + BOOST_TEST(FP_SUBNORMAL == (boost::math::fpclassify)(std::numeric_limits<Number>::denorm_min())); + BOOST_TEST((boost::math::isfinite)(std::numeric_limits<Number>::denorm_min())); + BOOST_TEST(!(boost::math::isnormal)(std::numeric_limits<Number>::denorm_min())); + BOOST_TEST(!(boost::math::isinf)(std::numeric_limits<Number>::denorm_min())); + BOOST_TEST(!(boost::math::isnan)(std::numeric_limits<Number>::denorm_min())); + } + } + Number n = 0; + BOOST_TEST((boost::math::fpclassify)(n) == FP_ZERO); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST(!(boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); + n = 2; + BOOST_TEST((boost::math::fpclassify)(n) == FP_NORMAL); + BOOST_TEST((boost::math::isfinite)(n)); + BOOST_TEST((boost::math::isnormal)(n)); + BOOST_TEST(!(boost::math::isinf)(n)); + BOOST_TEST(!(boost::math::isnan)(n)); + + if(std::numeric_limits<Number>::round_style == std::round_to_nearest) + { + BOOST_CHECK_EQUAL(std::numeric_limits<Number>::round_error(), 0.5); + } + else if(std::numeric_limits<Number>::round_style != std::round_indeterminate) + { + // Round error is 1.0: + BOOST_CHECK_EQUAL(std::numeric_limits<Number>::round_error(), 1); + } + else + { + // Round error is presumably somewhere between 0.5 and 1: + BOOST_CHECK((std::numeric_limits<Number>::round_error() <= 1) && (std::numeric_limits<Number>::round_error() >= 0.5)); + } +} + +template <class Number> +void test_specific(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&) +{ + if(std::numeric_limits<Number>::is_modulo) + { + if(!std::numeric_limits<Number>::is_signed) + { + BOOST_TEST(1 + (std::numeric_limits<Number>::max)() == 0); + BOOST_TEST(--Number(0) == (std::numeric_limits<Number>::max)()); + } + } +} + +template <class Number, class T> +void test_specific(const T&) +{ +} + +template <class Number> +void test() +{ + typedef typename boost::mpl::if_c< + std::numeric_limits<Number>::is_specialized, + typename boost::multiprecision::number_category<Number>::type, + boost::mpl::int_<500> // not a number type + >::type fp_test_type; + + test_specific<Number>(fp_test_type()); + + // + // Note really a test just yet, but we can at least print out all the values: + // + std::cout << "numeric_limits values for type " << typeid(Number).name() << std::endl; + + PRINT(is_specialized); + if(std::numeric_limits<Number>::is_integer) + { + std::cout << std::hex << std::showbase; + } + std::cout << "max()" << " = " << (std::numeric_limits<Number>::max)() << std::endl; + if(std::numeric_limits<Number>::is_integer) + { + std::cout << std::dec; + } + std::cout << "max()" << " = " << (std::numeric_limits<Number>::max)() << std::endl; + std::cout << "min()" << " = " << (std::numeric_limits<Number>::min)() << std::endl; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + PRINT(lowest()); +#endif + PRINT(digits); + PRINT(digits10); +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + PRINT(max_digits10); +#endif + PRINT(is_signed); + PRINT(is_integer); + PRINT(is_exact); + PRINT(radix); + PRINT(epsilon()); + PRINT(round_error()); + PRINT(min_exponent); + PRINT(min_exponent10); + PRINT(max_exponent); + PRINT(max_exponent10); + PRINT(has_infinity); + PRINT(has_quiet_NaN); + PRINT(has_signaling_NaN); + PRINT(has_denorm); + PRINT(has_denorm_loss); + PRINT(infinity()); + PRINT(quiet_NaN()); + PRINT(signaling_NaN()); + PRINT(denorm_min()); + PRINT(is_iec559); + PRINT(is_bounded); + PRINT(is_modulo); + PRINT(traps); + PRINT(tinyness_before); + PRINT(round_style); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); +#endif +#ifdef TEST_MPF + boost::multiprecision::mpf_float::default_precision(1000); + /* + boost::multiprecision::mpf_float r; + r.precision(50); + BOOST_TEST(r.precision() >= 50); + */ + BOOST_TEST(boost::multiprecision::mpf_float::default_precision() == 1000); + test<boost::multiprecision::mpf_float>(); +#endif +#ifdef TEST_MPZ + test<boost::multiprecision::mpz_int>(); +#endif +#ifdef TEST_MPQ + test<boost::multiprecision::mpq_rational>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#endif +#ifdef TEST_MPFR + test<boost::multiprecision::mpfr_float>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float>(); +#endif +#ifdef TEST_TOMMATH + test<boost::multiprecision::tom_int>(); +#endif +#ifdef TEST_CPP_INT + test<boost::multiprecision::cpp_int>(); + test<boost::multiprecision::int256_t>(); + test<boost::multiprecision::uint512_t>(); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<200, 200, boost::multiprecision::unsigned_magnitude, boost::multiprecision::checked, void> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<70, 70, boost::multiprecision::signed_magnitude, boost::multiprecision::unchecked, void> > >(); +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_pow.cpp b/libs/multiprecision/test/test_pow.cpp new file mode 100644 index 0000000000..6f2afea132 --- /dev/null +++ b/libs/multiprecision/test/test_pow.cpp @@ -0,0 +1,848 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +//# define TEST_MPF +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<boost::array<const char*, 3>, 702> data = + {{ + {{ "9.85291419463953934609889984130859375e4", "8.4167086266170372255146503448486328125e2", "8.66781019918879108354226292713799369912745098619466567318041467361236175866573114777000418440761829061824953361563557580935951901405814080757565313129904800947783606850513184296612628910656615168927761935861462770335134108408073175949783551491164949747086136599355880600420490275164555515512645668845e4202" }}, + {{ "1.652914355109703592461301013827323913574218750e1", "4.936528947862250937816952500725165009498596191406250e-2", "1.14852190138491736562279120519668390081141778746743826681517181158751264571350304943298501284647564489716027476004029804110782430201351750715968215799574772058637701195873519618784612525011353325208230847515250406858209757415407239793739704829281917272032288615255140733409015874140869835291148547238" }}, + {{ 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"9.9987834430235824472224814411122243776265486577981177293571821321821517441659311658576556678112989769575007643432909365063217328716826322973493501036244864951726160136161783061801068077323413577888781728469725649419290963386640028890564993827733767871754809898250945769328951487990853772174957746180e-1" }}, + {{ "1.83083205221824460440238624414632795378565788269042968750e-5", "8.5130581526808327907929196953773498535156250e1", "5.08759465190948202575969824985581134108808966132826957045953621966485495100532942367792704772987024490520063202480279983957515910756497430137889290866515761789926914423548570454774810411630371091100113544891279153106437138536746735808516608107152208446229082973737250416694137957514739571766896873306e-404" }}, + {{ "3.346653408259039663751391313617489231546642258763313293457031250e-6", "3.7868598858803215989610180258750915527343750e2", "3.52212078787830927194297643296251781134291925779877466674871728836105722487573580131785145484495276918545575844013070305855330551951353365366550132397674036846629030890995284036782751533644901503503905390007269189142085867922573306793968734446410118933272999821289312420310855129959801669881803865858e-2074" }}, + {{ "5.3392773503090527415166147151559528083453187718987464904785156250e-7", "6.207661898675727671229399029506623719498747959733009338378906250e-7", "9.99991034310800110010707678195555035460840436574922962233018600570397473321611757701145927433415065972844383465094874922585959664097551124468322387734536918015102243687653110114625528443011692213994065730522520240541725522418247328328568974843758308408263849244150678651666777627782107985602066092068e-1" }}, + {{ "2.19994195074324068173154955729842185974121093750e1", "3.06707480325778616969678580517211230471730232238769531250e-3", "1.00952545862365855685219042115608145190455235613268820530406120489310419092421063376518661644406509494089174786391890344365290616699827245940846567812410266752069452669091303167176618868615804832415636793311353407444727299687139263635273616648724056070625009496090575286667611858626054037393426920940" }}, + {{ "9.494261316265068537459392850053063739323988556861877441406250e-6", "3.33658593189578134285966370953246951103210449218750e-1", "2.10953513637051167906362488703903898283324995313357160919327331939686921714903739192273840983847338772103005796728222224591772689334463276313863779738778665022741134644128703431090827473653846081611135627094959784765932765625500258444912393296945910143335619574776807349923037475968356403544804516261e-2" }}, + {{ "1.58204381201744226359551248606294393539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "1.699670888752343416014042865036515195242827758193016052246093750e-6", "1.00000077966919198536118506000604021848342587459233214812502825319036185927111842640720441778472762148840769009480654434988580516960635247026640481971290957649218368276357248615028690535272593446475039055115505472342603119011692356413204456935489635677140077206818440909527541341514742179392759484948" }}, + {{ "7.89159836081502775182242026552614788670325651764869689941406250e-7", "4.816961061463680380256846547126770019531250e2", "1.94147359401180853490618926342983857830809890106752620847948172427377774972592621604834694930262822082783398795004418901297871494637794539318032606545630879764294273346094400196886499691750495365869112152459387957968585556903274684614177896724684391146995388586545846815713970966406314356957705636188e-2940" }}, + {{ "1.289097083842133870348334312438964843750e5", "6.9303987741382092058195496520056622102856636047363281250e-3", "1.08496647090160629262865176257751429047729744058064486558757367783712447981236338124011887293782800275409466363098994983981904989007840757365461380428739706364354348918768376442904733609028311603151255847131247523710764847675936168535507206845244124708518371354311381017836653040028826211975497871572" }}, + {{ "1.88979339146257488413205294364161090925335884094238281250e-3", "1.507462797900369366743689170107245445251464843750e1", "8.76918423991144038304021445193438173201942067819279237648900596695575024236585474624026460405210909663314261583560910578839787952809598740673148266220449752385049510413309645447866767727463403580780664879153239139760411591518829772808581212853680494395035365090735562853954119264286528501466090236373e-42" }}, + {{ "8.41517212362860789198748534545302391052246093750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "3.64690954096749919699504971504211425781250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "2.36385641555849335879047779054573450503531219143280186506059811952516602814802026798922317458022305556248077861115239238036534162971730930403784483407045473794360984711531633071954017599185535725837014265828161774595330813847033913388549400091383297967089159291617295023155265969142242902513558326176e3" }}, + {{ "7.794539153729454028507461771368980407714843750e1", "1.375701859744113164651935221627354621887207031250e1", "1.06022076559461302576262215724290203547920286581395364873074659478022575993646868223512587189711310741927159850526321306597320278985726000202501743927791980296512242522543006053260060771089791556404973296770985910119125940674256012428243689156025466514102435785983398909290409351186888763744330929933e26" }}, + {{ "1.53996830801468109712004661560058593750e5", "1.5575394558063157535165998979209689423441886901855468750e-2", "1.20447431374301175187511662239775886280442123057569989101048717965641664163683965122530380365781626549245733448495292659434928101251174655724999866929500920292760069066534315397658186379331270528348085084759405281722204998903474609597521346801285181467380964556686904383585877178604246579963496131145" }}, + {{ "1.58292085642406949773430824279785156250e5", "2.39839658341223938009534322191029787063598632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "2.95369184630899349835322600435195771430552393938403392920497743251505007693757163085390208500076347439614593692001276141903681987497427879862172599262551403341684739246319058993775975522937386429303489479759146923528741632009619169067978673180741577543638362298805900307916877489621750277562246056785e12" }}, + {{ "1.3400796278978785267099738121032714843750e4", "1.930784873528596304326221400060603627935051918029785156250e-3", "1.01851774851557016267678896947673493426952146980838508956199625705868791978344101642179134412654468177801448310465798049263061832294449615311708734175434429497593168411288076223275335865898358255932555661831601275564405349791579099870920484601878548075981946266790952650050188664408833668093366337128" }}, + {{ "6.575650904605106461531249806284904479980468750e1", "2.95349579102368409166956553235650062561035156250e1", "4.92883670959819008737323351550818895693909971573197862669756297233542900030950953480711710193053129535412775508169382249001427538228339649766961919628309117712145393012207284297044617755253176225355208718450804357511545954540599873761726532747435308616642768909463909723766874135347528684022648860560e53" }}, + {{ "7.73401481707858096115160151384770870208740234375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "2.491481202776960799383232370018959045410156250e2", "2.21022119284238444262099118632640694751857489911985882302778583637174384391251394588072250813144879442061174245455228341031066580984347413608919792407019123272438031870871777573323381609534176617167457318208979616222032754767955294734636001910121462806120247278470491361024670390806812831433737112379e221" }}, + {{ "1.109788988632283901134001347088542388519272208213806152343750e-5", "1.3221937740391638271830743178725242614746093750e1", "3.07947867569658321194458380597181231565685445537647073748124994390202466909582021155440785847623999110729024670271166064504654713592331835440877924887265726281088902886492996205474623955394661696347608605548560131153946508949187941058346142181719469523416895370937975489878692955467549849494731965625e-66" }}, + {{ "6.01388538493091151515557157836155965924263000488281250e-2", "2.600229311077009085274511224206150927784619852900505065917968750e-6", "9.99992690524283092045041727666257712294170472055655983655789156306985603524706361035867762480294454684826579379760817381252880474747063748101481751389649370586878847928039436815138481244723824252557644191693486953238362877605577315573573222917218930477592061427550313462645068276263623663297863327092e-1" }}, + {{ "2.155348014323840710737556491949362680315971374511718750e-2", "4.0581281467163221599037115083774551749229431152343750e-2", "8.55799445393602464144976083125961944702079982479924287374752573999342183140040918969698718557087349720031284500593972794455976395816766982409031253828819168807248785638632014800512514311905184872890032777260194266023572565329278809193542262172193713145497824126566400120337339261082686915643720103934e-1" }}, + // Integer exponents: + {{ "1.250e-01", "0.0e+00", "1.0e+00" }}, + {{ "-1.250e-01", "0.0e+00", "1.0e+00" }}, + {{ "7.50e-01", "0.0e+00", "1.0e+00" }}, + {{ "-7.50e-01", "0.0e+00", "1.0e+00" }}, + {{ "1.0e+00", "0.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "0.0e+00", "1.0e+00" }}, + {{ "1.250e+00", "0.0e+00", "1.0e+00" }}, + {{ "-1.250e+00", "0.0e+00", "1.0e+00" }}, + {{ "5.5250e+01", "0.0e+00", "1.0e+00" }}, + {{ "-5.5250e+01", "0.0e+00", "1.0e+00" }}, + {{ "1.250e-01", "1.0e+00", "1.250e-01" }}, + {{ "-1.250e-01", "1.0e+00", "-1.250e-01" }}, + {{ "7.50e-01", "1.0e+00", "7.50e-01" }}, + {{ "-7.50e-01", "1.0e+00", "-7.50e-01" }}, + {{ "1.0e+00", "1.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "1.0e+00", "-1.0e+00" }}, + {{ "1.250e+00", "1.0e+00", "1.250e+00" }}, + {{ "-1.250e+00", "1.0e+00", "-1.250e+00" }}, + {{ "5.5250e+01", "1.0e+00", "5.5250e+01" }}, + {{ "-5.5250e+01", "1.0e+00", "-5.5250e+01" }}, + {{ "1.250e-01", "2.0e+00", "1.56250e-02" }}, + {{ "-1.250e-01", "2.0e+00", "1.56250e-02" }}, + {{ "7.50e-01", "2.0e+00", "5.6250e-01" }}, + {{ "-7.50e-01", "2.0e+00", "5.6250e-01" }}, + {{ "1.0e+00", "2.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "2.0e+00", "1.0e+00" }}, + {{ "1.250e+00", "2.0e+00", "1.56250e+00" }}, + {{ "-1.250e+00", "2.0e+00", "1.56250e+00" }}, + {{ "5.5250e+01", "2.0e+00", "3.05256250e+03" }}, + {{ "-5.5250e+01", "2.0e+00", "3.05256250e+03" }}, + {{ "1.250e-01", "3.0e+00", "1.9531250e-03" }}, + {{ "-1.250e-01", "3.0e+00", "-1.9531250e-03" }}, + {{ "7.50e-01", "3.0e+00", "4.218750e-01" }}, + {{ "-7.50e-01", "3.0e+00", "-4.218750e-01" }}, + {{ "1.0e+00", "3.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "3.0e+00", "-1.0e+00" }}, + {{ "1.250e+00", "3.0e+00", "1.9531250e+00" }}, + {{ "-1.250e+00", "3.0e+00", "-1.9531250e+00" }}, + {{ "5.5250e+01", "3.0e+00", "1.686540781250e+05" }}, + {{ "-5.5250e+01", "3.0e+00", "-1.686540781250e+05" }}, + {{ "1.250e-01", "4.0e+00", "2.441406250e-04" }}, + {{ "-1.250e-01", "4.0e+00", "2.441406250e-04" }}, + {{ "7.50e-01", "4.0e+00", "3.16406250e-01" }}, + {{ "-7.50e-01", "4.0e+00", "3.16406250e-01" }}, + {{ "1.0e+00", "4.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "4.0e+00", "1.0e+00" }}, + {{ "1.250e+00", "4.0e+00", "2.441406250e+00" }}, + {{ "-1.250e+00", "4.0e+00", "2.441406250e+00" }}, + {{ "5.5250e+01", "4.0e+00", "9.318137816406250e+06" }}, + {{ "-5.5250e+01", "4.0e+00", "9.318137816406250e+06" }}, + {{ "1.250e-01", "5.0e+00", "3.05175781250e-05" }}, + {{ "-1.250e-01", "5.0e+00", "-3.05175781250e-05" }}, + {{ "7.50e-01", "5.0e+00", "2.3730468750e-01" }}, + {{ "-7.50e-01", "5.0e+00", "-2.3730468750e-01" }}, + {{ "1.0e+00", "5.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "5.0e+00", "-1.0e+00" }}, + {{ "1.250e+00", "5.0e+00", "3.05175781250e+00" }}, + {{ "-1.250e+00", "5.0e+00", "-3.05175781250e+00" }}, + {{ "5.5250e+01", "5.0e+00", "5.1482711435644531250e+08" }}, + {{ "-5.5250e+01", "5.0e+00", "-5.1482711435644531250e+08" }}, + {{ "1.250e-01", "6.0e+00", "3.8146972656250e-06" }}, + {{ "-1.250e-01", "6.0e+00", "3.8146972656250e-06" }}, + {{ "7.50e-01", "6.0e+00", "1.779785156250e-01" }}, + {{ "-7.50e-01", "6.0e+00", "1.779785156250e-01" }}, + {{ "1.0e+00", "6.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "6.0e+00", "1.0e+00" }}, + {{ "1.250e+00", "6.0e+00", "3.8146972656250e+00" }}, + {{ "-1.250e+00", "6.0e+00", "3.8146972656250e+00" }}, + {{ "5.5250e+01", "6.0e+00", "2.84441980681936035156250e+10" }}, + {{ "-5.5250e+01", "6.0e+00", "2.84441980681936035156250e+10" }}, + {{ "1.250e-01", "7.0e+00", "4.768371582031250e-07" }}, + {{ "-1.250e-01", "7.0e+00", "-4.768371582031250e-07" }}, + {{ "7.50e-01", "7.0e+00", "1.33483886718750e-01" }}, + {{ "-7.50e-01", "7.0e+00", "-1.33483886718750e-01" }}, + {{ "1.0e+00", "7.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "7.0e+00", "-1.0e+00" }}, + {{ "1.250e+00", "7.0e+00", "4.768371582031250e+00" }}, + {{ "-1.250e+00", "7.0e+00", "-4.768371582031250e+00" }}, + {{ "5.5250e+01", "7.0e+00", "1.571541943267696594238281250e+12" }}, + {{ "-5.5250e+01", "7.0e+00", "-1.571541943267696594238281250e+12" }}, + {{ "1.250e-01", "8.0e+00", "5.96046447753906250e-08" }}, + {{ "-1.250e-01", "8.0e+00", "5.96046447753906250e-08" }}, + {{ "7.50e-01", "8.0e+00", "1.0011291503906250e-01" }}, + {{ "-7.50e-01", "8.0e+00", "1.0011291503906250e-01" }}, + {{ "1.0e+00", "8.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "8.0e+00", "1.0e+00" }}, + {{ "1.250e+00", "8.0e+00", "5.96046447753906250e+00" }}, + {{ "-1.250e+00", "8.0e+00", "5.96046447753906250e+00" }}, + {{ "5.5250e+01", "8.0e+00", "8.682769236554023683166503906250e+13" }}, + {{ "-5.5250e+01", "8.0e+00", "8.682769236554023683166503906250e+13" }}, + {{ "1.250e-01", "9.0e+00", "7.4505805969238281250e-09" }}, + {{ "-1.250e-01", "9.0e+00", "-7.4505805969238281250e-09" }}, + {{ "7.50e-01", "9.0e+00", "7.50846862792968750e-02" }}, + {{ "-7.50e-01", "9.0e+00", "-7.50846862792968750e-02" }}, + {{ "1.0e+00", "9.0e+00", "1.0e+00" }}, + {{ "-1.0e+00", "9.0e+00", "-1.0e+00" }}, + {{ "1.250e+00", "9.0e+00", "7.4505805969238281250e+00" }}, + {{ "-1.250e+00", "9.0e+00", "-7.4505805969238281250e+00" }}, + {{ "5.5250e+01", "9.0e+00", "4.7972300031960980849494934082031250e+15" }}, + {{ "-5.5250e+01", "9.0e+00", "-4.7972300031960980849494934082031250e+15" }}, + {{ "1.250e-01", "1.0e+01", "9.313225746154785156250e-10" }}, + {{ "-1.250e-01", "1.0e+01", "9.313225746154785156250e-10" }}, + {{ "7.50e-01", "1.0e+01", "5.6313514709472656250e-02" }}, + {{ "-7.50e-01", "1.0e+01", "5.6313514709472656250e-02" }}, + {{ "1.0e+00", "1.0e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.0e+01", "1.0e+00" }}, + {{ "1.250e+00", "1.0e+01", "9.313225746154785156250e+00" }}, + {{ "-1.250e+00", "1.0e+01", "9.313225746154785156250e+00" }}, + {{ "5.5250e+01", "1.0e+01", "2.65046957676584419193459510803222656250e+17" }}, + {{ "-5.5250e+01", "1.0e+01", "2.65046957676584419193459510803222656250e+17" }}, + {{ "1.250e-01", "1.10e+01", "1.164153218269348144531250e-10" }}, + {{ "-1.250e-01", "1.10e+01", "-1.164153218269348144531250e-10" }}, + {{ "7.50e-01", "1.10e+01", "4.223513603210449218750e-02" }}, + {{ "-7.50e-01", "1.10e+01", "-4.223513603210449218750e-02" }}, + {{ "1.0e+00", "1.10e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.10e+01", "-1.0e+00" }}, + {{ "1.250e+00", "1.10e+01", "1.164153218269348144531250e+01" }}, + {{ "-1.250e+00", "1.10e+01", "-1.164153218269348144531250e+01" }}, + {{ "5.5250e+01", "1.10e+01", "1.464384441163128916043863797187805175781250e+19" }}, + {{ "-5.5250e+01", "1.10e+01", "-1.464384441163128916043863797187805175781250e+19" }}, + {{ "1.250e-01", "1.20e+01", "1.45519152283668518066406250e-11" }}, + {{ "-1.250e-01", "1.20e+01", "1.45519152283668518066406250e-11" }}, + {{ "7.50e-01", "1.20e+01", "3.16763520240783691406250e-02" }}, + {{ "-7.50e-01", "1.20e+01", "3.16763520240783691406250e-02" }}, + {{ "1.0e+00", "1.20e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.20e+01", "1.0e+00" }}, + {{ "1.250e+00", "1.20e+01", "1.45519152283668518066406250e+01" }}, + {{ "-1.250e+00", "1.20e+01", "1.45519152283668518066406250e+01" }}, + {{ "5.5250e+01", "1.20e+01", "8.090724037426287261142347479462623596191406250e+20" }}, + {{ "-5.5250e+01", "1.20e+01", "8.090724037426287261142347479462623596191406250e+20" }}, + {{ "1.250e-01", "1.30e+01", "1.8189894035458564758300781250e-12" }}, + {{ "-1.250e-01", "1.30e+01", "-1.8189894035458564758300781250e-12" }}, + {{ "7.50e-01", "1.30e+01", "2.3757264018058776855468750e-02" }}, + {{ "-7.50e-01", "1.30e+01", "-2.3757264018058776855468750e-02" }}, + {{ "1.0e+00", "1.30e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.30e+01", "-1.0e+00" }}, + {{ "1.250e+00", "1.30e+01", "1.8189894035458564758300781250e+01" }}, + {{ "-1.250e+00", "1.30e+01", "-1.8189894035458564758300781250e+01" }}, + {{ "5.5250e+01", "1.30e+01", "4.4701250306780237117811469824030995368957519531250e+22" }}, + {{ "-5.5250e+01", "1.30e+01", "-4.4701250306780237117811469824030995368957519531250e+22" }}, + {{ "1.250e-01", "1.40e+01", "2.273736754432320594787597656250e-13" }}, + {{ "-1.250e-01", "1.40e+01", "2.273736754432320594787597656250e-13" }}, + {{ "7.50e-01", "1.40e+01", "1.781794801354408264160156250e-02" }}, + {{ "-7.50e-01", "1.40e+01", "1.781794801354408264160156250e-02" }}, + {{ "1.0e+00", "1.40e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.40e+01", "1.0e+00" }}, + {{ "1.250e+00", "1.40e+01", "2.273736754432320594787597656250e+01" }}, + {{ "-1.250e+00", "1.40e+01", "2.273736754432320594787597656250e+01" }}, + {{ "5.5250e+01", "1.40e+01", "2.46974407944960810075908370777771249413490295410156250e+24" }}, + {{ "-5.5250e+01", "1.40e+01", "2.46974407944960810075908370777771249413490295410156250e+24" }}, + {{ "1.250e-01", "1.50e+01", "2.84217094304040074348449707031250e-14" }}, + {{ "-1.250e-01", "1.50e+01", "-2.84217094304040074348449707031250e-14" }}, + {{ "7.50e-01", "1.50e+01", "1.33634610101580619812011718750e-02" }}, + {{ "-7.50e-01", "1.50e+01", "-1.33634610101580619812011718750e-02" }}, + {{ "1.0e+00", "1.50e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.50e+01", "-1.0e+00" }}, + {{ "1.250e+00", "1.50e+01", "2.84217094304040074348449707031250e+01" }}, + {{ "-1.250e+00", "1.50e+01", "-2.84217094304040074348449707031250e+01" }}, + {{ "5.5250e+01", "1.50e+01", "1.364533603895908475669393748547186153009533882141113281250e+26" }}, + {{ "-5.5250e+01", "1.50e+01", "-1.364533603895908475669393748547186153009533882141113281250e+26" }}, + {{ "1.250e-01", "1.60e+01", "3.5527136788005009293556213378906250e-15" }}, + {{ "-1.250e-01", "1.60e+01", "3.5527136788005009293556213378906250e-15" }}, + {{ "7.50e-01", "1.60e+01", "1.0022595757618546485900878906250e-02" }}, + {{ "-7.50e-01", "1.60e+01", "1.0022595757618546485900878906250e-02" }}, + {{ "1.0e+00", "1.60e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.60e+01", "1.0e+00" }}, + {{ "1.250e+00", "1.60e+01", "3.5527136788005009293556213378906250e+01" }}, + {{ "-1.250e+00", "1.60e+01", "3.5527136788005009293556213378906250e+01" }}, + {{ "5.5250e+01", "1.60e+01", "7.539048161524894328073400460723203495377674698829650878906250e+27" }}, + {{ "-5.5250e+01", "1.60e+01", "7.539048161524894328073400460723203495377674698829650878906250e+27" }}, + {{ "1.250e-01", "1.70e+01", "4.440892098500626161694526672363281250e-16" }}, + {{ "-1.250e-01", "1.70e+01", "-4.440892098500626161694526672363281250e-16" }}, + {{ "7.50e-01", "1.70e+01", "7.51694681821390986442565917968750e-03" }}, + {{ "-7.50e-01", "1.70e+01", "-7.51694681821390986442565917968750e-03" }}, + {{ "1.0e+00", "1.70e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.70e+01", "-1.0e+00" }}, + {{ "1.250e+00", "1.70e+01", "4.440892098500626161694526672363281250e+01" }}, + {{ "-1.250e+00", "1.70e+01", "-4.440892098500626161694526672363281250e+01" }}, + {{ "5.5250e+01", "1.70e+01", "4.1653241092425041162605537545495699311961652711033821105957031250e+29" }}, + {{ "-5.5250e+01", "1.70e+01", "-4.1653241092425041162605537545495699311961652711033821105957031250e+29" }}, + {{ "1.250e-01", "1.80e+01", "5.55111512312578270211815834045410156250e-17" }}, + {{ "-1.250e-01", "1.80e+01", "5.55111512312578270211815834045410156250e-17" }}, + {{ "7.50e-01", "1.80e+01", "5.6377101136604323983192443847656250e-03" }}, + {{ "-7.50e-01", "1.80e+01", "5.6377101136604323983192443847656250e-03" }}, + {{ "1.0e+00", "1.80e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.80e+01", "1.0e+00" }}, + {{ "1.250e+00", "1.80e+01", "5.55111512312578270211815834045410156250e+01" }}, + {{ "-1.250e+00", "1.80e+01", "5.55111512312578270211815834045410156250e+01" }}, + {{ "5.5250e+01", "1.80e+01", "2.30134157035648352423395594938863738698588131228461861610412597656250e+31" }}, + {{ "-5.5250e+01", "1.80e+01", "2.30134157035648352423395594938863738698588131228461861610412597656250e+31" }}, + {{ "1.250e-01", "1.90e+01", "6.9388939039072283776476979255676269531250e-18" }}, + {{ "-1.250e-01", "1.90e+01", "-6.9388939039072283776476979255676269531250e-18" }}, + {{ "7.50e-01", "1.90e+01", "4.228282585245324298739433288574218750e-03" }}, + {{ "-7.50e-01", "1.90e+01", "-4.228282585245324298739433288574218750e-03" }}, + {{ "1.0e+00", "1.90e+01", "1.0e+00" }}, + {{ "-1.0e+00", "1.90e+01", "-1.0e+00" }}, + {{ "1.250e+00", "1.90e+01", "6.9388939039072283776476979255676269531250e+01" }}, + {{ "-1.250e+00", "1.90e+01", "-6.9388939039072283776476979255676269531250e+01" }}, + {{ "5.5250e+01", "1.90e+01", "1.271491217621957147139260662037222156309699425037251785397529602050781250e+33" }}, + {{ "-5.5250e+01", "1.90e+01", "-1.271491217621957147139260662037222156309699425037251785397529602050781250e+33" }}, + {{ "-1", "18446744073709551615", "-1", }}, + {{ "-1", "18446744073709551614", "1", }}, + }}; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = pow(T(data[k][0]), T(data[k][1])); + T e = relative_error(val, T(data[k][2])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = pow(T(data[k][0]), -T(data[k][1])); + e = relative_error(val, T(1/T(data[k][2]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; + // + // Special cases come last: + // + BOOST_CHECK_EQUAL(pow(T(0), T(0)), 1); + BOOST_CHECK_EQUAL(pow(T(0), 0), 1); + BOOST_CHECK_EQUAL(pow(T(0), T(2)), 0); + BOOST_CHECK_EQUAL(pow(T(0), 2), 0); + BOOST_CHECK_EQUAL(pow(T(1), T(0)), 1); + BOOST_CHECK_EQUAL(pow(T(1), 0), 1); + BOOST_CHECK_EQUAL(pow(T(1), T(2)), 1); + BOOST_CHECK_EQUAL(pow(T(1), 2), 1); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_rat_float_interconv.cpp b/libs/multiprecision/test/test_rat_float_interconv.cpp new file mode 100644 index 0000000000..618797c2ff --- /dev/null +++ b/libs/multiprecision/test/test_rat_float_interconv.cpp @@ -0,0 +1,260 @@ +// Copyright John Maddock 2013. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if defined(TEST1) || defined(TEST2) || defined(TEST3) || defined(TEST4) +#include <boost/multiprecision/cpp_bin_float.hpp> +#include <boost/multiprecision/cpp_int.hpp> +#else +#include <boost/multiprecision/mpfr.hpp> +#endif +#include <boost/math/special_functions/next.hpp> + +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/chrono.hpp> +#include "test.hpp" +#include <boost/array.hpp> +#include <iostream> +#include <iomanip> + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +template <class Clock> +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + +template <class T> +struct exponent_type +{ + typedef int type; +}; +template <class T, boost::multiprecision::expression_template_option ET> +struct exponent_type<boost::multiprecision::number<T, ET> > +{ + typedef typename T::exponent_type type; +}; + +template <class T> +T generate_random_float() +{ + BOOST_MATH_STD_USING + typedef typename exponent_type<T>::type e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static const int max_exponent_value = (std::min)(static_cast<int>(std::numeric_limits<T>::max_exponent - std::numeric_limits<T>::digits - 20), 2000); + static boost::random::uniform_int_distribution<e_type> ui(0, max_exponent_value); + return ldexp(val, ui(gen)); +} + +template <class Float, class Rat> +void do_round_trip(const Float& val) +{ +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + BOOST_MATH_STD_USING + Rat rat(val); + Float new_f(rat); + BOOST_CHECK_EQUAL(val, new_f); + // + // Try adding or subtracting an insignificant amount + // (0.25ulp) from rat and check that it rounds to the same value: + // + typename exponent_type<Float>::type e; + Float t = frexp(val, &e); + (void)t; // warning suppression + e -= std::numeric_limits<Float>::digits + 2; + BOOST_ASSERT(val == (val + ldexp(Float(1), e))); + Rat delta, rounded; + typedef typename boost::multiprecision::component_type<Rat>::type i_type; + i_type i(1); + i <<= (e < 0 ? -e : e); + if(e > 0) + delta.assign(i); + else + delta = Rat(i_type(1), i); + rounded = rat + delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); + rounded = rat - delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); + + delta /= 2; + rounded = rat + delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); + rounded = rat - delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); + + delta /= 2; + rounded = rat + delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); + rounded = rat - delta; + new_f = static_cast<Float>(rounded); + BOOST_CHECK_EQUAL(val, new_f); +#endif +} + +template <class Float, class Rat> +void test_round_trip() +{ +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + std::cout << "Testing types " << typeid(Float).name() << " <<==>> " << typeid(Rat).name() << std::endl; + std::cout << "digits = " << std::numeric_limits<Float>::digits << std::endl; + std::cout << "digits10 = " << std::numeric_limits<Float>::digits10 << std::endl; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + std::cout << "max_digits10 = " << std::numeric_limits<Float>::max_digits10 << std::endl; +#endif + + stopwatch<boost::chrono::high_resolution_clock> w; + + int count = 0; + + while(boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() < 200) + { + Float val = generate_random_float<Float>(); + do_round_trip<Float, Rat>(val); + do_round_trip<Float, Rat>(Float(-val)); + do_round_trip<Float, Rat>(Float(1/val)); + do_round_trip<Float, Rat>(Float(-1/val)); + count += 4; + if(boost::detail::test_errors() > 100) + break; + } + + std::cout << "Execution time = " << boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() << "s" << std::endl; + std::cout << "Total values tested: " << count << std::endl; +#endif +} + +template <class Int> +Int generate_random_int() +{ + static boost::random::mt19937 gen; + static boost::random::uniform_int_distribution<boost::random::mt19937::result_type> d(1, 20); + + int lim; + Int cppi(0); + + lim = d(gen); + + for(int i = 0; i < lim; ++i) + { + cppi *= (gen.max)(); + cppi += gen(); + } + return cppi; +} + +template <class Float, class Rat> +void test_random_rationals() +{ +#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS + std::cout << "Testing types " << typeid(Float).name() << " <<==>> " << typeid(Rat).name() << std::endl; + std::cout << "digits = " << std::numeric_limits<Float>::digits << std::endl; + std::cout << "digits10 = " << std::numeric_limits<Float>::digits10 << std::endl; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + std::cout << "max_digits10 = " << std::numeric_limits<Float>::max_digits10 << std::endl; +#endif + + typedef typename boost::multiprecision::component_type<Rat>::type i_type; + stopwatch<boost::chrono::high_resolution_clock> w; + + int count = 0; + + while(boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() < 200) + { + Rat rat(generate_random_int<i_type>(), generate_random_int<i_type>()); + Float f(rat); + Rat new_rat(f); // rounded value + int c = new_rat.compare(rat); + if(c < 0) + { + // If f was rounded down, next float up must be above the original value: + f = boost::math::float_next(f); + new_rat.assign(f); + BOOST_CHECK(new_rat >= rat); + } + else if(c > 0) + { + // If f was rounded up, next float down must be below the original value: + f = boost::math::float_prior(f); + new_rat.assign(f); + BOOST_CHECK(new_rat <= rat); + } + else + { + // Values were equal... nothing to test. + } + if(boost::detail::test_errors() > 100) + break; + } + + std::cout << "Execution time = " << boost::chrono::duration_cast<boost::chrono::duration<double> >(w.elapsed()).count() << "s" << std::endl; + std::cout << "Total values tested: " << count << std::endl; +#endif +} + +int main() +{ + using namespace boost::multiprecision; +#if defined(TEST1) && !defined(BOOST_MSVC) + test_round_trip<number<cpp_bin_float<113, digit_base_2, void, boost::int16_t> >, cpp_rational>(); +#elif defined(TEST2) + test_round_trip<double, cpp_rational>(); +#elif defined(TEST3) && !defined(BOOST_MSVC) + test_random_rationals<number<cpp_bin_float<113, digit_base_2, void, boost::int16_t> >, cpp_rational>(); +#elif defined(TEST4) + test_random_rationals<double, cpp_rational>(); +#elif defined(TEST5) + // This does not work: gmp does not correctly round integer to float or + // rational to float conversions: + test_round_trip<double, mpq_rational>(); +#elif defined(TEST6) + test_round_trip<mpfr_float_100, mpq_rational>(); +#elif defined(TEST7) + test_random_rationals<mpfr_float_100, mpq_rational>(); +#elif defined(TEST8) + test_random_rationals<double, mpq_rational>(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_rational_io.cpp b/libs/multiprecision/test/test_rational_io.cpp new file mode 100644 index 0000000000..05e5a9ba52 --- /dev/null +++ b/libs/multiprecision/test/test_rational_io.cpp @@ -0,0 +1,146 @@ +// Copyright John Maddock 2011. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#if !defined(TEST_MPQ) && !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) +# define TEST_MPQ +# define TEST_TOMMATH +# define TEST_CPP_INT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPQ) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_TOMMATH) +#include <boost/multiprecision/tommath.hpp> +#endif +#ifdef TEST_CPP_INT +#include <boost/multiprecision/cpp_int.hpp> +#endif + +#include <boost/algorithm/string/case_conv.hpp> +#include <boost/random/mersenne_twister.hpp> +#include <boost/random/uniform_int.hpp> +#include <boost/multiprecision/rational_adaptor.hpp> +#include "test.hpp" +#include <iostream> +#include <iomanip> + +template <class T> +T generate_random() +{ + typedef typename boost::multiprecision::component_type<T>::type int_type; + static boost::random::uniform_int_distribution<unsigned> ui(0, 20); + static boost::random::mt19937 gen; + int_type val = int_type(gen()); + unsigned lim = ui(gen); + for(unsigned i = 0; i < lim; ++i) + { + val *= (gen.max)(); + val += gen(); + } + int_type denom = int_type(gen()); + lim = ui(gen); + for(unsigned i = 0; i < lim; ++i) + { + denom *= (gen.max)(); + denom += gen(); + } + return T(val, denom); +} + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::true_&) +{ + std::stringstream ss; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + ss << std::setprecision(std::numeric_limits<T>::max_digits10); +#else + ss << std::setprecision(std::numeric_limits<T>::digits10 + 5); +#endif + ss.flags(f); + ss << val; + T new_val = static_cast<T>(ss.str()); + BOOST_CHECK_EQUAL(new_val, val); + new_val = static_cast<T>(val.str(0, f)); + BOOST_CHECK_EQUAL(new_val, val); +} + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f, const boost::mpl::false_&) +{ + std::stringstream ss; + ss << std::setprecision(std::numeric_limits<T>::digits10 + 4); + ss.flags(f); + ss << val; + T new_val; + ss >> new_val; + BOOST_CHECK_EQUAL(new_val, val); +} + +template <class T> +struct is_number : public boost::mpl::false_{}; +template <class T> +struct is_number<boost::multiprecision::number<T> > : public boost::mpl::true_{}; + +template <class T> +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + do_round_trip(val, f, is_number<T>()); +} + +template <class T> +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + if(val >= 0) + { + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::hex)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::showbase|std::ios_base::oct)); + } +} + +template <class T> +void test_round_trip() +{ + for(unsigned i = 0; i < 1000; ++i) + { + T val = generate_random<T>(); + do_round_trip(val); + do_round_trip(T(-val)); + } +} + +int main() +{ +#ifdef TEST_MPQ + test_round_trip<boost::multiprecision::mpq_rational>(); + test_round_trip<boost::rational<boost::multiprecision::mpz_int> >(); + test_round_trip<boost::multiprecision::number<boost::multiprecision::rational_adaptor<boost::multiprecision::gmp_int> > >(); +#endif +#ifdef TEST_TOMMATH + test_round_trip<boost::rational<boost::multiprecision::tom_int> >(); + test_round_trip<boost::multiprecision::tom_rational >(); +#endif +#ifdef TEST_CPP_INT + test_round_trip<boost::rational<boost::multiprecision::cpp_int> >(); + test_round_trip<boost::multiprecision::cpp_rational >(); +#endif + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/test_round.cpp b/libs/multiprecision/test/test_round.cpp new file mode 100644 index 0000000000..5009dd06f2 --- /dev/null +++ b/libs/multiprecision/test/test_round.cpp @@ -0,0 +1,468 @@ +// (C) Copyright John Maddock 2007. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/math/special_functions/round.hpp> +#include <boost/math/special_functions/trunc.hpp> +#include <boost/math/special_functions/modf.hpp> +#include <boost/math/special_functions/sign.hpp> +#include <boost/random/mersenne_twister.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT)\ + && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128)\ + && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#ifdef TEST_MPFR_50 +#include <boost/multiprecision/mpfr.hpp> +#endif +#ifdef TEST_MPFI_50 +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +boost::mt19937 rng; + +template <class T> +T get_random() +{ + // + // Fill all the bits in T with random values, + // likewise set the exponent to a random value + // that will still fit inside a T, and always + // have a remainder as well as an integer part. + // + int bits = boost::math::tools::digits<T>(); + int shift = 0; + int exponent = rng() % (bits - 4); + T result = 0; + while(bits > 0) + { + result += ldexp(static_cast<T>(rng()), shift); + shift += std::numeric_limits<int>::digits; + bits -= std::numeric_limits<int>::digits; + } + return rng() & 1u ? T(-ldexp(frexp(result, &bits), exponent)) : T(ldexp(frexp(result, &bits), exponent)); +} + +template <class T, class U> +typename boost::disable_if_c<boost::multiprecision::is_interval_number<T>::value>::type check_within_half(T a, U u) +{ + BOOST_MATH_STD_USING + if(fabs(a-u) > 0.5f) + { + BOOST_ERROR("Rounded result differed by more than 0.5 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if((fabs(a - u) == 0.5f) && (fabs(static_cast<T>(u)) < fabs(a))) + { + BOOST_ERROR("Rounded result was towards zero with boost::round"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } +} +template <class T, class U> +typename boost::enable_if_c<boost::multiprecision::is_interval_number<T>::value>::type check_within_half(T a, U u) +{ + BOOST_MATH_STD_USING + if(upper(T(fabs(a-u))) > 0.5f) + { + BOOST_ERROR("Rounded result differed by more than 0.5 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if((upper(T(fabs(a - u))) == 0.5f) && (fabs(static_cast<T>(u)) < fabs(a))) + { + BOOST_ERROR("Rounded result was towards zero with boost::round"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } +} + +// +// We may not have an abs overload for long long so provide a fall back: +// +inline unsigned safe_abs(int const& v) +{ + return v < 0 ? static_cast<unsigned>(1u) + static_cast<unsigned>(-(v+1)) : v; +} +inline unsigned long safe_abs(long const& v) +{ + return v < 0 ? static_cast<unsigned long>(1u) + static_cast<unsigned long>(-(v+1)) : v; +} +inline unsigned long long safe_abs(long long const& v) +{ + return v < 0 ? static_cast<unsigned long long>(1u) + static_cast<unsigned long long>(-(v+1)) : v; +} +template <class T> +inline typename boost::disable_if_c<boost::is_integral<T>::value, T>::type safe_abs(T const& v) +{ + return v < 0 ? -v : v; +} + +template <class T, class U> +void check_trunc_result(T a, U u) +{ + BOOST_MATH_STD_USING + if(fabs(a-u) >= 1) + { + BOOST_ERROR("Rounded result differed by more than 1 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if(abs(a) < safe_abs(u)) + { + BOOST_ERROR("Truncated result had larger absolute value than the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } + if(fabs(static_cast<T>(u)) > fabs(a)) + { + BOOST_ERROR("Rounded result was away from zero with boost::trunc"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << u << std::endl; + } +} + +template <class T, class U> +void check_modf_result(T a, T fract, U ipart) +{ + BOOST_MATH_STD_USING + if(fract + ipart != a) + { + BOOST_ERROR("Fractional and integer results do not add up to the original value"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << fract << std::endl; + } + if((boost::math::sign(a) != boost::math::sign(fract)) && boost::math::sign(fract)) + { + BOOST_ERROR("Original and fractional parts have differing signs"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << fract << std::endl; + } + if((boost::math::sign(a) != boost::math::sign(ipart)) && boost::math::sign(ipart)) + { + BOOST_ERROR("Original and integer parts have differing signs"); + std::cerr << "Values were: " << std::setprecision(35) << " " + << std::left << a << ipart << " " << ipart << std::endl; + } + if(fabs(a-ipart) >= 1) + { + BOOST_ERROR("Rounded result differed by more than 1 from the original"); + std::cerr << "Values were: " << std::setprecision(35) << std::setw(40) + << std::left << a << ipart << std::endl; + } +} + +template <class T> +void test() +{ + BOOST_MATH_STD_USING + + for(int i = 0; i < 1000; ++i) + { + T arg = get_random<T>(); + T r = round(arg); + check_within_half(arg, r); + BOOST_TEST(r == round(arg + 0)); + r = trunc(arg); + check_trunc_result(arg, r); + BOOST_TEST(r == trunc(arg + 0)); + T frac = modf(arg, &r); + check_modf_result(arg, frac, r); + + if(abs(r) < (std::numeric_limits<int>::max)()) + { + int i = iround(arg); + check_within_half(arg, i); + BOOST_TEST(i == iround(arg + 0)); + i = itrunc(arg); + check_trunc_result(arg, i); + BOOST_TEST(i == itrunc(arg + 0)); + r = modf(arg, &i); + check_modf_result(arg, r, i); + } + if(abs(r) < (std::numeric_limits<long>::max)()) + { + long l = lround(arg); + check_within_half(arg, l); + BOOST_TEST(l == lround(arg + 0)); + l = ltrunc(arg); + check_trunc_result(arg, l); + BOOST_TEST(l == ltrunc(arg + 0)); + r = modf(arg, &l); + check_modf_result(arg, r, l); + } + +#ifdef BOOST_HAS_LONG_LONG + if(abs(r) < (std::numeric_limits<boost::long_long_type>::max)()) + { + boost::long_long_type ll = llround(arg); + check_within_half(arg, ll); + BOOST_TEST(ll == llround(arg + 0)); + ll = lltrunc(arg); + check_trunc_result(arg, ll); + BOOST_TEST(ll == lltrunc(arg + 0)); + r = modf(arg, &ll); + check_modf_result(arg, r, ll); + } +#endif + } + // + // Test boundary cases: + // + if(std::numeric_limits<T>::digits >= std::numeric_limits<int>::digits) + { + int si = iround(static_cast<T>((std::numeric_limits<int>::max)())); + check_within_half(static_cast<T>((std::numeric_limits<int>::max)()), si); + BOOST_TEST(si == iround(static_cast<T>((std::numeric_limits<int>::max)()) + 0)); + si = iround(static_cast<T>((std::numeric_limits<int>::min)())); + check_within_half(static_cast<T>((std::numeric_limits<int>::min)()), si); + BOOST_TEST(si == iround(static_cast<T>((std::numeric_limits<int>::min)()) + 0)); + si = itrunc(static_cast<T>((std::numeric_limits<int>::max)())); + check_trunc_result(static_cast<T>((std::numeric_limits<int>::max)()), si); + BOOST_TEST(si == itrunc(static_cast<T>((std::numeric_limits<int>::max)()) + 0)); + si = itrunc(static_cast<T>((std::numeric_limits<int>::min)())); + check_trunc_result(static_cast<T>((std::numeric_limits<int>::min)()), si); + BOOST_TEST(si == itrunc(static_cast<T>((std::numeric_limits<int>::min)()) + 0)); + + si = iround(static_cast<T>((std::numeric_limits<int>::max)() - 1)); + check_within_half(static_cast<T>((std::numeric_limits<int>::max)() - 1), si); + si = iround(static_cast<T>((std::numeric_limits<int>::min)() + 1)); + check_within_half(static_cast<T>((std::numeric_limits<int>::min)() + 1), si); + si = itrunc(static_cast<T>((std::numeric_limits<int>::max)() - 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<int>::max)() - 1), si); + si = itrunc(static_cast<T>((std::numeric_limits<int>::min)() + 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<int>::min)() + 1), si); + } + if(std::numeric_limits<T>::digits >= std::numeric_limits<long>::digits) + { + long k = lround(static_cast<T>((std::numeric_limits<long>::max)())); + check_within_half(static_cast<T>((std::numeric_limits<long>::max)()), k); + BOOST_TEST(k == lround(static_cast<T>((std::numeric_limits<long>::max)()) + 0)); + k = lround(static_cast<T>((std::numeric_limits<long>::min)())); + check_within_half(static_cast<T>((std::numeric_limits<long>::min)()), k); + BOOST_TEST(k == lround(static_cast<T>((std::numeric_limits<long>::min)()) + 0)); + k = ltrunc(static_cast<T>((std::numeric_limits<long>::max)())); + check_trunc_result(static_cast<T>((std::numeric_limits<long>::max)()), k); + BOOST_TEST(k == ltrunc(static_cast<T>((std::numeric_limits<long>::max)()) + 0)); + k = ltrunc(static_cast<T>((std::numeric_limits<long>::min)())); + check_trunc_result(static_cast<T>((std::numeric_limits<long>::min)()), k); + BOOST_TEST(k == ltrunc(static_cast<T>((std::numeric_limits<long>::min)()) + 0)); + + k = lround(static_cast<T>((std::numeric_limits<long>::max)() - 1)); + check_within_half(static_cast<T>((std::numeric_limits<long>::max)() - 1), k); + k = lround(static_cast<T>((std::numeric_limits<long>::min)() + 1)); + check_within_half(static_cast<T>((std::numeric_limits<long>::min)() + 1), k); + k = ltrunc(static_cast<T>((std::numeric_limits<long>::max)() - 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<long>::max)() - 1), k); + k = ltrunc(static_cast<T>((std::numeric_limits<long>::min)() + 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<long>::min)() + 1), k); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits<T>::digits >= std::numeric_limits<boost::long_long_type>::digits) + { + boost::long_long_type j = llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)())); + check_within_half(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)()), j); + BOOST_TEST(j == llround(static_cast<T>((std::numeric_limits<long long>::max)()) + 0)); + j = llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)())); + check_within_half(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)()), j); + BOOST_TEST(j == llround(static_cast<T>((std::numeric_limits<long long>::min)()) + 0)); + j = lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)())); + check_trunc_result(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)()), j); + BOOST_TEST(j == lltrunc(static_cast<T>((std::numeric_limits<long long>::max)()) + 0)); + j = lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)())); + check_trunc_result(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)()), j); + BOOST_TEST(j == lltrunc(static_cast<T>((std::numeric_limits<long long>::min)()) + 0)); + + j = llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)() - 1)); + check_within_half(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)() - 1), j); + j = llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)() + 1)); + check_within_half(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)() + 1), j); + j = lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)() - 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)() - 1), j); + j = lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)() + 1)); + check_trunc_result(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)() + 1), j); + } +#endif + // + // Finish off by testing the error handlers: + // + BOOST_CHECK_THROW(static_cast<T>(iround(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(iround(static_cast<T>(-1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(static_cast<T>(-1e20))), boost::math::rounding_error); +#ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(llround(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(llround(static_cast<T>(-1e20))), boost::math::rounding_error); +#endif + if(std::numeric_limits<T>::has_infinity) + { + BOOST_CHECK_THROW(static_cast<T>(round(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(iround(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(iround(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(llround(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(llround(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits<T>::has_quiet_NaN) + { + BOOST_CHECK_THROW(static_cast<T>(round(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(iround(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(llround(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + #endif + } + BOOST_CHECK_THROW(static_cast<T>(itrunc(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(itrunc(static_cast<T>(-1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(static_cast<T>(-1e20))), boost::math::rounding_error); +#ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(lltrunc(static_cast<T>(1e20))), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lltrunc(static_cast<T>(-1e20))), boost::math::rounding_error); +#endif + if(std::numeric_limits<T>::has_infinity) + { + BOOST_CHECK_THROW(static_cast<T>(trunc(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(itrunc(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(itrunc(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(lltrunc(std::numeric_limits<T>::infinity())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lltrunc(-std::numeric_limits<T>::infinity())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits<T>::has_quiet_NaN) + { + BOOST_CHECK_THROW(static_cast<T>(trunc(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(itrunc(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + #ifdef BOOST_HAS_LONG_LONG + BOOST_CHECK_THROW(static_cast<T>(lltrunc(std::numeric_limits<T>::quiet_NaN())), boost::math::rounding_error); + #endif + } + if(std::numeric_limits<T>::digits >= std::numeric_limits<int>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(itrunc(static_cast<T>((std::numeric_limits<int>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(itrunc(static_cast<T>((std::numeric_limits<int>::min)()) - 1)), boost::math::rounding_error); + } + if(std::numeric_limits<T>::digits >= std::numeric_limits<long>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(ltrunc(static_cast<T>((std::numeric_limits<long>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(ltrunc(static_cast<T>((std::numeric_limits<long>::min)()) - 1)), boost::math::rounding_error); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits<T>::digits >= std::numeric_limits<boost::long_long_type>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lltrunc(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)()) - 1)), boost::math::rounding_error); + } +#endif + if(std::numeric_limits<T>::digits >= std::numeric_limits<int>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(iround(static_cast<T>((std::numeric_limits<int>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(iround(static_cast<T>((std::numeric_limits<int>::min)()) - 1)), boost::math::rounding_error); + } + if(std::numeric_limits<T>::digits >= std::numeric_limits<long>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(lround(static_cast<T>((std::numeric_limits<long>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(lround(static_cast<T>((std::numeric_limits<long>::min)()) - 1)), boost::math::rounding_error); + } +#ifndef BOOST_NO_LONG_LONG + if(std::numeric_limits<T>::digits >= std::numeric_limits<boost::long_long_type>::digits) + { + BOOST_CHECK_THROW(static_cast<T>(llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::max)()) + 1)), boost::math::rounding_error); + BOOST_CHECK_THROW(static_cast<T>(llround(static_cast<T>((std::numeric_limits<boost::long_long_type>::min)()) - 1)), boost::math::rounding_error); + } +#endif +} + +int main() +{ +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); +#endif +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); + test<boost::multiprecision::cpp_bin_float_100>(); +#endif +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif + return boost::report_errors(); +} + + diff --git a/libs/multiprecision/test/test_sin.cpp b/libs/multiprecision/test/test_sin.cpp new file mode 100644 index 0000000000..bfdb9ff34f --- /dev/null +++ b/libs/multiprecision/test/test_sin.cpp @@ -0,0 +1,351 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<const char*, 101u> data = + {{ + 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convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 5000000000uLL); + + static const boost::array<const char*, 51u> small_data = + {{ + "0.010890646307437399028563191160252839599929232814970922208664909237494716181484215717644776933044418903207919912063594159099133490979634344811936925144447725948305353257042599564404885434349760121009797816724142318243738364307036155852011004353462651092012819894667485840322627440332163428546845499107471983896711023161969130462687924045508477090891879273259947713367290982391204265694893491531721581439", + 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static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); + T val = sin((euler_gamma + k) / 53); + T e = relative_error(val, T(small_data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = sin(-(euler_gamma + k) / 53); + e = relative_error(val, T(-T(small_data[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + + + // + // Test with some exact binary values as input - this tests our code + // rather than the test data: + // + static const boost::array<boost::array<T, 2>, 9> exact_data = + {{ + {{ 0.5, static_cast<T>("0.479425538604203000273287935215571388081803367940600675188616613125535000287814832209631274684348269086132091084505717418") }}, + {{ 0.25, static_cast<T>("0.247403959254522929596848704849389195893390980386965810676544830494398136043486821690984848527973792338327197752176516138") }}, + {{0.75, static_cast<T>("0.681638760023334166733241952779893935338382394659229909213625262151100388887003782753145274849781911981438190343146876189") }}, + {{std::ldexp(1.0, -20), static_cast<T>("9.53674316406105439710335272649306549801506698739838753888815787489707114648106832493113326022411646219016312547902694921e-7") }}, + {{ 2, static_cast<T>("0.909297426825681695396019865911744842702254971447890268378973011530967301540783544620126688924959380309967896742399486261") }}, + {{ 5, static_cast<T>("-0.958924274663138468893154406155993973352461543964601778131672454235102558086559603076995955429532866596530638461663378937") }}, + {{ 10, static_cast<T>("-0.544021110889369813404747661851377281683643012916223891574184012616757209640493425707075673894983216158293824238262832286") }}, + {{ 0, 0 }}, + {{ static_cast<T>("1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404325664115332354692230477529111586267970406424055872514205135096926055277982231147447746519098221440548783296672306423782411689339158263560095457282428346173017430522716332410669680363012457064"), 1 }} + }}; + max_err = 0; + for(unsigned k = 0; k < exact_data.size(); k++) + { + T val = sin(exact_data[k][0]); + T e = relative_error(val, exact_data[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + +#include "sincos.ipp" + max_err = 0; + for(unsigned k = 0; k < sincos.size(); k++) + { + T val = sin(sincos[k][0]); + T e = relative_error(val, sincos[k][1]); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_sinh.cpp b/libs/multiprecision/test/test_sinh.cpp new file mode 100644 index 0000000000..3fe4ec3278 --- /dev/null +++ b/libs/multiprecision/test/test_sinh.cpp @@ -0,0 +1,261 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<const char*, 51u> data = + {{ + 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"4.9861251931207080923785686798881789193813879610842675205361210155894774686328710893906543682447029206928934967525495260314937837003448878215156341411477636831113484416124080974502217578408248150338565305116223944900839866528622960352723938548713319425798453345402992146078868053263606234074443024155243450623634720912438841022969909473424559262711669905282193529250216454066716533180418518228387188393e862", + "7.1012569014339068241101751233953234216522840280342406520909288232012799547871960723719836516359548198842749536961644100550279020276709043358260853581760590386456213180291689322352732545965831405519844109680619067101311180959399339922706596098526969148981173519865139508665631317310424178378833370605922449094745510812618563813537347841030916512147874232760564378443782164868016244561788356251308121716e901", + "7.4730215360486642135431754747074885377840195683583018254892502245011973712084221116813364423492802080799768174534590613188275471080608467087354983850284805514875889145266688973752185071777341375422809910165581997555433091939959406569831183459872344778707098094941193489061532160249775856426569696127193453339548371679229676272663084782830276508737129506676031759345288056484158647796152349867328841634e941", + "5.8109375364209112227579654658730977030869454388607076903639465992296616832002964138000947668837140543325908222688655359602408511410663722770167244801973012245657865182739637159804595049180263175014778215232564251739259624759589953677661356104554831551073263668188283861123521688445132164147762321111597028523130093864153999974376790494383016372210442340324038686843345053322425194077414241243050491297e982", + "3.33875955701899627718146291382268063073604182131575843695486667154496711979350813988644889979275310892951143249901398447859083674739840084454465850475774696325142148671937407108540250845900941142800157345665761403930889797424808979569550325271558518404559007551625637761142662107757913763221912282957681784053564387104062317729788737215450574233690655931888608424916152893688106181220341997128198692e1024", + "1.4174672877823334709610117319768830739080734407353905145632612088824955720198734996604261250019291955883620333545750761619015467840567122066622229379056280064206319780047687015558007624774062399477328822231085767309831266032616053065858739373818651687128093335640388513396191118537181280334430292439188737524362269789272308905723812818882228503013875816702686587035844437102478263525616196832018321602e1067", + "4.4466189016791091516801723880812533528438597080549410911235655611382010503145789286158745555771483577943662768773465284793798720178177605712848440200402906836390133865748188969184005230383247111166918721449908133920663776952786683837038180436264738937354101153867171804315769471050303182129269442292354388037298125177941217926845803005587166270803697433886463469168814941555804311717400657004050157245e1110", + }}; + + T eg = static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::sinh(x * x); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + val = boost::multiprecision::sinh(-x * x); + e = relative_error(val, T(-T(data[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + + boost::array<const char*, 50> small_values = + {{ + "8.223167319358299807036616344469138485821440027829633696917375433348917938654659351596020080036406671343718039863220496616e-01", + "2.526123168081683079141251505420579055197542874276608074880949653019810769068593790606537020961198741487692473633089323967e-01", + "8.342981744595282037256218647969712476322487890550784823763249893556153270975172951404094950587944959561849750490537201329e-02", + "2.778135016068299789938671680845480653984976507019542653788637161116587306168290886761259072846829249121589698206609261524e-02", + "9.259391565199916442789400306996794489540862711193761818262415211084389468754315525525896238827358889826875006042447587516e-03", + "3.086424653287772358219607529932097884435043040527155440187640095572710676452654803730003577747633690318001961509535020849e-03", + "1.028806765851002064810061084014826478832745077469708149635730407866217436751337520417458090265791086156438275231514030381e-03", + "3.429355348425226988441198390119109217716503769838753365112550442738406326637684639052252898314646892490045395290022292013e-04", + "1.143118429558603374406653541544292690548937361618336125287018361332072426474632105217297150810234138626767253281422813482e-04", + "3.810394757818873406266877296641684693312194735341898368873067089928172619067423751257049691985638480762032673977695116880e-05", + "1.270131585666421832817527834137477593266387525701388601975733237436369505733715799310429349744168792375082834509467436523e-05", + "4.233771952120219947940459634636576539101577724347428305072378100562649548884420218224692461748739725090626754420296122389e-06", + "1.411257317369659013704209000288436132710449162963127340562961271337242582661013580874165903770246169179192268836124421074e-06", + "4.704191057897475365825409916786898392364235667906752767514580467152163619657508910797742266406961516358439252434955007668e-07", + "1.568063685965773714045928492719360014894368531987759414833778466374819836545157375950693756664550256136222396871173634254e-07", + "5.226878953219226673524993193392503058475862017726848548717100658392470633650387274004511940515056405069137033934323251644e-08", + "1.742292984406408185991240874995689487745140228031202510923711784729440494088066989430128101759261047316736074663327672115e-08", + "5.807643281354693692124967044009687283114597355717062156493618245876910131607338183944830908381903728560328284173507220743e-09", + "1.935881093784897887701686451485601671131342930785061493703969418728524594573922282309665275558709040519461560600768780392e-09", + "6.452936979282992955422916851920785543106383715381924626175995859924351552325880931187614903984801793287071578640505194508e-10", + "2.150978993094330985008279519046512957825521218238790792201835497215534851989750722105234826300738623838446309250309905466e-10", + "7.169929976981103283311786261663531258230547972690500493476881079295129579131280734024784107219045379345460886663104148486e-11", + "2.389976658993701094435441884684454421835327948893136184573938864819002944442339456827931472237274353903634036758669394620e-11", + "7.966588863312336981450798799860506345287566898810744342680146925029151178981033890759916168189916177504592939240995619757e-12", + "2.655529621104112327150241298135440075805848488054800577703768668100658036999584228451100239039042920681377381394421710121e-12", + "8.851765403680374423834128412864530361591097252230621965426275532533242581680245794741067906285298655116802944992368126680e-13", + "2.950588467893458141278042461784956914687338675140497707333871358819185395356569206661450997145748756956497959702280685427e-13", + "9.835294892978193804260141412430145318398649753331401112621871794012928366988233744354238387090649589382104704221708773516e-14", + "3.278431630992731268086713799445120869198593899364655036314007566906378666339665297288092596796135684816883503781385164489e-14", + "1.092810543664243756028904599641030626636532928735904320784337625844108091213506619051042206148385975354700234586478575025e-14", + "3.642701812214145853429681998738987398752764686754626492252324567456938623579239392678142797020213493844816454129960310753e-15", + "1.214233937404715284476560666243942169089106312534317920490462975351305354471020532764015606315872085933262687299655265697e-15", + "4.047446458015717614921868887478923169619805517194433471908835726595116905187672132801369948377551282604828733616045843751e-16", + "1.349148819338572538307289629159608313551890152969010184597042496758528297346351553643241208769191557898925543369605617734e-16", + "4.497162731128575127690965430532015584807024576774799020494128293451281927637267192489558050090835454302448780391749096414e-17", + "1.499054243709525042563655143510671412452985626833998379862387948592418229228808284088934491020852037924756758483008288052e-17", + "4.996847479031750141878850478368904541825005460277179305602161748681654262243578435201096986093377131577325573917436618470e-18", + "1.665615826343916713959616826122968174447164290616980189746184851537351248309665330601503343215376981550822569162631313560e-18", + "5.552052754479722379865389420409893912541965834349657578615232567585047309856390957625702896178052275806406957076143469634e-19", + "1.850684251493240793288463140136631304096139902769381795814754672989850701401641374814254071564872119933498619234778448524e-19", + "6.168947504977469310961543800455437680289164351695283493312025632359317744715643192414807145394613572397590534364339391526e-20", + "2.056315834992489770320514600151812560095228784236601072113743484455321300338926430301421880927367590178440922006775473367e-20", + "6.854386116641632567735048667172708533650333231531203539518552950777817440179277823487619201513258000884052637516041835420e-21", + "2.284795372213877522578349555724236177883428507451482660054557452824460619777642844796449091646418601791047308814504431261e-21", + "7.615984574046258408594498519080787259611422468149787192854095139994568043598766360557598146279482678180281335390895949036e-22", + "2.538661524682086136198166173026929086537140604567639372655275057673980680372673609490963070062819520295998328327889923353e-22", + "8.462205082273620453993887243423096955123801934429554813185698344472203995997708879527322555715697860578416576045982358004e-23", + "2.820735027424540151331295747807698985041267308484077168753311108116374235508697904826049959781116012127075951788533527897e-23", + "9.402450091415133837770985826025663283470891027171945709804152456669015193736201020401750153196590359525341207466344738924e-24", + "3.134150030471711279256995275341887761156963675682933328476437810109959425395050019306074135780459168092270327572635795510e-24", + }}; + + max_err = 0; + T v = 0.75; + for(unsigned k = 0; k < small_values.size(); ++k) + { + T val = boost::multiprecision::sinh(v); + T e = relative_error(val, T(small_values[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = boost::multiprecision::sinh(-v); + e = relative_error(val, T(-T(small_values[k]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + v /= 3; + } + + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 2000); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_sqrt.cpp b/libs/multiprecision/test/test_sqrt.cpp new file mode 100644 index 0000000000..f845492e08 --- /dev/null +++ b/libs/multiprecision/test/test_sqrt.cpp @@ -0,0 +1,242 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + static const boost::array<const char*, 101u> data = + {{ + "0", + "1.77245385090551602729816748334114518279754945612238712821380778985291128459103218137495065673854466541622682362428257066623615286572442260252509370960278706846203769865310512284992517302895082622893209537926796280017463901535147972051670019018523401858544697449491264031392177552590621640541933250090639840761373347747515343366798978936585183640879545116516173876005906739343179133280985484624818490205465485219561325156164746751504273876105610799612710721006037204448367236529661370809432349883166842421384570960912042042778577806869476657000521830568512541339663694465418151071669388332194292935706226886522442054214994804992075648639887483850593064021821402928581123306497894520362114907896228738940324597819851313487126651250629326004465638210967502681249693059542046156076195221739152507020779275809905433290066222306761446966124818874306997883520506146444385418530797357425717918563595974995995226384924220388910396640644729397284134504300214056423343303926175613417633632001703765416347632066927654181283576249032690450848532013419243598973087119379948293873011126256165881888478597787596376136", + 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"17.6356931450223847051632626336912129159953047631160231255194263214719736745345056574006334052947783704789851124650942357806440283438448075865374177648755421744889004812088237415174002112721888433569481184443980026560025069439822330036408245659699705607208167409459718244781459151859701286920686791397587316924683661006361446569736280386659169943463243969853737516308403647389899899943288964539074045777396061094245615020794569618969810767286161759163196190210263374998456288778623199988233761901113536316735857956970778148341712538680960137046414511920334125306354736321418705129785669231702905296255118678564162795574424588337165553826200448066730531304621451838136219021244379504974116096097930348202146495020513154705219076501726427281405053157307369058563911985328395372478199002802154489559015174957595775902617263259894306671438880488104887489699278033942889387921168112741333336787578922278486757542524555357598873580646861232908497366240101359399679018683387336026768844320636768908505456317105807294092097672788610628498171867123780698747648210099920520967511623044818811130645542567309932834", + "17.7245385090551602729816748334114518279754945612238712821380778985291128459103218137495065673854466541622682362428257066623615286572442260252509370960278706846203769865310512284992517302895082622893209537926796280017463901535147972051670019018523401858544697449491264031392177552590621640541933250090639840761373347747515343366798978936585183640879545116516173876005906739343179133280985484624818490205465485219561325156164746751504273876105610799612710721006037204448367236529661370809432349883166842421384570960912042042778577806869476657000521830568512541339663694465418151071669388332194292935706226886522442054214994804992075648639887483850593064021821402928581123306497894520362114907896228738940324597819851313487126651250629326004465638210967502681249693059542046156076195221739152507020779275809905433290066222306761446966124818874306997883520506146444385418530797357425717918563595974995995226384924220388910396640644729397284134504300214056423343303926175613417633632001703765416347632066927654181283576249032690450848532013419243598973087119379948293873011126256165881888478597787596376136", + }}; + + T pi = static_cast<T>("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = sqrt(pi * k); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; +#if defined(BOOST_INTEL) && defined(TEST_FLOAT128) + BOOST_TEST(max_err < 30); +#else + BOOST_TEST(max_err < 20); +#endif + // + // Some tricky special cases: + // + BOOST_CHECK((boost::math::isfinite)(sqrt((std::numeric_limits<T>::max)()))); + BOOST_CHECK((boost::math::isfinite)(sqrt((std::numeric_limits<T>::min)()))); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); + // Check up to 1000 multiprecision digits. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<500> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<1000> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_tan.cpp b/libs/multiprecision/test/test_tan.cpp new file mode 100644 index 0000000000..8dc9dcbdcd --- /dev/null +++ b/libs/multiprecision/test/test_tan.cpp @@ -0,0 +1,634 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_MPFR_50 +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<boost::array<const char*, 2>, 500> data = + {{ + {{ "0", "0" }}, + {{ "0.03125", "0.03126017650125595642059651621507489147877835880393069701338513042228140662868270178810496567920444849" }}, + {{ "0.0625", "0.06258150756627501465828481747745378814263718044751609194477198396918772026898277636891147279909599223" }}, + {{ "0.09375", "0.09402562724573195576489755283678159034525247904824579838425258406126459673745015890895186868431790389" }}, + {{ "0.125", "0.1256551365751309677926782186297740007586657638922255426688666139272557034809288714758416649081949452" }}, + {{ "0.15625", "0.1575341073252716106852257741724104906661974475121544257009051769486388715993896887955248205741956572" }}, + {{ "0.1875", "0.1897286107180591328910833700730338162710122536010363055257273177325079653665703027537671734777793159" }}, + {{ "0.21875", "0.2223072805534313308722888175879995822319104918387718270273535559005416973923742249393961682186904743" }}, + {{ "0.25", "0.2553419212210362665044822364904736782042016388008226217404756502588831981346542579493165026310550454" }}, + {{ "0.28125", "0.2889081724405147260015884454642448286982056723714186732378896291489603033944207768995735063901118923" }}, + {{ "0.3125", "0.3230862443517455201183006557179619743037036164759656335249943943470835620899848486165999610265179128" }}, + {{ "0.34375", "0.3579617388480169983883959631794471406375375900948760280972554801967920011385682070576100261097824193" }}, + {{ "0.375", "0.3936265759256327582294137871012180981856966444080712949818309739116951585799388015457993878787997269" }}, + {{ "0.40625", "0.4301800474642300490203296054472752679963181652078151755042924196261397876727827800621729454863519218" }}, + {{ "0.4375", "0.467730025452391799921342706961992620413738282701114114727311802060193364671415150855360089743973883" }}, + {{ "0.46875", "0.5063943574962298120708227547071771387085972911587370796115595547436950963394141008177411206688111652" }}, + {{ "0.5", "0.5463024898437905132551794657802853832975517201797912461640913859329075105180258157151806482706562186" }}, + {{ "0.53125", "0.5875973675914432213941588631578976924522062928763012976297627647411436985181631978010052165746790249" }}, + {{ "0.5625", "0.630437673835884766852611429299775209903293946951939898251650513745196222165381994293674222073197888" }}, + {{ "0.59375", "0.6750004851442429076631779494777229128864061685897319107997999948317524157945835559284790797708856594" }}, + {{ "0.625", "0.7214844409909044199895178832795946807605892812145963657590722733756611374332889471678213489198161525" }}, + {{ "0.65625", "0.770113551344208705005983660052773240245517035179766333813336659352553100285016757206110401160028615" }}, + {{ "0.6875", "0.8211418015898941219114239653747117008753716453086877023306268412086961091026737960147423436480371207" }}, + {{ "0.71875", "0.874858760554482349539671907932155532231782257040588572549027780010892786023906162883923961511720127" }}, + {{ "0.75", "0.9315964599440724611652027565739364281886913399722189970823760758473440872606463942290222395451727347" }}, + {{ "0.78125", "0.9917378983632686802568573899299023689572109767948642785884455151680071204845003794305054375396567381" }}, + {{ "0.8125", "1.055727639411919906905928322585893795895648561782414602487481288436493656539800004691156074588329712" }}, + {{ "0.84375", "1.124085134704560944131255965236688143403009777898521429483610660496648114350313475950507899270640935" }}, + {{ "0.875", "1.197421629234347972339226617276609445975806623418086002265951386950959459751336541541255052511392263" }}, + {{ "0.90625", "1.276461828982383445402617843263224436254612963462020761243811395954456362359102470162910199798207331" }}, + {{ "0.9375", "1.362071976376228231137266640571127531383954502011184315622281795551984309995647087587519913956728759" }}, + {{ "0.96875", "1.455296662469072910283351203225910848640458285194500237036240390915811463257413817682188441906818248" }}, + {{ "1", "1.557407724654902230506974807458360173087250772381520038383946605698861397151727289555099965202242984" }}, + {{ "1.03125", "1.669970130353601668362228999287655840466243330137306547430306024592587314737242276409239980979443174" }}, + {{ "1.0625", "1.794932157265411111412512666640647365321540790157497713363548060626019826336277151761592643681562889" }}, + {{ "1.09375", "1.934751011916103924218794082343652203808222523749686394781135509079848569244264225172363092871198012" }}, + {{ "1.125", "2.092571276372179004423733981234886782259941716148720572913991515339894408382371607574079035650497628" }}, + {{ "1.15625", "2.272484060247449371554848155118626331407879143446651944395567708418983252993702557436552564850427597" }}, + {{ "1.1875", "2.479912917556758792437515574454698934001624072586467858166295252178386457324268836053055868956236971" }}, + {{ "1.21875", "2.722205296368710926927932441765877991142333599010908457349133016162381084884183783877142234320889929" }}, + {{ "1.25", "3.009569673862831288157563894386243931391637699606062181047618417194668052548525026087449023543493348" }}, + {{ "1.28125", "3.356619539863437446801254212059537717694035906934171604782430676182834617443082960603002796648697006" }}, + {{ "1.3125", "3.785038166535876194630450975067081020082611278470578710038656250838244608554256510046862645943214168" }}, + {{ "1.34375", "4.328443997051826678273102914917348524900160978527585314859991445919675557868173766988955991311583481" }}, + {{ "1.375", "5.04191525648136332110647205436422898660842030191113551461354742130497045161358084541551547909572374" }}, + {{ "1.40625", "6.02236781523945747670227618692239447637023828129226996489330674807031833318199939459376428890858723" }}, + {{ "1.4375", "7.457597366497314807346683309400119820853357043059007743950216525315136075258562571085388447049580691" }}, + {{ "1.46875", "9.765431722939984318153137075537986427219225446494026346174651506537333303940271000197727980305021618" }}, + {{ "1.5", "14.10141994717171938764608365198775644565954357723586186612326758608969627041415526864870292630944229" }}, + {{ "1.53125", "25.27361509038201021888564593774203447137999639112919943365223977030408052066444435679945642193151117" }}, + {{ "1.5625", "120.5325057225426126499709994255564804478992494692406282802019970839232698437518852292295322760051977" }}, + {{ "1.59375", "-43.55836040673973128976461522014256814059799632626649998645431997677346427573993827534701436489680689" }}, + {{ "1.625", "-18.43086276236962258434966752738448975654856844592479276671012332110139541995382323486170528839748939" }}, + {{ "1.65625", "-11.67374867215481348216513536293945130766869617358776549669176281104274968860961548954064974733991076" }}, + {{ "1.6875", "-8.529773993911653209272999783778324026196719414411590092375294867302897481134537117581472896391856125" }}, + {{ "1.71875", "-6.709482397820695376442251396240149572345307174060614879543507453718786710576833294867753884694537068" }}, + {{ "1.75", "-5.520379922509330168089935698420205500301122430036809938027371836902288281994865833387763391132527793" }}, + {{ "1.78125", "-4.681280325336429567316481395066494078522124421106252324368679821712511116596067067167862140573504461" }}, + {{ "1.8125", "-4.056414052170035671394695838412072312925972547334020477371203912084804008892977770267448199074447777" }}, + {{ "1.84375", "-3.572185661861125859870109039981697499670205624150737204067785923886464814599307447743073100872203818" }}, + {{ "1.875", "-3.185238919501229169914672833591055563068190813252958079987355697225012578404488535638528315769681186" }}, + {{ "1.90625", "-2.868371726567042158384165205507273428429609298347592604875428057959086996590505442480814626239318494" }}, + {{ "1.9375", "-2.603652912010850547260718033703880538638622594696262109914178307203938532760442947667909676035790898" }}, + {{ "1.96875", "-2.378782114044268462754557076702009514149544247914950239975234530609231791907385965883627186285245033" }}, + {{ "2", "-2.185039863261518991643306102313682543432017746227663164562955869966773747209194182319743542104728548" }}, + {{ "2.03125", 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"-2.634069132503832833409607035052858278935807513368801311481801280408668028920599740332367971681453643" }}, + {{ "14.53125", "-2.404794639925577553244012746285864594559572350297129379452932406519481483010765023196033751578709703" }}, + {{ "14.5625", "-2.207581089523679545128355853946391835592464237094323506839360879131859583353800754571132350944473674" }}, + {{ "14.59375", "-2.035829586659772321235017007716845648434117124540496962900856683971781311984497273615528750368081422" }}, + {{ "14.625", "-1.884630768865435904935595378906947231717012177189752377379403964925875302521199447518722408719775981" }}, + {{ "14.65625", "-1.750256190835124208623312849116061326812165846025415986783560739453729962659158203940996884358758139" }}, + {{ "14.6875", "-1.629822991609989147184189043054819627629510818289435539398133590083260226275976603564527843030512624" }}, + {{ "14.71875", "-1.521066667289361457373930052890176846963182405346389200320517277799503677666772192617687500257521097" }}, + {{ "14.75", "-1.42218336083774197380789085745137021789867848279597800468450871698744869740438289092755542692570482" }}, + {{ "14.78125", "-1.331718058572613129017722401996663023341875099157808098995252549045562547044521935057437210333349552" }}, + {{ "14.8125", "-1.248483823169844883793467308858957913772012915051151771810074084965259104516379708093866536649015936" }}, + {{ "14.84375", "-1.171502454280969620050113939757468091964527953537892858826299161314598145955301346129774398985079725" }}, + {{ "14.875", "-1.09996022360423379094065298284739111500559223495806048377446355428125902586706149601540328954397664" }}, + {{ "14.90625", "-1.033174396383465269461739738697259215672589493553897443441659340076220701053186730617856132398548093" }}, + {{ "14.9375", "-0.9705675907155131163149460322607739770705545946870992276893226926978460501228871025636381103213358614" }}, + {{ "14.96875", "-0.9116479124475490508064737825953723368462225788875404013990634500526165327350899245784037598875471869" }}, + {{ "15", "-0.8559934009085187640261927782380296049897864414742962979687446281783012594486541122545103129259226012" }}, + {{ "15.03125", "-0.8032397302332296612432159755337281904284459733163994877022298441144059785603187789136637043263789466" }}, + {{ "15.0625", "-0.7530703960754939484978446924032015414437125508200990314934869704250553438069278960228507610120908637" }}, + {{ "15.09375", "-0.7052088187318415299725928408540094093554358958059088325375638362095004704432693353838375709463129551" }}, + {{ "15.125", "-0.659411937622644225218300893404169827076548649885412227383887901950221923526355502978543776575055119" }}, + {{ "15.15625", "-0.6154649762727536414801474029122625793755198617269250343988631456453788448149731706979351529235579577" }}, + {{ "15.1875", "-0.5731771332183040948793178896118867037269598773610412277642977614409075169432893108977656087532808068" }}, + {{ "15.21875", "-0.5323780107028691176788965668440942781647156607765742951342412648358988559400799809724920990286528734" }}, + {{ "15.25", "-0.4929146351866012621666401573415074523464609163340854530825224584649245974424596583470196176643838565" }}, + {{ "15.28125", "-0.4546489554738299415350063572461193751006928326854122963028434583535719327916356408447934270192962049" }}, + {{ "15.3125", "-0.4174557284251085623680148206370333657407709127949181945517726979253617292255491330234726669774559159" }}, + {{ "15.34375", "-0.3812207207302419203446046603506711987787377766806738457878506795815713138223264722913354548269137032" }}, + {{ "15.375", "-0.3458391695028422582485004568448026536356203654713446806415710694635885346246660520826948870993463705" }}, + {{ "15.40625", "-0.311214455551825073642663079591570618837743590849903018274057606911872122304533000910107606645650336" }}, + {{ "15.4375", "-0.2772569518534830079599506190692912755868921271423525814120233867695893487373304945292237740353757468" }}, + {{ "15.46875", "-0.2438830165543173054192587099181568413614402066070223778896735213919894343566763962867244846621486138" }}, + {{ "15.5", "-0.2110141052012553133863173741408514435037061655011970687100846880180438182550528565062101594891245018" }}, + {{ "15.53125", "-0.1785759811388596991279739233477573236616687666102227187311862264495771634608666297275574790232136991" }}, + {{ "15.5625", "-0.1464980063716879847555275878278898667317766571375499828106145375100216949704230935552550931052323183" }}, + {{ "15.59375", "-0.1147124978452713735943481847220917786442201384229215777788278473922030662630912256721375261600875605" }}, + }}; + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + T val = tan(T(data[k][0])); + T e = relative_error(val, T(data[k][1])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + val = tan(-T(data[k][0])); + e = relative_error(val, T(-T(data[k][1]))); + err = e.template convert_to<unsigned>(); + if(err > max_err) + { + max_err = err; + } + } + std::cout << "Max error was: " << max_err << std::endl; +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); + // Check low multiprecision digit counts. + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<9> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<18> > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_tanh.cpp b/libs/multiprecision/test/test_tanh.cpp new file mode 100644 index 0000000000..e45c6bce6c --- /dev/null +++ b/libs/multiprecision/test/test_tanh.cpp @@ -0,0 +1,177 @@ +/////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2011. +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ +// +// This work is based on an earlier work: +// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", +// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include <boost/detail/lightweight_test.hpp> +#include <boost/array.hpp> +#include "test.hpp" + +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) +# define TEST_MPF_50 +# define TEST_MPFR_50 +# define TEST_MPFI_50 +# define TEST_BACKEND +# define TEST_CPP_DEC_FLOAT +# define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT + +#ifdef _MSC_VER +#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") +#endif +#ifdef __GNUC__ +#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!" +#endif + +#endif + +#if defined(TEST_MPF_50) +#include <boost/multiprecision/gmp.hpp> +#endif +#if defined(TEST_MPFR_50) +#include <boost/multiprecision/mpfr.hpp> +#endif +#if defined(TEST_MPFI_50) +#include <boost/multiprecision/mpfi.hpp> +#endif +#ifdef TEST_BACKEND +#include <boost/multiprecision/concepts/mp_number_archetypes.hpp> +#endif +#ifdef TEST_CPP_DEC_FLOAT +#include <boost/multiprecision/cpp_dec_float.hpp> +#endif +#ifdef TEST_FLOAT128 +#include <boost/multiprecision/float128.hpp> +#endif +#ifdef TEST_CPP_BIN_FLOAT +#include <boost/multiprecision/cpp_bin_float.hpp> +#endif + +template <class T> +void test() +{ + std::cout << "Testing type: " << typeid(T).name() << std::endl; + static const boost::array<const char*, 51u> data = + {{ + "0.32137338579537729992840434899278935725496267444911714908205287462634251052210833615032073534299473485492692600156322137421801432333125051088723502425037485776412801577568405892077585206768190530859883094571475323319480739773193974206966728764224286661945738178210577326172938196062277314761537881936346874075881338768208490193827960565412814349738654540520356903367084438822830345189856017860672463017", + "0.98628073997374759901559180515206275902189609982907214282364143439537215491113710345866034807991101303183938339561499559327886956280789743287824488269072297413440935381715378233031399015496124706604318545539544610760151756970229801074280545428642122005982857974921606264103186878499260552388713716032507770319550435738767597150644370033277228635793175246197730488375240713357827246166262087899961098648", + "0.99999659728082161113542951278514830809677661658635225532792520501703544628367875293677270218317428676793098034276042396396797568103263882451732810190507733063467333056356770774002596898762991629653041854653269824642873291146068535300466473399592751219449187768646625229500705182676930009096545254478199838990703077597971823456671241141900968900216742636822174010867343154474773040184900973368250708724", + "0.9999999999846483268200051609594321550129159997920576480976206867496512752486590660437091205989616108531910897733432934135954788151766561209164605337537937873588006552145390152387235783207736999759875845070169747521389728857476525437483543080651125798739562649414879487621858466223255239845627205850217328574865852922872737234283038190096982410137471391847466112651349436875974689271288261759782261321", + "0.9999999999999999987314527242099750648171958211319474558707792311593804963057878814487720997303512134007272111464990650500302215773762906820778949397525329109311974741708703536680512747226155618703318739024344621256722269608969415280035337052044425138281821760268269187377517243951584969175035549994883451471918693502477485385682884154959809285569290940740978684264145737164182111806308430952867505356", + "0.9999999999999999999999999980800953069847308586840237590563929855339557065536765765234844240789584487443451033349994294426525006157530320529970966048109743850154174651033567146346966529198814047607015842020039899630884318521543225160212193994911746894335846264878066530266737005606770102869237101848445559941638381625615207320468184414917265299980278164193202897754476112968080358662232635784904263624", + "0.9999999999999999999999999999999999999467800140220866754762922747687784133233134010432889959570821554455247528344437918197518545105332713456859236726383195243056599177018396579766073961540714510399202497404647103138524118065391185503678895059096790300665805648569647351935897874460587855127436472608470703384261586158923066272124216158518232588330799027603391275039552776308636189531809031683723259525", + "0.9999999999999999999999999999999999999999999999999729795912960133359928587562229512337339217831178574875626619226954752643039860388090399659478676726654102118545764943682017611574275691203710439707807193180604656837503862242700430179591666329131728631752773789406064618682879167351725013888294859467540832310795515139677375807407622028485242969471516812171475098378942187864794497220152019202351747432", + "0.9999999999999999999999999999999999999999999999999999999999999997487354938310440650220692519525261552411539996830587326435051159231522052011310872619940247463640019105467860778515384738650636054646551611609757125760437266415865214306396520500343113189907306851418957620080971645943305760132385139924583154317156560414548076370893360020924960120441059315311380109752919823616149973862196846266297710225", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999572050575304159358359221596743379014313563214857593401545331495211888415913558896516895286943572966865708195832339959764445194449615969154689769557903166971249521898883489362426386924297872088925852892350150865941427355319827260914834268754732102528105919811851193667193380541054520023003326858641189063542651960743457613", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998665016733514821204959171836698281165918083005790816030823236096080522860514417075411055633676502699904415882389102672678124683084429720879962355892225321369091298491658349178472270952759208443767848312111069127329160464884932271685986610697222434145553035947750809388321614695213754318979469071722942883", + "0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992372516628147584832950728021842198359205201519966391076994594773600474674435473005118571751514446148292787696117866094991476340344341061706866751156257825144909115117822189019766805825304055482958970512463798453229341693148012213183553546720540880444569824125592343803193018989122964", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920180539244323143459416025663362517256166793900312667214543096238752838226369161775531456005541374878274529461511286842988937830155704737448202558382612829022464635400289328916240002670783433827234852858267621807568393874737879853500598862298495727481132883728328", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998470116425957155787153557938061034698436461173594805292722874130433614266475136267606498346730583487791266503943659174886554170377537630914770998114573340081594827150737005158607830579000912020838690230498119348251553312722575955142752845289", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999462931048083476382670449719737943481963930626760625326765703815392249622625483433043363664396638162612437367800102332819699131841317348173451308570776544874933173719394861336636728378134900422312720743996219523365098", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996546783689748726752364896615532860288057097437452774779386074906915819380531729493071959232887620213723607155628959529584572083388979892309086717786559916703004365603135284141639480887703759", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999593332381019647939423999969519583099837564321056588766269967853479478603122899456262904869063959564274215899007623362296377022418464303752396325625838280378647335", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999122842714667567128203355585346559126606029196080721845292399104475997315344844970601651757832506169948906646054332493537761143729664", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965347272050374435790597917065458623422102880662825928396981295898014081371503733411536311258910851858", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974926240515037403282500845454464621558236030794140169313830052413917", + "0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999667705192725716176070161727364499", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + "1.", + }}; + + T eg = static_cast<T>("5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224173997644923536253500333742937337737673942792595258247094916008735203948165670853233151776611528621199501507984793745085705740029921354786146694029604325421519e-1"); + + unsigned max_err = 0; + for(unsigned k = 0; k < data.size(); k++) + { + const T x = eg + k; + T val = boost::multiprecision::tanh(x * x); + T e = relative_error(val, T(data[k])); + unsigned err = e.template convert_to<unsigned>(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 100); +} + + +int main() +{ +#ifdef TEST_BACKEND + test<boost::multiprecision::number<boost::multiprecision::concepts::number_backend_float_architype> >(); +#endif +#ifdef TEST_MPF_50 + test<boost::multiprecision::mpf_float_50>(); + test<boost::multiprecision::mpf_float_100>(); +#endif +#ifdef TEST_MPFR_50 + test<boost::multiprecision::mpfr_float_50>(); + test<boost::multiprecision::mpfr_float_100>(); +#endif +#ifdef TEST_MPFI_50 + test<boost::multiprecision::mpfi_float_50>(); + test<boost::multiprecision::mpfi_float_100>(); +#endif +#ifdef TEST_CPP_DEC_FLOAT + test<boost::multiprecision::cpp_dec_float_50>(); + test<boost::multiprecision::cpp_dec_float_100>(); +#ifndef SLOW_COMPLER + // Some "peculiar" digit counts which stress our code: + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<65> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<64> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<63> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<62> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<61, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<60, long long> > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<59, long long, std::allocator<void> > > >(); + test<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<58, long long, std::allocator<void> > > >(); +#endif +#endif +#ifdef TEST_FLOAT128 + test<boost::multiprecision::float128>(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test<boost::multiprecision::cpp_bin_float_50>(); +#endif + return boost::report_errors(); +} + + + diff --git a/libs/multiprecision/test/test_test.cpp b/libs/multiprecision/test/test_test.cpp new file mode 100644 index 0000000000..68a277f431 --- /dev/null +++ b/libs/multiprecision/test/test_test.cpp @@ -0,0 +1,89 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2011 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include "test.hpp" +#include <boost/multiprecision/cpp_dec_float.hpp> + +void proc_that_throws() +{ + throw std::runtime_error(""); +} + +int main() +{ + boost::multiprecision::cpp_dec_float_50 a1(1), a2(1), b(3), c(-2); + + BOOST_WARN(a1); + BOOST_WARN(a1 == b); + BOOST_CHECK(a1); + BOOST_CHECK(a1 == b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + boost::multiprecision::cpp_dec_float_50 a_tol = a1 + a1 * 100 * std::numeric_limits<boost::multiprecision::cpp_dec_float_50>::epsilon(); + boost::multiprecision::cpp_dec_float_50 tol = 100 * std::numeric_limits<boost::multiprecision::cpp_dec_float_50>::epsilon(); + + BOOST_CHECK_CLOSE(a1, a_tol, tol * 102); // Passes + BOOST_WARN_CLOSE(a1, a_tol, tol * 98); // fails + BOOST_CHECK_CLOSE(a1, a_tol, tol * 98); // fails + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_CLOSE_FRACTION(a1, a_tol, tol * 1.02); // Passes + BOOST_WARN_CLOSE_FRACTION(a1, a_tol, tol * 0.98); // fails + BOOST_CHECK_CLOSE_FRACTION(a1, a_tol, tol * 0.98); // fails + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_EQUAL(a1, a2); + BOOST_WARN_EQUAL(a1, b); + BOOST_CHECK_EQUAL(a1, b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_NE(a1, b); + BOOST_WARN_NE(a1, a2); + BOOST_CHECK_NE(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_GT(a1, c); + BOOST_WARN_GT(a1, a2); + BOOST_CHECK_GT(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_LT(a1, b); + BOOST_WARN_LT(a1, a2); + BOOST_CHECK_LT(a1, a2); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_GE(a1, a2); + BOOST_CHECK_GE(a1, c); + BOOST_WARN_GE(a1, b); + BOOST_CHECK_GE(a1, b); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_LE(a1, a2); + BOOST_CHECK_LE(a1, b); + BOOST_WARN_LE(a1, c); + BOOST_CHECK_LE(a1, c); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + BOOST_CHECK_THROW(proc_that_throws(), std::runtime_error); + BOOST_CHECK_THROW(a1+b+c, std::runtime_error); + BOOST_CHECK(boost::detail::test_errors() == 1); + --boost::detail::test_errors(); + + return boost::report_errors(); +} + diff --git a/libs/multiprecision/test/ublas_interop/common/init.hpp b/libs/multiprecision/test/ublas_interop/common/init.hpp new file mode 100644 index 0000000000..a9691b4ed0 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/common/init.hpp @@ -0,0 +1,100 @@ +/* + * Copyright (c) 2004 Michael Stevens + * Use, modification and distribution are subject to the + * Boost Software License, Version 1.0. (See accompanying file + * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + */ + +/* + * Default construct test when possible + */ + +template <class E> +struct default_construct +{ + static void test() {} +}; +template <class VC> +struct default_construct<boost::numeric::ublas::vector_container<VC> > +{ + static void test () + { + VC default_constuct; + initialize_vector (default_constuct); + std::cout << "default construct = " << default_constuct << std::endl; + } +}; +template <class MC> +struct default_construct<boost::numeric::ublas::matrix_container<MC> > +{ + static void test () + { + MC default_constuct; + initialize_vector (default_constuct); + std::cout << "default construct = " << default_constuct << std::endl; + } +}; + +/* + * Initialise test values in vector/matrix + */ + +template<class V> +void initialize_vector (V &v) { + typename V::size_type size = v.size (); + for (typename V::size_type i = 0; i < size; ++ i) + v [i] = typename V::value_type ( i + 1.f ); +} + +template<class M> +void initialize_matrix_impl (M &m, ublas::packed_proxy_tag) { + typename M::size_type size1 = m.size1 (); +#ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION + for (typename M::iterator1 i = m.begin1(); i != m.end1(); ++ i) + for (typename M::iterator2 j = i.begin(); j != i.end(); ++ j) + *j = typename M::value_type ( i.index1() * size1 + j.index2() + 1.f ); +#else + for (typename M::iterator1 i = m.begin1(); i != m.end1(); ++ i) + for (typename M::iterator2 j = ublas::begin (i, ublas::iterator1_tag ()); j != ublas::end (i, ublas::iterator1_tag ()); ++ j) + *j = typename M::value_type ( i.index1() * size1 + j.index2() + 1.f ); +#endif +} + +template<class M> +void initialize_matrix_impl (M &m, ublas::sparse_proxy_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) + for (typename M::size_type j = 0; j < size2; ++ j) + m (i, j) = typename M::value_type (i * size1 + j + 1.f); +} + +template<class M> +void initialize_matrix (M &m) { + initialize_matrix_impl (m, typename M::storage_category()); +} + +template<class M> +void initialize_matrix (M &m, ublas::lower_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) { + typename M::size_type j = 0; + for (; j <= i; ++ j) + m (i, j) = i * size1 + j + 1.f; + for (; j < size2; ++ j) + m (i, j) = 0.f; + } +} +template<class M> +void initialize_matrix (M &m, ublas::upper_tag) { + typename M::size_type size1 = m.size1 (); + typename M::size_type size2 = m.size2 (); + for (typename M::size_type i = 0; i < size1; ++ i) { + typename M::size_type j = 0; + for (; j < i; ++ j) + m (i, j) = 0.f; + for (; j < size2; ++ j) + m (i, j) = i * size1 + j + 1.f; + } +} diff --git a/libs/multiprecision/test/ublas_interop/common/testhelper.hpp b/libs/multiprecision/test/ublas_interop/common/testhelper.hpp new file mode 100644 index 0000000000..4fbf9c4d15 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/common/testhelper.hpp @@ -0,0 +1,74 @@ +// Copyright 2008 Gunter Winkler <guwi17@gmx.de> +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + + +#ifndef _HPP_TESTHELPER_ +#define _HPP_TESTHELPER_ + +#include <utility> + +static unsigned _success_counter = 0; +static unsigned _fail_counter = 0; + +static inline +void assertTrue(const char* message, bool condition) { +#ifndef NOMESSAGES + std::cout << message; +#endif + if ( condition ) { + ++ _success_counter; + std::cout << "1\n"; // success + } else { + ++ _fail_counter; + std::cout << "0\n"; // failed + } +} + +template < class T > +void assertEquals(const char* message, T expected, T actual) { +#ifndef NOMESSAGES + std::cout << message; +#endif + if ( expected == actual ) { + ++ _success_counter; + std::cout << "1\n"; // success + } else { + #ifndef NOMESSAGES + std::cout << " expected " << expected << " actual " << actual << " "; + #endif + ++ _fail_counter; + std::cout << "0\n"; // failed + } +} + +static +std::pair<unsigned, unsigned> getResults() { + return std::make_pair(_success_counter, _fail_counter); +} + +template < class M1, class M2 > +bool compare( const boost::numeric::ublas::matrix_expression<M1> & m1, + const boost::numeric::ublas::matrix_expression<M2> & m2 ) { + size_t size1 = (std::min)(m1().size1(), m2().size1()); + size_t size2 = (std::min)(m1().size2(), m2().size2()); + for (size_t i=0; i < size1; ++i) { + for (size_t j=0; j < size2; ++j) { + if ( m1()(i,j) != m2()(i,j) ) return false; + } + } + return true; +} + +template < class M1, class M2 > +bool compare( const boost::numeric::ublas::vector_expression<M1> & m1, + const boost::numeric::ublas::vector_expression<M2> & m2 ) { + size_t size = (std::min)(m1().size(), m2().size()); + for (size_t i=0; i < size; ++i) { + if ( m1()(i) != m2()(i) ) return false; + } + return true; +} + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test1.cpp b/libs/multiprecision/test/ublas_interop/test1.cpp new file mode 100644 index 0000000000..53de790192 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test1.cpp @@ -0,0 +1,20 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test1.hpp b/libs/multiprecision/test/ublas_interop/test1.hpp new file mode 100644 index 0000000000..1bcb024f16 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test1.hpp @@ -0,0 +1,62 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST1_H +#define TEST1_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/vector_proxy.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test11.cpp b/libs/multiprecision/test/ublas_interop/test11.cpp new file mode 100644 index 0000000000..085bd90c39 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test11.cpp @@ -0,0 +1,265 @@ +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. + +#include "test1.hpp" + +// Test vector expression templates +template<class V, int N> +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits<value_type>::real_type real_type; + + template<class VP> + void test_container_with (VP &v1) const { + // Container type tests in addition to expression types + // Insert and erase + v1.insert_element (0, 55); + v1.erase_element (1); + v1.clear (); + } + + template<class VP> + void test_expression_with (VP &v1, VP &v2, VP &v3) const { + // Expression type tests + value_type t; + size_type i; + real_type n; + + // Default Construct + default_construct<VP>::test (); + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector<> (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_vector (v1); + initialize_vector (v2); + project (v1, ublas::range(0,1)) = project (v2, ublas::range(0,1)); + project (v1, ublas::range(0,1)) = project (v2, ublas::slice(0,1,1)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::slice(0,1,2)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::range(0,2)); + std::cout << "v1 = range/slice " << v1 << std::endl; +#endif + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + v3 = ublas::element_prod (v1, v2); + std::cout << "element_prod (v1, v2) = " << v3 << std::endl; + + // Scaling a vector + t = N; + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; + v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); + v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; + v2 = v1 * t; + std::cout << "v1 * value_type(N) = " << v2 << std::endl; + // test interop with integer + v2 = v1 * N; + + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= value_type(N) = " << v1 << std::endl; + // test interop with integer + v1 *= N; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + + // Scalar and Binary vector expression resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v1 = v1 * ublas::inner_prod (v1, v2); + std::cout << "v1 * inner_prod (v1, v2) = " << v1 << std::endl; + } + + void operator () () const { + V v1 (N), v2 (N), v3 (N); + test_expression_with (v1, v2, v3); + test_container_with (v1); + +#ifdef USE_RANGE + ublas::vector_range<V> vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_expression_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice<V> vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_expression_with (vs1, vs2, vs3); +#endif + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_vector<ublas::vector<double, ublas::unbounded_array<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_vector<ublas::vector<double, std::vector<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_BOUNDED_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded" << std::endl; + test_my_vector<ublas::bounded_vector<mp_test_type, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_vector<ublas::bounded_vector<double, 3>, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded" << std::endl; + test_my_vector<ublas::bounded_vector<std::complex<mp_test_type>, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded" << std::endl; + test_my_vector<ublas::bounded_vector<std::complex<double>, 3>, 3> () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test12.cpp b/libs/multiprecision/test/ublas_interop/test12.cpp new file mode 100644 index 0000000000..7059fb9e9b --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test12.cpp @@ -0,0 +1,277 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, 0), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 0), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::matrix<double, ublas::row_major, std::vector<double> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); +#endif +#endif +#endif +#endif + +#ifdef USE_BOUNDED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded" << std::endl; + test_my_matrix_vector<ublas::bounded_vector<mp_test_type, 3>, + ublas::bounded_matrix<mp_test_type, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_matrix_vector<ublas::bounded_vector<double, 3>, + ublas::bounded_matrix<double, 3, 3>, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded" << std::endl; + test_my_matrix_vector<ublas::bounded_vector<std::complex<mp_test_type>, 3>, + ublas::bounded_matrix<std::complex<mp_test_type>, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded" << std::endl; + test_my_matrix_vector<ublas::bounded_vector<std::complex<double>, 3>, + ublas::bounded_matrix<std::complex<double>, 3, 3>, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::vector_of_vector<mp_test_type, ublas::row_major, ublas::bounded_array<ublas::bounded_array<mp_test_type, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::vector_of_vector<double, ublas::row_major, ublas::bounded_array<ublas::bounded_array<double, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<std::complex<mp_test_type>, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::vector_of_vector<std::complex<double>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<std::complex<double>, 3>, 3 + 1> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::vector_of_vector<mp_test_type, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::vector_of_vector<double, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<double> > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<std::complex<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::vector_of_vector<std::complex<double>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<std::complex<double> > > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::vector_of_vector<mp_test_type, ublas::row_major, std::vector<std::vector<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::vector_of_vector<double, ublas::row_major, std::vector<std::vector<double> > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, std::vector<std::vector<std::complex<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::vector_of_vector<std::complex<double>, ublas::row_major, std::vector<std::vector<std::complex<double> > > >, 3> () (); +#endif +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test13.cpp b/libs/multiprecision/test/ublas_interop/test13.cpp new file mode 100644 index 0000000000..d2f803777b --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test13.cpp @@ -0,0 +1,321 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test1.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class VP> + void test_container_with (VP &v1) const { + // Container type tests in addition to expression types + // Insert and erase + v1.insert_element (0,0, 55); + v1.erase_element (1,1); + v1.clear (); + } + + template<class MP> + void test_expression_with (MP &m1, MP &m2, MP &m3) const { + value_type t; + + // Default Construct + default_construct<MP>::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_matrix (m1); + initialize_matrix (m2); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::range(0,1),ublas::range(0,1)); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::slice(0,1,1),ublas::slice(0,1,1)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::slice(0,1,2),ublas::slice(0,1,2)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::range(0,2),ublas::range(0,2)); + std::cout << "m1 = range/slice " << m1 << std::endl; +#endif + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + m3 = ublas::element_prod (m1, m2); + std::cout << "element_prod (m1, m2) = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + + void operator () () const { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_expression_with (m1, m2, m3); + test_container_with (m1); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_expression_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_expression_with (ms1, ms2, ms3); +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::matrix<double, ublas::row_major, std::vector<double> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); +#endif +#endif +#endif +#endif + +#ifdef USE_BOUNDED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded" << std::endl; + test_my_matrix<ublas::bounded_matrix<mp_test_type, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded" << std::endl; + test_my_matrix<ublas::bounded_matrix<double, 3, 3>, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded" << std::endl; + test_my_matrix<ublas::bounded_matrix<std::complex<mp_test_type>, 3, 3>, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded" << std::endl; + test_my_matrix<ublas::bounded_matrix<std::complex<double>, 3, 3>, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<mp_test_type, ublas::row_major, ublas::bounded_array<ublas::bounded_array<mp_test_type, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<double, ublas::row_major, ublas::bounded_array<ublas::bounded_array<double, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<std::complex<mp_test_type>, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<double>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<std::complex<double>, 3>, 3 + 1> >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<mp_test_type, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<double, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<double> > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<std::complex<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<double>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<std::complex<double> > > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<mp_test_type, ublas::row_major, std::vector<std::vector<mp_test_type > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<double, ublas::row_major, std::vector<std::vector<double> > >, 3> () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<mp_test_type>, ublas::row_major, std::vector<std::vector<std::complex<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<std::complex<double>, ublas::row_major, std::vector<std::vector<std::complex<double> > > >, 3> () (); +#endif +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test2.cpp b/libs/multiprecision/test/ublas_interop/test2.cpp new file mode 100644 index 0000000000..0550dc8018 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test2.cpp @@ -0,0 +1,87 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +int main () { +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_1<ublas::vector<mp_test_type>, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_1<ublas::vector<double>, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>" << std::endl; + test_blas_1<ublas::vector<std::complex<mp_test_type> >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>" << std::endl; + test_blas_1<ublas::vector<std::complex<double> >, 3> ().test (); +#endif +#endif + + std::cout << "test_blas_2" << std::endl; + +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_2<ublas::vector<mp_test_type>, ublas::matrix<mp_test_type>, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_2<ublas::vector<double>, ublas::matrix<double>, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>" << std::endl; + test_blas_2<ublas::vector<std::complex<mp_test_type> >, ublas::matrix<std::complex<mp_test_type> >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>" << std::endl; + test_blas_2<ublas::vector<std::complex<double> >, ublas::matrix<std::complex<double> >, 3> ().test (); +#endif +#endif + + std::cout << "test_blas_3" << std::endl; + +#ifdef USE_FLOAT + std::cout << "mp_test_type" << std::endl; + test_blas_3<ublas::matrix<mp_test_type>, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double" << std::endl; + test_blas_3<ublas::matrix<double>, 3> ().test (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>" << std::endl; + test_blas_3<ublas::matrix<std::complex<mp_test_type> >, 3> ().test (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>" << std::endl; + test_blas_3<ublas::matrix<std::complex<double> >, 3> ().test (); +#endif +#endif + + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test2.hpp b/libs/multiprecision/test/ublas_interop/test2.hpp new file mode 100644 index 0000000000..6aca3df9a3 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test2.hpp @@ -0,0 +1,79 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST2_H +#define TEST2_H +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100 4018) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/triangular.hpp> +#include <boost/numeric/ublas/io.hpp> +#include <boost/numeric/ublas/blas.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +template<class V, int N> +struct test_blas_1 { + typedef typename V::value_type value_type; + typedef typename ublas::type_traits<value_type>::real_type real_type; + + void test (); +}; + +template<class V, class M, int N> +struct test_blas_2 { + typedef typename V::value_type value_type; + + void test (); +}; + +template<class M, int N> +struct test_blas_3 { + typedef typename M::value_type value_type; + + void test (); +}; + + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test21.cpp b/libs/multiprecision/test/ublas_interop/test21.cpp new file mode 100644 index 0000000000..252d1f1c10 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test21.cpp @@ -0,0 +1,95 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template<class V, int N> +void test_blas_1<V, N>::test () { + { + value_type t; + real_type n; + V v1 (N), v2 (N); + + // _asum + initialize_vector (v1); + n = ublas::blas_1::asum (v1); + std::cout << "asum (v1) = " << n << std::endl; + + // _amax + initialize_vector (v1); + n = ublas::blas_1::amax (v1); + std::cout << "amax (v1) = " << n << std::endl; + + // _nrm2 + initialize_vector (v1); + n = ublas::blas_1::nrm2 (v1); + std::cout << "nrm2 (v1) = " << n << std::endl; + + // _dot + // _dotu + // _dotc + initialize_vector (v1); + initialize_vector (v2); + t = ublas::blas_1::dot (v1, v2); + std::cout << "dot (v1, v2) = " << t << std::endl; + t = ublas::blas_1::dot (ublas::conj (v1), v2); + std::cout << "dot (conj (v1), v2) = " << t << std::endl; + + // _copy + initialize_vector (v2); + ublas::blas_1::copy (v1, v2); + std::cout << "copy (v1, v2) = " << v1 << std::endl; + + // _swap + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::swap (v1, v2); + std::cout << "swap (v1, v2) = " << v1 << " " << v2 << std::endl; + + // _scal + // csscal + // zdscal + initialize_vector (v1); + ublas::blas_1::scal (v1, value_type (1)); + std::cout << "scal (v1, 1) = " << v1 << std::endl; + + // _axpy + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::axpy (v1, value_type (1), v2); + std::cout << "axpy (v1, 1, v2) = " << v1 << std::endl; + + // _rot + initialize_vector (v1); + initialize_vector (v2); + ublas::blas_1::rot (value_type (1), v1, value_type (1), v2); + std::cout << "rot (1, v1, 1, v2) = " << v1 << " " << v2 << std::endl; + } +} + +#ifdef USE_FLOAT +template struct test_blas_1<ublas::vector<mp_test_type>, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_1<ublas::vector<double>, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_1<ublas::vector<std::complex<mp_test_type> >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_1<ublas::vector<std::complex<double> >, 3>; +#endif +#endif diff --git a/libs/multiprecision/test/ublas_interop/test22.cpp b/libs/multiprecision/test/ublas_interop/test22.cpp new file mode 100644 index 0000000000..297bb06a8f --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test22.cpp @@ -0,0 +1,147 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template<class V, class M, int N> +void test_blas_2<V, M, N>::test () { + { + V v1 (N), v2 (N); + M m (N, N); + + // _t_mv + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, m); + std::cout << "tmv (v1, m) = " << v1 << std::endl; + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, ublas::trans (m)); + std::cout << "tmv (v1, trans (m)) = " << v1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::tmv (v1, ublas::herm (m)); + std::cout << "tmv (v1, herm (m)) = " << v1 << std::endl; +#endif + + // _t_sv + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, m, ublas::lower_tag ()); + std::cout << "tsv (v1, m) = " << v1 << " " << ublas::prod (m, v1) - v2 << std::endl; + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, ublas::trans (m), ublas::lower_tag ()); + std::cout << "tsv (v1, trans (m)) = " << v1 << " " << ublas::prod (ublas::trans (m), v1) - v2 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, ublas::herm (m), ublas::lower_tag ()); + std::cout << "tsv (v1, herm (m)) = " << v1 << " " << ublas::prod (ublas::herm (m), v1) - v2 << std::endl; +#endif + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::upper_tag ()); + ublas::blas_2::tsv (v1, m, ublas::upper_tag ()); + std::cout << "tsv (v1, m) = " << v1 << " " << ublas::prod (m, v1) - v2 << std::endl; + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, ublas::trans (m), ublas::upper_tag ()); + std::cout << "tsv (v1, trans (m)) = " << v1 << " " << ublas::prod (ublas::trans (m), v1) - v2 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m, ublas::lower_tag ()); + ublas::blas_2::tsv (v1, ublas::herm (m), ublas::upper_tag ()); + std::cout << "tsv (v1, herm (m)) = " << v1 << " " << ublas::prod (ublas::herm (m), v1) - v2 << std::endl; +#endif + + // _g_mv + // _s_mv + // _h_mv + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::gmv (v1, value_type (1), value_type (1), m, v2); + std::cout << "gmv (v1, 1, 1, m, v2) = " << v1 << std::endl; + ublas::blas_2::gmv (v1, value_type (1), value_type (1), ublas::trans (m), v2); + std::cout << "gmv (v1, 1, 1, trans (m), v2) = " << v1 << std::endl; +#ifdef USE_STD_COMPLEX + ublas::blas_2::gmv (v1, value_type (1), value_type (1), ublas::herm (m), v2); + std::cout << "gmv (v1, 1, 1, herm (m), v2) = " << v1 << std::endl; +#endif + + // _g_r + // _g_ru + // _g_rc + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::gr (m, value_type (1), v1, v2); + std::cout << "gr (m, 1, v1, v2) = " << m << std::endl; + ublas::blas_2::gr (m, value_type (1), v1, ublas::conj (v2)); + std::cout << "gr (m, 1, v1, conj (v2)) = " << m << std::endl; + + // _s_r + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::sr (m, value_type (1), v1); + std::cout << "sr (m, 1, v1) = " << m << std::endl; + +#ifdef USE_STD_COMPLEX + // _h_r + initialize_vector (v1); + initialize_matrix (m); + ublas::blas_2::hr (m, value_type (1), v1); + std::cout << "hr (m, 1, v1) = " << m << std::endl; +#endif + + // _s_r2 + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::sr2 (m, value_type (1), v1, v2); + std::cout << "sr2 (m, 1, v1, v2) = " << m << std::endl; + +#ifdef USE_STD_COMPLEX + // _h_r2 + initialize_vector (v1); + initialize_vector (v2); + initialize_matrix (m); + ublas::blas_2::hr2 (m, value_type (1), v1, v2); + std::cout << "hr2 (m, 1, v1, v2) = " << m << std::endl; +#endif + } +} + +#ifdef USE_FLOAT +template struct test_blas_2<ublas::vector<mp_test_type>, ublas::matrix<mp_test_type>, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_2<ublas::vector<double>, ublas::matrix<double>, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_2<ublas::vector<std::complex<mp_test_type> >, ublas::matrix<std::complex<mp_test_type> >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_2<ublas::vector<std::complex<double> >, ublas::matrix<std::complex<double> >, 3>; +#endif +#endif diff --git a/libs/multiprecision/test/ublas_interop/test23.cpp b/libs/multiprecision/test/ublas_interop/test23.cpp new file mode 100644 index 0000000000..d56771c25b --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test23.cpp @@ -0,0 +1,208 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test2.hpp" + +template<class M, int N> +void test_blas_3<M, N>::test () { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + + // _t_mm + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, m1); + std::cout << "tmm (m1, 1, m2, m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, ublas::trans (m1)); + std::cout << "tmm (m1, 1, m2, trans (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), m1); + std::cout << "tmm (m1, 1, trans (m2), m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), ublas::trans (m1)); + std::cout << "tmm (m1, 1, trans (m2), trans (m1)) = " << m1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), m2, ublas::herm (m1)); + std::cout << "tmm (m1, 1, m2, herm (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), m1); + std::cout << "tmm (m1, 1, herm (m2), m1) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::trans (m2), ublas::herm (m1)); + std::cout << "tmm (m1, 1, trans (m2), herm (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), ublas::trans (m1)); + std::cout << "tmm (m1, 1, herm (m2), trans (m1)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::tmm (m1, value_type (1), ublas::herm (m2), ublas::herm (m1)); + std::cout << "tmm (m1, 1, herm (m2), herm (m1)) = " << m1 << std::endl; +#endif + + // _t_sm + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + initialize_matrix (m3); + ublas::blas_3::tsm (m1, value_type (1), m2, ublas::lower_tag ()); + std::cout << "tsm (m1, 1, m2) = " << m1 << " " << ublas::prod (m2, m1) - value_type (1) * m3 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::trans (m2), ublas::lower_tag ()); + std::cout << "tsm (m1, 1, trans (m2)) = " << m1 << " " << ublas::prod (ublas::trans (m2), m1) - value_type (1) * m3 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::herm (m2), ublas::lower_tag ()); + std::cout << "tsm (m1, 1, herm (m2)) = " << m1 << " " << ublas::prod (ublas::herm (m2), m1) - value_type (1) * m3 << std::endl; +#endif + initialize_matrix (m1); + initialize_matrix (m2, ublas::upper_tag ()); + ublas::blas_3::tsm (m1, value_type (1), m2, ublas::upper_tag ()); + std::cout << "tsm (m1, 1, m2) = " << m1 << " " << ublas::prod (m2, m1) - value_type (1) * m3 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::trans (m2), ublas::upper_tag ()); + std::cout << "tsm (m1, 1, trans (m2)) = " << m1 << " " << ublas::prod (ublas::trans (m2), m1) - value_type (1) * m3 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2, ublas::lower_tag ()); + ublas::blas_3::tsm (m1, value_type (1), ublas::herm (m2), ublas::upper_tag ()); + std::cout << "tsm (m1, 1, herm (m2)) = " << m1 << " " << ublas::prod (ublas::herm (m2), m1) - value_type (1) * m3 << std::endl; +#endif + + // _g_mm + // _s_mm + // _h_mm + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, m3); + std::cout << "gmm (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), m3); + std::cout << "gmm (m1, 1, 1, trans (m2), m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, m2, trans (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, trans (m2), trans (m3)) = " << m1 << std::endl; +#ifdef USE_STD_COMPLEX + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), m3); + std::cout << "gmm (m1, 1, 1, herm (m2), m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), m2, ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, m2, herm (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::trans (m3)); + std::cout << "gmm (m1, 1, 1, herm (m2), trans (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, trans (m2), herm (m3)) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::gmm (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::herm (m3)); + std::cout << "gmm (m1, 1, 1, herm (m2), herm (m3)) = " << m1 << std::endl; +#endif + + // s_rk + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::srk (m1, value_type (1), value_type (1), m2); + std::cout << "srk (m1, 1, 1, m2) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::srk (m1, value_type (1), value_type (1), ublas::trans (m2)); + std::cout << "srk (m1, 1, 1, trans (m2)) = " << m1 << std::endl; + +#ifdef USE_STD_COMPLEX + // h_rk + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::hrk (m1, value_type (1), value_type (1), m2); + std::cout << "hrk (m1, 1, 1, m2) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + ublas::blas_3::hrk (m1, value_type (1), value_type (1), ublas::herm (m2)); + std::cout << "hrk (m1, 1, 1, herm (m2)) = " << m1 << std::endl; +#endif + + // s_r2k + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::sr2k (m1, value_type (1), value_type (1), m2, m3); + std::cout << "sr2k (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::sr2k (m1, value_type (1), value_type (1), ublas::trans (m2), ublas::trans (m3)); + std::cout << "sr2k (m1, 1, 1, trans (m2), trans (m3)) = " << m1 << std::endl; + +#ifdef USE_STD_COMPLEX + // h_r2k + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::hr2k (m1, value_type (1), value_type (1), m2, m3); + std::cout << "hr2k (m1, 1, 1, m2, m3) = " << m1 << std::endl; + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + ublas::blas_3::hr2k (m1, value_type (1), value_type (1), ublas::herm (m2), ublas::herm (m3)); + std::cout << "hr2k (m1, 1, 1, herm (m2), herm (m3)) = " << m1 << std::endl; +#endif + } +} + +#ifdef USE_FLOAT +template struct test_blas_3<ublas::matrix<mp_test_type>, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_3<ublas::matrix<double>, 3>; +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT +template struct test_blas_3<ublas::matrix<std::complex<mp_test_type> >, 3>; +#endif + +#ifdef USE_DOUBLE +template struct test_blas_3<ublas::matrix<std::complex<double> >, 3>; +#endif +#endif diff --git a/libs/multiprecision/test/ublas_interop/test3.cpp b/libs/multiprecision/test/ublas_interop/test3.cpp new file mode 100644 index 0000000000..fb2b94dadb --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test3.cpp @@ -0,0 +1,20 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test3.hpp b/libs/multiprecision/test/ublas_interop/test3.hpp new file mode 100644 index 0000000000..d38d1d8647 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test3.hpp @@ -0,0 +1,67 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST3_H +#define TEST3_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/vector_proxy.hpp> +#include <boost/numeric/ublas/vector_sparse.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/matrix_sparse.hpp> +#include <boost/numeric/ublas/vector_sparse.hpp> +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#include <boost/numeric/ublas/vector_of_vector.hpp> +#endif +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test31.cpp b/libs/multiprecision/test/ublas_interop/test31.cpp new file mode 100644 index 0000000000..a1484cfdcd --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test31.cpp @@ -0,0 +1,248 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test vector expression templates +template<class V, int N> +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits<value_type>::real_type real_type; + + template<class VP> + void test_with (VP &v1, VP &v2, VP &v3) const { + { + value_type t; + size_type i; + real_type n; + + // Default Construct + default_construct<VP>::test (); + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector<> (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_vector (v1); + initialize_vector (v2); + project (v1, ublas::range(0,1)) = project (v2, ublas::range(0,1)); + project (v1, ublas::range(0,1)) = project (v2, ublas::slice(0,1,1)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::slice(0,1,2)); + project (v1, ublas::slice(2,-1,2)) = project (v2, ublas::range(0,2)); + std::cout << "v1 = range/slice " << v1 << std::endl; +#endif + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + initialize_vector (v3); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + + // Scaling a vector + t = N; + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; + v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); + v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; + v2 = v1 * t; + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + } + } + void operator () () const { + { + V v1 (N, N), v2 (N, N), v3 (N, N); + test_with (v1, v2, v3); + +#ifdef USE_RANGE + ublas::vector_range<V> vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice<V> vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_with (vs1, vs2, vs3); +#endif + } + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + +#ifdef USE_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, map_array" << std::endl; + test_my_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, map_array" << std::endl; + test_my_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, map_array" << std::endl; + test_my_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, map_array" << std::endl; + test_my_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::map" << std::endl; + test_my_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::map" << std::endl; + test_my_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::map" << std::endl; + test_my_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::map" << std::endl; + test_my_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > > , 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed" << std::endl; + test_my_vector<ublas::compressed_vector<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed" << std::endl; + test_my_vector<ublas::compressed_vector<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> compressed" << std::endl; + test_my_vector<ublas::compressed_vector<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> compressed" << std::endl; + test_my_vector<ublas::compressed_vector<std::complex<double> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate" << std::endl; + test_my_vector<ublas::coordinate_vector<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate" << std::endl; + test_my_vector<ublas::coordinate_vector<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> coordinate" << std::endl; + test_my_vector<ublas::coordinate_vector<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> coordinate" << std::endl; + test_my_vector<ublas::coordinate_vector<std::complex<double> >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test32.cpp b/libs/multiprecision/test/ublas_interop/test32.cpp new file mode 100644 index 0000000000..7240b4ce6f --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test32.cpp @@ -0,0 +1,324 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N, N), v2 (N, N); + M m1 (N, N, N * N); + + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, 0), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 0), mc2 (m1, N - 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_SPARSE_MATRIX +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, + ublas::mapped_matrix<mp_test_type, ublas::row_major, ublas::map_array<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, + ublas::mapped_matrix<double, ublas::row_major, ublas::map_array<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, + ublas::mapped_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, + ublas::mapped_matrix<std::complex<double>, ublas::row_major, ublas::map_array<std::size_t, std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, + ublas::mapped_matrix<mp_test_type, ublas::row_major, std::map<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, + ublas::mapped_matrix<double, ublas::row_major, std::map<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, + ublas::mapped_matrix<std::complex<mp_test_type>, ublas::row_major, std::map<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, + ublas::mapped_matrix<std::complex<double>, ublas::row_major, std::map<std::size_t, std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_SPARSE_VECTOR_OF_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, + ublas::mapped_vector<mp_test_type, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, + ublas::mapped_vector<double, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, double> > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, + ublas::mapped_vector<std::complex<mp_test_type>, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, std::complex<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>,mapped_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, + ublas::mapped_vector<std::complex<double>, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, std::complex<double> > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, + ublas::mapped_vector<mp_test_type, ublas::row_major, std::map<std::size_t, std::map<std::size_t, mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, + ublas::mapped_vector<double, ublas::row_major, std::map<std::size_t, std::map<std::size_t, double> > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, + ublas::mapped_vector<std::complex<mp_test_type>, ublas::row_major, std::map<std::size_t, std::map<std::size_t, std::complex<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, mapped_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, + ublas::mapped_vector<std::complex<double>, ublas::row_major, std::map<std::size_t, std::map<std::size_t, std::complex<double> > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, + ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, + ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, ublas::map_array<std::size_t, ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, + ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, + ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, ublas::map_array<std::size_t, ublas::mapped_vector<double, ublas::map_array<std::size_t, double> > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, + ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, + ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, ublas::map_array<std::size_t, ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, + ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, + ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, ublas::map_array<std::size_t, ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > > > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, + ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, + ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, std::map<std::size_t, ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, + ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::vector<ublas::mapped_vector<double, std::map<std::size_t, double> > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, + ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, std::map<std::size_t, ublas::mapped_vector<double, std::map<std::size_t, double> > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, + ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, + ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, std::map<std::size_t, ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, + ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > > > >, 3 > () (); + test_my_matrix_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, + ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, std::map<std::size_t, ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > > > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed" << std::endl; + test_my_matrix_vector<ublas::compressed_vector<mp_test_type>, + ublas::compressed_matrix<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed" << std::endl; + test_my_matrix_vector<ublas::compressed_vector<double>, + ublas::compressed_matrix<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> compressed" << std::endl; + test_my_matrix_vector<ublas::compressed_vector<std::complex<mp_test_type> >, + ublas::compressed_matrix<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> compressed" << std::endl; + test_my_matrix_vector<ublas::compressed_vector<std::complex<double> >, + ublas::compressed_matrix<std::complex<double> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate" << std::endl; + test_my_matrix_vector<ublas::coordinate_vector<mp_test_type>, + ublas::coordinate_matrix<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate" << std::endl; + test_my_matrix_vector<ublas::coordinate_vector<double>, + ublas::coordinate_matrix<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> coordinate" << std::endl; + test_my_matrix_vector<ublas::coordinate_vector<std::complex<mp_test_type> >, + ublas::coordinate_matrix<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> coordinate" << std::endl; + test_my_matrix_vector<ublas::coordinate_vector<std::complex<double> >, + ublas::coordinate_matrix<std::complex<double> >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test33.cpp b/libs/multiprecision/test/ublas_interop/test33.cpp new file mode 100644 index 0000000000..46d735194b --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test33.cpp @@ -0,0 +1,347 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test3.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class MP> + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct<MP>::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + +#ifndef BOOST_NO_FUNCTION_TEMPLATE_ORDERING + // Project range and slice + initialize_matrix (m1); + initialize_matrix (m2); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::range(0,1),ublas::range(0,1)); + project (m1, ublas::range(0,1),ublas::range(0,1)) = project (m2, ublas::slice(0,1,1),ublas::slice(0,1,1)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::slice(0,1,2),ublas::slice(0,1,2)); + project (m1, ublas::slice(2,-1,2),ublas::slice(2,-1,2)) = project (m2, ublas::range(0,2),ublas::range(0,2)); + std::cout << "m1 = range/slice " << m1 << std::endl; +#endif + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + initialize_matrix (m3); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N, N * N), m2 (N, N, N * N), m3 (N, N, N * N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_SPARSE_MATRIX +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_matrix map_array" << std::endl; + test_my_matrix<ublas::mapped_matrix<mp_test_type, ublas::row_major, ublas::map_array<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_matrix map_array" << std::endl; + test_my_matrix<ublas::mapped_matrix<double, ublas::row_major, ublas::map_array<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_matrix map_array" << std::endl; + test_my_matrix<ublas::mapped_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, mapped_matrix map_array" << std::endl; + test_my_matrix<ublas::mapped_matrix<std::complex<double>, ublas::row_major, ublas::map_array<std::size_t, std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_matrix std::map" << std::endl; + test_my_matrix<ublas::mapped_matrix<mp_test_type, ublas::row_major, std::map<std::size_t, mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_matrix std::map" << std::endl; + test_my_matrix<ublas::mapped_matrix<double, ublas::row_major, std::map<std::size_t, double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_matrix std::map" << std::endl; + test_my_matrix<ublas::mapped_matrix<std::complex<mp_test_type>, ublas::row_major, std::map<std::size_t, std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, mapped_matrix std::map" << std::endl; + test_my_matrix<ublas::mapped_matrix<std::complex<double>, ublas::row_major, std::map<std::size_t, std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_SPARSE_VECTOR_OF_SPARSE_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<mp_test_type, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<double, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, double> > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_vector_of_mapped_vector map_array" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<std::complex<mp_test_type>, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, std::complex<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, mapped_vector_of_mapped_vectormap_array" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<std::complex<double>, ublas::row_major, ublas::map_array<std::size_t, ublas::map_array<std::size_t, std::complex<double> > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<mp_test_type, ublas::row_major, std::map<std::size_t, std::map<std::size_t, mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<double, ublas::row_major, std::map<std::size_t, std::map<std::size_t, double> > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<std::complex<mp_test_type>, ublas::row_major, std::map<std::size_t, std::map<std::size_t, std::complex<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, mapped_vector_of_mapped_vector std::map" << std::endl; + test_my_matrix<ublas::mapped_vector_of_mapped_vector<std::complex<double>, ublas::row_major, std::map<std::size_t, std::map<std::size_t, std::complex<double> > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_GENERALIZED_VECTOR_OF_VECTOR +#ifdef USE_MAP_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type,generalized_vector_of_vector map_array" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> >, ublas::map_array<std::size_t, ublas::mapped_vector<mp_test_type, ublas::map_array<std::size_t, mp_test_type> > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<double, ublas::map_array<std::size_t, double> >, ublas::map_array<std::size_t, ublas::mapped_vector<double, ublas::map_array<std::size_t, double> > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > >, ublas::map_array<std::size_t, ublas::mapped_vector<std::complex<mp_test_type>, ublas::map_array<std::size_t, std::complex<mp_test_type> > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, generalized_vector_of_vector map_array" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > >, ublas::map_array<std::size_t, ublas::mapped_vector<std::complex<double>, ublas::map_array<std::size_t, std::complex<double> > > > > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_MAP +#ifdef USE_FLOAT + std::cout << "mp_test_type, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<mp_test_type, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> >, std::map<std::size_t, ublas::mapped_vector<mp_test_type, std::map<std::size_t, mp_test_type> > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::vector<ublas::mapped_vector<double, std::map<std::size_t, double> > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<double, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<double, std::map<std::size_t, double> >, std::map<std::size_t, ublas::mapped_vector<double, std::map<std::size_t, double> > > > >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<mp_test_type>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > >, std::map<std::size_t, ublas::mapped_vector<std::complex<mp_test_type>, std::map<std::size_t, std::complex<mp_test_type> > > > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, generalized_vector_of_vector std::map" << std::endl; + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > > > >, 3 > () (); + test_my_matrix<ublas::generalized_vector_of_vector<std::complex<double>, ublas::row_major, ublas::mapped_vector<ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > >, std::map<std::size_t, ublas::mapped_vector<std::complex<double>, std::map<std::size_t, std::complex<double> > > > > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_COMPRESSED_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type compressed_matrix" << std::endl; + test_my_matrix<ublas::compressed_matrix<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double compressed_matrix" << std::endl; + test_my_matrix<ublas::compressed_matrix<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> compressed_matrix" << std::endl; + test_my_matrix<ublas::compressed_matrix<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> compressed_matrix" << std::endl; + test_my_matrix<ublas::compressed_matrix<std::complex<double> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_COORDINATE_MATRIX +#ifdef USE_FLOAT + std::cout << "mp_test_type coordinate_matrix" << std::endl; + test_my_matrix<ublas::coordinate_matrix<mp_test_type>, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double coordinate_matrix" << std::endl; + test_my_matrix<ublas::coordinate_matrix<double>, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type> coordinate_matrix" << std::endl; + test_my_matrix<ublas::coordinate_matrix<std::complex<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double> coordinate_matrix" << std::endl; + test_my_matrix<ublas::coordinate_matrix<std::complex<double> >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test4.cpp b/libs/multiprecision/test/ublas_interop/test4.cpp new file mode 100644 index 0000000000..bf5816f5e7 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test4.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test4.hpp b/libs/multiprecision/test/ublas_interop/test4.hpp new file mode 100644 index 0000000000..d81e5a28d0 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test4.hpp @@ -0,0 +1,68 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST4_H +#define TEST4_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/banded.hpp> +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +//#define USE_BANDED +#define USE_DIAGONAL + + +void test_matrix_vector (); +void test_matrix (); + + +// FIXME slice are failing in assignment to zero elements +#undef USE_SLICE + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test42.cpp b/libs/multiprecision/test/ublas_interop/test42.cpp new file mode 100644 index 0000000000..325d8094dc --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test42.cpp @@ -0,0 +1,361 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { +#ifndef USE_DIAGONAL + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v1 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; +#endif + } + } + void operator () () const { + { + V v1 (N), v2 (N); +#ifdef USE_BANDED + M m1 (N, N, 1, 1); +#endif +#ifdef USE_DIAGONAL + M m1 (N, N); +#endif + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, 1), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 1), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { +#ifdef USE_BANDED + V v1 (N), v2 (N); + M m1 (N, N, 1, 1); + ublas::banded_adaptor<M> bam1 (m1, 1, 1); + test_with (v1, v2, bam1); + + ublas::matrix_row<ublas::banded_adaptor<M> > mr1 (bam1, 1), mr2 (bam1, 1); + test_with (mr1, mr2, bam1); + + ublas::matrix_column<ublas::banded_adaptor<M> > mc1 (bam1, 1), mc2 (bam1, 1); + test_with (mc1, mc2, bam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<ublas::banded_adaptor<M> > mvr1 (bam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (bam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, bam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<ublas::banded_adaptor<M> > mvs1 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, bam1); +#endif +#endif +#ifdef USE_DIAGONAL + V v1 (N), v2 (N); + M m1 (N, N); + ublas::diagonal_adaptor<M> dam1 (m1); + test_with (v1, v2, dam1); + + ublas::matrix_row<ublas::diagonal_adaptor<M> > mr1 (dam1, 1), mr2 (dam1, 1); + test_with (mr1, mr2, dam1); + + ublas::matrix_column<ublas::diagonal_adaptor<M> > mc1 (dam1, 1), mc2 (dam1, 1); + test_with (mc1, mc2, dam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<ublas::diagonal_adaptor<M> > mvr1 (dam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (dam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, dam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<ublas::diagonal_adaptor<M> > mvs1 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, dam1); +#endif +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BANDED +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::banded_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::banded_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::banded_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::banded_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::banded_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::banded_matrix<double, ublas::row_major, std::vector<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::banded_matrix<double, ublas::row_major, std::vector<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::banded_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif +#endif + +#ifdef USE_DIAGONAL +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::diagonal_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::diagonal_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::diagonal_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::diagonal_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::diagonal_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::diagonal_matrix<double, ublas::row_major, std::vector<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::diagonal_matrix<double, ublas::row_major, std::vector<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::diagonal_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test43.cpp b/libs/multiprecision/test/ublas_interop/test43.cpp new file mode 100644 index 0000000000..82682c9765 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test43.cpp @@ -0,0 +1,326 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test4.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class MP> + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct<MP>::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + // Banded times banded isn't banded + std::cout << "prod (m1, m2) = " << ublas::prod (m1, m2) << std::endl; + } + } + void operator () () const { + { +#ifdef USE_BANDED + M m1 (N, N, 1, 1), m2 (N, N, 1, 1), m3 (N, N, 1, 1); +#endif +#ifdef USE_DIAGONAL + M m1 (N, N), m2 (N, N), m3 (N, N); +#endif + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { +#ifdef USE_BANDED + M m1 (N, N, 1, 1), m2 (N, N, 1, 1), m3 (N, N, 1, 1); + ublas::banded_adaptor<M> bam1 (m1, 1, 1), bam2 (m2, 1, 1), bam3 (m3, 1, 1); + test_with (bam1, bam2, bam3); + +#ifdef USE_RANGE + ublas::matrix_range<ublas::banded_adaptor<M> > mr1 (bam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (bam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (bam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<ublas::banded_adaptor<M> > ms1 (bam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (bam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (bam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif +#endif +#ifdef USE_DIAGONAL + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::diagonal_adaptor<M> dam1 (m1), dam2 (m2), dam3 (m3); + test_with (dam1, dam2, dam3); + +#ifdef USE_RANGE + ublas::matrix_range<ublas::diagonal_adaptor<M> > mr1 (dam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (dam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (dam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<ublas::diagonal_adaptor<M> > ms1 (dam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (dam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (dam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif +#endif + } +#endif + + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BANDED +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::banded_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::banded_matrix<double, ublas::row_major, std::vector<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::banded_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +#endif + +#ifdef USE_DIAGONAL +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<double, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<mp_test_type, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<double, ublas::row_major, ublas::unbounded_array<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<double>, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::diagonal_matrix<mp_test_type, ublas::row_major, std::vector<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::diagonal_matrix<double, ublas::row_major, std::vector<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<mp_test_type>, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::diagonal_matrix<std::complex<double>, ublas::row_major, std::vector<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test5.cpp b/libs/multiprecision/test/ublas_interop/test5.cpp new file mode 100644 index 0000000000..548cd60334 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test5.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test5.hpp b/libs/multiprecision/test/ublas_interop/test5.hpp new file mode 100644 index 0000000000..d867dc5f66 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test5.hpp @@ -0,0 +1,64 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST5_H +#define TEST5_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/triangular.hpp> +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_matrix_vector (); +void test_matrix (); + + +// FIXME slice are failing in assignment to zero elements +#undef USE_SLICE + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test52.cpp b/libs/multiprecision/test/ublas_interop/test52.cpp new file mode 100644 index 0000000000..9e13dfde7a --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test52.cpp @@ -0,0 +1,214 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v2 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, N - 1), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 0), mc2 (m1, 0); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { + V v1 (N), v2 (N); + M m1 (N, N); + ublas::triangular_adaptor<M> tam1 (m1); + test_with (v1, v2, tam1); + + ublas::matrix_row<ublas::triangular_adaptor<M> > mr1 (tam1, N - 1), mr2 (tam1, N - 1); + test_with (mr1, mr2, tam1); + + ublas::matrix_column<ublas::triangular_adaptor<M> > mc1 (tam1, 0), mc2 (tam1, 0); + test_with (mc1, mc2, tam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<ublas::triangular_adaptor<M> > mvr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (tam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, tam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<ublas::triangular_adaptor<M> > mvs1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, tam1); +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::triangular_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (0); + + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test53.cpp b/libs/multiprecision/test/ublas_interop/test53.cpp new file mode 100644 index 0000000000..041be1f5b7 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test53.cpp @@ -0,0 +1,223 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test5.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class MP> + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct<MP>::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m2 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + // Transpose of a triangular isn't triangular of the same kind + std::cout << "trans (m1) = " << ublas::trans (m1) << std::endl; + + // Hermitian + initialize_matrix (m1); + // Hermitian of a triangular isn't hermitian of the same kind + std::cout << "herm (m1) = " << ublas::herm (m1) << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::triangular_adaptor<M> tam1 (m1), tam2 (m2), tam3 (m3); + test_with (tam1, tam2, tam3); + +#ifdef USE_RANGE + ublas::matrix_range<ublas::triangular_adaptor<M> > mr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (tam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (tam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<ublas::triangular_adaptor<M> > ms1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (tam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (tam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::triangular_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::triangular_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE +std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::triangular_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test6.cpp b/libs/multiprecision/test/ublas_interop/test6.cpp new file mode 100644 index 0000000000..61a5c3105e --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test6.cpp @@ -0,0 +1,19 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +int main () { + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test6.hpp b/libs/multiprecision/test/ublas_interop/test6.hpp new file mode 100644 index 0000000000..e84c2a0549 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test6.hpp @@ -0,0 +1,62 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST6_H +#define TEST6_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996 4127 4100) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_BOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/symmetric.hpp> +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_matrix_vector (); +void test_matrix (); + + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test62.cpp b/libs/multiprecision/test/ublas_interop/test62.cpp new file mode 100644 index 0000000000..a7529d2940 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test62.cpp @@ -0,0 +1,218 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v2 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v2 << std::endl; + v2 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v2 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + v1 (0) = 0; + v1 (N - 1) = 0; + v2 (0) = 0; + v2 (N - 1) = 0; + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, N - 1), mr2 (m1, N - 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 0), mc2 (m1, 0); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } + + void operator () (int) const { +#ifdef USE_ADAPTOR + { + V v1 (N), v2 (N); + M m1 (N, N); + ublas::symmetric_adaptor<M> tam1 (m1); + test_with (v1, v2, tam1); + + ublas::matrix_row<ublas::symmetric_adaptor<M> > mr1 (tam1, N - 1), mr2 (tam1, N - 1); + test_with (mr1, mr2, tam1); + + ublas::matrix_column<ublas::symmetric_adaptor<M> > mc1 (tam1, 0), mc2 (tam1, 0); + test_with (mc1, mc2, tam1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<ublas::symmetric_adaptor<M> > mvr1 (tam1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (tam1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, tam1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<ublas::symmetric_adaptor<M> > mvs1 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (tam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, tam1); +#endif + } +#endif + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::bounded_array<mp_test_type, 3> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::bounded_array<double, 3> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::bounded_array<std::complex<mp_test_type>, 3> >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::bounded_array<std::complex<double>, 3> >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, ublas::unbounded_array<mp_test_type> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, ublas::unbounded_array<double> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, ublas::unbounded_array<std::complex<mp_test_type> > >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, ublas::unbounded_array<std::complex<double> > >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3> () (); + test_my_matrix_vector<ublas::vector<mp_test_type, std::vector<mp_test_type> >, + ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3> () (); + test_my_matrix_vector<ublas::vector<double, std::vector<double> >, + ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3> () (0); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<mp_test_type>, std::vector<std::complex<mp_test_type> > >, + ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3> () (0); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3> () (); + test_my_matrix_vector<ublas::vector<std::complex<double>, std::vector<std::complex<double> > >, + ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3> () (0); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test63.cpp b/libs/multiprecision/test/ublas_interop/test63.cpp new file mode 100644 index 0000000000..d36f09c1d6 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test63.cpp @@ -0,0 +1,223 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test6.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class MP> + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Default Construct + default_construct<MP>::test (); + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m1 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + +#ifdef USE_ADAPTOR + { + M m1 (N, N), m2 (N, N), m3 (N, N); + ublas::symmetric_adaptor<M> sam1 (m1), sam2 (m2), sam3 (m3); + test_with (sam1, sam2, sam3); + +#ifdef USE_RANGE + ublas::matrix_range<ublas::symmetric_adaptor<M> > mr1 (sam1, ublas::range (0, N), ublas::range (0, N)), + mr2 (sam2, ublas::range (0, N), ublas::range (0, N)), + mr3 (sam3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<ublas::symmetric_adaptor<M> > ms1 (sam1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (sam2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (sam3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } +#endif + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, bounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::bounded_array<mp_test_type, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, bounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::bounded_array<double, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<mp_test_type>, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, bounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::bounded_array<std::complex<double>, 3 * 3> >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "mp_test_type, unbounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, ublas::unbounded_array<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, unbounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, ublas::unbounded_array<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, ublas::unbounded_array<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "mp_test_type, std::vector" << std::endl; + test_my_matrix<ublas::symmetric_matrix<mp_test_type, ublas::lower, ublas::row_major, std::vector<mp_test_type> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "double, std::vector" << std::endl; + test_my_matrix<ublas::symmetric_matrix<double, ublas::lower, ublas::row_major, std::vector<double> >, 3 > () (); +#endif + +#ifdef USE_STD_COMPLEX +#ifdef USE_FLOAT + std::cout << "std::complex<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<mp_test_type>, ublas::lower, ublas::row_major, std::vector<std::complex<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "std::complex<double>, std::vector" << std::endl; + test_my_matrix<ublas::symmetric_matrix<std::complex<double>, ublas::lower, ublas::row_major, std::vector<std::complex<double> > >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test7.cpp b/libs/multiprecision/test/ublas_interop/test7.cpp new file mode 100644 index 0000000000..f564031cef --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test7.cpp @@ -0,0 +1,31 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include <iostream> + +#include <boost/numeric/interval.hpp> +#include <boost/numeric/interval/io.hpp> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/io.hpp> + +#include "test7.hpp" + +// this testcase requires fix of task #2473 + +int main () { + test_vector (); + test_matrix_vector (); + test_matrix (); + return 0; +} diff --git a/libs/multiprecision/test/ublas_interop/test7.hpp b/libs/multiprecision/test/ublas_interop/test7.hpp new file mode 100644 index 0000000000..65325a2619 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test7.hpp @@ -0,0 +1,66 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#ifndef TEST7_H +#define TEST7_H + +#ifdef _MSC_VER +# pragma warning(disable:4800 4996) +#endif + +#include <boost/multiprecision/cpp_dec_float.hpp> + +#ifdef TEST_ET +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_on> mp_test_type; +#else +typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off> mp_test_type; +#endif +//typedef double mp_test_type; + +#define USE_RANGE +#define USE_SLICE +#define USE_FLOAT +#define USE_UNBOUNDED_ARRAY +#define USE_BOUNDED_ARRAY +#define USE_STD_VECTOR +#define USE_BOUNDED_VECTOR USE_MATRIX +#define USE_UNBOUNDED_ARRAY +#define USE_MAP_ARRAY +#define USE_STD_MAP +#define USE_MAPPED_VECTOR +#define USE_COMPRESSED_VECTOR +#define USE_COORDINATE_VECTOR +#define USE_MAPPED_MATRIX +#define USE_COMPRESSED_MATRIX +#define USE_COORDINATE_MATRIX + +#include <iostream> + +#include <boost/numeric/interval.hpp> +#include <boost/numeric/interval/io.hpp> + +#include <boost/numeric/ublas/vector.hpp> +#include <boost/numeric/ublas/vector_proxy.hpp> +#include <boost/numeric/ublas/matrix.hpp> +#include <boost/numeric/ublas/matrix_proxy.hpp> +#include <boost/numeric/ublas/io.hpp> + +namespace ublas = boost::numeric::ublas; + +#include "common/init.hpp" + +void test_vector (); +void test_matrix_vector (); +void test_matrix (); + + +#endif diff --git a/libs/multiprecision/test/ublas_interop/test71.cpp b/libs/multiprecision/test/ublas_interop/test71.cpp new file mode 100644 index 0000000000..5fc6c2b0f4 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test71.cpp @@ -0,0 +1,174 @@ +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +// +// This file fails to compile - appears to be a known uBlas issue :-( +// + +#include "test7.hpp" + +// Test vector expression templates +template<class V, int N> +struct test_my_vector { + typedef typename V::value_type value_type; + typedef typename V::size_type size_type; + typedef typename ublas::type_traits<value_type>::real_type real_type; + + template<class VP> + void test_with (VP &v1, VP &v2, VP &v3) const { + { + value_type t; + size_type i; + real_type n; + + // Copy and swap + initialize_vector (v1); + initialize_vector (v2); + v1 = v2; + std::cout << "v1 = v2 = " << v1 << std::endl; + v1.assign_temporary (v2); + std::cout << "v1.assign_temporary (v2) = " << v1 << std::endl; + v1.swap (v2); + std::cout << "v1.swap (v2) = " << v1 << " " << v2 << std::endl; + + // Zero assignment + v1 = ublas::zero_vector<value_type> (v1.size ()); + std::cout << "v1.zero_vector = " << v1 << std::endl; + v1 = v2; + + // Unary vector operations resulting in a vector + initialize_vector (v1); + v2 = - v1; + std::cout << "- v1 = " << v2 << std::endl; + v2 = ublas::conj (v1); + std::cout << "conj (v1) = " << v2 << std::endl; + + // Binary vector operations resulting in a vector + initialize_vector (v1); + initialize_vector (v2); + v3 = v1 + v2; + std::cout << "v1 + v2 = " << v3 << std::endl; + + v3 = v1 - v2; + std::cout << "v1 - v2 = " << v3 << std::endl; + + // Scaling a vector + t = value_type (N); + initialize_vector (v1); + v2 = value_type (1.) * v1; + std::cout << "1. * v1 = " << v2 << std::endl; +// v2 = t * v1; + std::cout << "N * v1 = " << v2 << std::endl; + initialize_vector (v1); +// v2 = v1 * value_type (1.); + std::cout << "v1 * 1. = " << v2 << std::endl; +// v2 = v1 * t; + std::cout << "v1 * N = " << v2 << std::endl; + + // Some assignments + initialize_vector (v1); + initialize_vector (v2); + v2 += v1; + std::cout << "v2 += v1 = " << v2 << std::endl; + v2 -= v1; + std::cout << "v2 -= v1 = " << v2 << std::endl; + v2 = v2 + v1; + std::cout << "v2 = v2 + v1 = " << v2 << std::endl; + v2 = v2 - v1; + std::cout << "v2 = v2 - v1 = " << v2 << std::endl; + v1 *= value_type (1.); + std::cout << "v1 *= 1. = " << v1 << std::endl; + v1 *= t; + std::cout << "v1 *= N = " << v1 << std::endl; + + // Unary vector operations resulting in a scalar + initialize_vector (v1); + t = ublas::sum (v1); + std::cout << "sum (v1) = " << t << std::endl; + n = ublas::norm_1 (v1); + std::cout << "norm_1 (v1) = " << n << std::endl; + n = ublas::norm_2 (v1); + std::cout << "norm_2 (v1) = " << n << std::endl; + n = ublas::norm_inf (v1); + std::cout << "norm_inf (v1) = " << n << std::endl; + + i = ublas::index_norm_inf (v1); + std::cout << "index_norm_inf (v1) = " << i << std::endl; + + // Binary vector operations resulting in a scalar + initialize_vector (v1); + initialize_vector (v2); + t = ublas::inner_prod (v1, v2); + std::cout << "inner_prod (v1, v2) = " << t << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N), v3 (N); + test_with (v1, v2, v3); + +#ifdef USE_RANGE + ublas::vector_range<V> vr1 (v1, ublas::range (0, N)), + vr2 (v2, ublas::range (0, N)), + vr3 (v3, ublas::range (0, N)); + test_with (vr1, vr2, vr3); +#endif + +#ifdef USE_SLICE + ublas::vector_slice<V> vs1 (v1, ublas::slice (0, 1, N)), + vs2 (v2, ublas::slice (0, 1, N)), + vs3 (v3, ublas::slice (0, 1, N)); + test_with (vs1, vs2, vs3); +#endif + } + } +}; + +// Test vector +void test_vector () { + std::cout << "test_vector" << std::endl; + +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, bounded_array" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, bounded_array" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<double>, ublas::bounded_array<boost::numeric::interval<double>, 3> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, unbounded_array" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::unbounded_array<boost::numeric::interval<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, unbounded_array" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<double>, ublas::unbounded_array<boost::numeric::interval<double> > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, std::vector" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<mp_test_type>, std::vector<boost::numeric::interval<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, std::vector" << std::endl; + test_my_vector<ublas::vector<boost::numeric::interval<double>, std::vector<boost::numeric::interval<double> > >, 3 > () (); +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test72.cpp b/libs/multiprecision/test/ublas_interop/test72.cpp new file mode 100644 index 0000000000..07b1d8a07b --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test72.cpp @@ -0,0 +1,165 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test7.hpp" + +// Test matrix & vector expression templates +template<class V, class M, int N> +struct test_my_matrix_vector { + typedef typename V::value_type value_type; + + template<class VP, class MP> + void test_with (VP &v1, VP &v2, MP &m1) const { + { + // Rows and columns + initialize_matrix (m1); + for (int i = 0; i < N; ++ i) { + v1 = ublas::row (m1, i); + std::cout << "row (m, " << i << ") = " << v1 << std::endl; + v1 = ublas::column (m1, i); + std::cout << "column (m, " << i << ") = " << v1 << std::endl; + } + + // Outer product + initialize_vector (v1); + initialize_vector (v2); + m1 = ublas::outer_prod (v1, v2); + std::cout << "outer_prod (v1, v2) = " << m1 << std::endl; + + // Matrix vector product + initialize_matrix (m1); + initialize_vector (v1); + v2 = ublas::prod (m1, v1); + std::cout << "prod (m1, v1) = " << v2 << std::endl; + v2 = ublas::prod (v1, m1); + std::cout << "prod (v1, m1) = " << v2 << std::endl; + } + } + void operator () () const { + { + V v1 (N), v2 (N); + M m1 (N, N); + test_with (v1, v2, m1); + + ublas::matrix_row<M> mr1 (m1, 0), mr2 (m1, 1); + test_with (mr1, mr2, m1); + + ublas::matrix_column<M> mc1 (m1, 0), mc2 (m1, 1); + test_with (mc1, mc2, m1); + +#ifdef USE_RANGE + ublas::matrix_vector_range<M> mvr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mvr2 (m1, ublas::range (0, N), ublas::range (0, N)); + test_with (mvr1, mvr2, m1); +#endif + +#ifdef USE_SLICE + ublas::matrix_vector_slice<M> mvs1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + mvs2 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (mvs1, mvs2, m1); +#endif + } + } +}; + +// Test matrix & vector +void test_matrix_vector () { + std::cout << "test_matrix_vector" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3> >, + ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3 * 3> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, ublas::bounded_array<boost::numeric::interval<double>, 3> >, + ublas::matrix<boost::numeric::interval<double>, ublas::row_major, ublas::bounded_array<boost::numeric::interval<double>, 3 * 3> >, 3> () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::unbounded_array<boost::numeric::interval<mp_test_type> > >, + ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::unbounded_array<boost::numeric::interval<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, ublas::unbounded_array<boost::numeric::interval<double> > >, + ublas::matrix<boost::numeric::interval<double>, ublas::row_major, ublas::unbounded_array<boost::numeric::interval<double> > >, 3> () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, std::vector<boost::numeric::interval<mp_test_type> > >, + ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, std::vector<boost::numeric::interval<mp_test_type> > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, std::vector<boost::numeric::interval<double> > >, + ublas::matrix<boost::numeric::interval<double>, ublas::row_major, std::vector<boost::numeric::interval<double> > >, 3> () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3> >, + ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3>, 3 + 1> >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, bounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, ublas::bounded_array<boost::numeric::interval<double>, 3> >, + ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<boost::numeric::interval<double>, 3>, 3 + 1> >, 3> () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, ublas::unbounded_array<boost::numeric::interval<mp_test_type> > >, + ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<boost::numeric::interval<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, unbounded_array" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, ublas::unbounded_array<boost::numeric::interval<double> > >, + ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<boost::numeric::interval<double> > > >, 3> () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<mp_test_type>, std::vector<boost::numeric::interval<mp_test_type> > >, + ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, std::vector<std::vector<boost::numeric::interval<mp_test_type> > > >, 3> () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, std::vector" << std::endl; + test_my_matrix_vector<ublas::vector<boost::numeric::interval<double>, std::vector<boost::numeric::interval<double> > >, + ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, std::vector<std::vector<boost::numeric::interval<double> > > >, 3> () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/test/ublas_interop/test73.cpp b/libs/multiprecision/test/ublas_interop/test73.cpp new file mode 100644 index 0000000000..60b10bb764 --- /dev/null +++ b/libs/multiprecision/test/ublas_interop/test73.cpp @@ -0,0 +1,202 @@ +// +// Copyright (c) 2000-2002 +// Joerg Walter, Mathias Koch +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) +// +// The authors gratefully acknowledge the support of +// GeNeSys mbH & Co. KG in producing this work. +// + +#include "test7.hpp" + +// Test matrix expression templates +template<class M, int N> +struct test_my_matrix { + typedef typename M::value_type value_type; + + template<class MP> + void test_with (MP &m1, MP &m2, MP &m3) const { + { + value_type t; + + // Copy and swap + initialize_matrix (m1); + initialize_matrix (m2); + m1 = m2; + std::cout << "m1 = m2 = " << m1 << std::endl; + m1.assign_temporary (m2); + std::cout << "m1.assign_temporary (m2) = " << m1 << std::endl; + m1.swap (m2); + std::cout << "m1.swap (m2) = " << m1 << " " << m2 << std::endl; + + // Zero assignment + m1 = ublas::zero_matrix<value_type> (m1.size1 (), m1.size2 ()); + std::cout << "m1.zero_matrix = " << m1 << std::endl; + m1 = m2; + + // Unary matrix operations resulting in a matrix + initialize_matrix (m1); + m2 = - m1; + std::cout << "- m1 = " << m2 << std::endl; + m2 = ublas::conj (m1); + std::cout << "conj (m1) = " << m2 << std::endl; + + // Binary matrix operations resulting in a matrix + initialize_matrix (m1); + initialize_matrix (m2); + m3 = m1 + m2; + std::cout << "m1 + m2 = " << m3 << std::endl; + m3 = m1 - m2; + std::cout << "m1 - m2 = " << m3 << std::endl; + + // Scaling a matrix + t = N; + initialize_matrix (m1); + m2 = value_type (1.) * m1; + std::cout << "1. * m1 = " << m2 << std::endl; + m2 = t * m1; + std::cout << "N * m1 = " << m2 << std::endl; + initialize_matrix (m1); + m2 = m1 * value_type (1.); + std::cout << "m1 * 1. = " << m2 << std::endl; + m2 = m1 * t; + std::cout << "m1 * N = " << m2 << std::endl; + + // Some assignments + initialize_matrix (m1); + initialize_matrix (m2); + m2 += m1; + std::cout << "m2 += m1 = " << m2 << std::endl; + m2 -= m1; + std::cout << "m2 -= m1 = " << m2 << std::endl; + m2 = m2 + m1; + std::cout << "m2 = m2 + m1 = " << m2 << std::endl; + m2 = m2 - m1; + std::cout << "m2 = m1 - m1 = " << m2 << std::endl; + m1 *= value_type (1.); + std::cout << "m1 *= 1. = " << m1 << std::endl; + m1 *= t; + std::cout << "m1 *= N = " << m1 << std::endl; + + // Transpose + initialize_matrix (m1); + m2 = ublas::trans (m1); + std::cout << "trans (m1) = " << m2 << std::endl; + + // Hermitean + initialize_matrix (m1); + m2 = ublas::herm (m1); + std::cout << "herm (m1) = " << m2 << std::endl; + + // Matrix multiplication + initialize_matrix (m1); + initialize_matrix (m2); + m3 = ublas::prod (m1, m2); + std::cout << "prod (m1, m2) = " << m3 << std::endl; + } + } + void operator () () const { + { + M m1 (N, N), m2 (N, N), m3 (N, N); + test_with (m1, m2, m3); + +#ifdef USE_RANGE + ublas::matrix_range<M> mr1 (m1, ublas::range (0, N), ublas::range (0, N)), + mr2 (m2, ublas::range (0, N), ublas::range (0, N)), + mr3 (m3, ublas::range (0, N), ublas::range (0, N)); + test_with (mr1, mr2, mr3); +#endif + +#ifdef USE_SLICE + ublas::matrix_slice<M> ms1 (m1, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms2 (m2, ublas::slice (0, 1, N), ublas::slice (0, 1, N)), + ms3 (m3, ublas::slice (0, 1, N), ublas::slice (0, 1, N)); + test_with (ms1, ms2, ms3); +#endif + } + } +}; + +// Test matrix +void test_matrix () { + std::cout << "test_matrix" << std::endl; + +#ifdef USE_MATRIX +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3 * 3> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, bounded_array" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<double>, ublas::row_major, ublas::bounded_array<boost::numeric::interval<double>, 3 * 3> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::unbounded_array<boost::numeric::interval<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<double>, ublas::row_major, ublas::unbounded_array<boost::numeric::interval<double> > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<mp_test_type>, ublas::row_major, std::vector<boost::numeric::interval<mp_test_type> > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, std::vector" << std::endl; + test_my_matrix<ublas::matrix<boost::numeric::interval<double>, ublas::row_major, std::vector<boost::numeric::interval<double> > >, 3 > () (); +#endif +#endif +#endif + +#ifdef USE_VECTOR_OF_VECTOR +#ifdef USE_BOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<boost::numeric::interval<mp_test_type>, 3>, 3 + 1> >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, bounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, ublas::bounded_array<ublas::bounded_array<boost::numeric::interval<double>, 3>, 3 + 1> >, 3 > () (); +#endif +#endif + +#ifdef USE_UNBOUNDED_ARRAY +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<boost::numeric::interval<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, unbounded_array" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, ublas::unbounded_array<ublas::unbounded_array<boost::numeric::interval<double> > > >, 3 > () (); +#endif +#endif + +#ifdef USE_STD_VECTOR +#ifdef USE_FLOAT + std::cout << "boost::numeric::interval<mp_test_type>, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<mp_test_type>, ublas::row_major, std::vector<std::vector<boost::numeric::interval<mp_test_type> > > >, 3 > () (); +#endif + +#ifdef USE_DOUBLE + std::cout << "boost::numeric::interval<double>, std::vector" << std::endl; + test_my_matrix<ublas::vector_of_vector<boost::numeric::interval<double>, ublas::row_major, std::vector<std::vector<boost::numeric::interval<double> > > >, 3 > () (); +#endif +#endif +#endif +} diff --git a/libs/multiprecision/tools/sincos.cpp b/libs/multiprecision/tools/sincos.cpp new file mode 100644 index 0000000000..88dde74283 --- /dev/null +++ b/libs/multiprecision/tools/sincos.cpp @@ -0,0 +1,75 @@ +// Copyright John Maddock 2013. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +//[special_data_example + +#include <boost/multiprecision/mpfr.hpp> +#include <boost/math/tools/test_data.hpp> +#include <boost/test/included/prg_exec_monitor.hpp> +#include <boost/math/tools/tuple.hpp> +#include <fstream> + +using namespace boost::math::tools; +using namespace boost::math; +using namespace std; +using namespace boost::multiprecision; + +typedef number<mpfr_float_backend<1000> > mp_type; + + +boost::math::tuple<mp_type, mp_type, mp_type> generate(mp_type a) +{ + mp_type ts, tc; + ts = sin(a); + tc = cos(a); + return boost::math::make_tuple(a, ts, tc); +} + +int cpp_main(int argc, char*argv []) +{ + parameter_info<mp_type> arg1, arg2; + test_data<mp_type> data; + + bool cont; + std::string line; + + if(argc < 1) + return 1; + + do{ + // + // User interface which prompts for + // range of input parameters: + // + if(0 == get_user_parameter_info(arg1, "a")) + return 1; + arg1.type |= dummy_param; + + data.insert(&generate, arg1); + + std::cout << "Any more data [y/n]?"; + std::getline(std::cin, line); + boost::algorithm::trim(line); + cont = (line == "y"); + }while(cont); + // + // Just need to write the results to a file: + // + std::cout << "Enter name of test data file [default=sincos.ipp]"; + std::getline(std::cin, line); + boost::algorithm::trim(line); + if(line == "") + line = "sincos.ipp"; + std::ofstream ofs(line.c_str()); + line.erase(line.find('.')); + ofs << std::scientific << std::setprecision(500); + write_code(ofs, data, line.c_str()); + + return 0; +} + +//] + |
