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<title>Using With MPFR / GMP - a High-Precision Floating-Point Library</title>
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<div class="section math_toolkit_using_udt_use_mpfr">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.using_udt.use_mpfr"></a><a class="link" href="use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP
- a High-Precision Floating-Point Library</a>
</h3></div></div></div>
<p>
The special functions and tools in this library can be used with <a href="http://www.mpfr.org" target="_top">MPFR
(an arbitrary precision number type based on the GMP library)</a>, either
via the bindings in <a href="../../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpfr.hpp</a>,
or via <a href="../../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpreal.hpp</a>.
</p>
<p>
In order to use these binings you will need to have installed <a href="http://www.mpfr.org" target="_top">MPFR</a>
plus its dependency the <a href="http://gmplib.org" target="_top">GMP library</a>.
You will also need one of the two supported C++ wrappers for MPFR: <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">gmpfrxx (or mpfr_class)</a>,
or <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpfr-C++ (mpreal)</a>.
</p>
<p>
Unfortunately neither <code class="computeroutput"><span class="identifier">mpfr_class</span></code>
nor <code class="computeroutput"><span class="identifier">mpreal</span></code> quite satisfy
our conceptual requirements, so there is a very thin set of additional interfaces
and some helper traits defined in <a href="../../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpfr.hpp</a>
and <a href="../../../../../../../boost/math/bindings/mpreal.hpp" target="_top">boost/math/bindings/mpreal.hpp</a>
that you should use in place of including 'gmpfrxx.h' or 'mpreal.h' directly.
The classes <code class="computeroutput"><span class="identifier">mpfr_class</span></code> or
<code class="computeroutput"><span class="identifier">mpreal</span></code> are then usable unchanged
once this header is included, so for example <code class="computeroutput"><span class="identifier">mpfr_class</span></code>'s
performance-enhancing expression templates are preserved and fully supported
by this library:
</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">bindings</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="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">mpfr_class</span><span class="special">::</span><span class="identifier">set_dprec</span><span class="special">(</span><span class="number">500</span><span class="special">);</span> <span class="comment">// 500 bit precision</span>
<span class="comment">//</span>
<span class="comment">// Note that the argument to tgamma is an expression template,</span>
<span class="comment">// that's just fine here:</span>
<span class="comment">//</span>
<span class="identifier">mpfr_class</span> <span class="identifier">v</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">sqrt</span><span class="special">(</span><span class="identifier">mpfr_class</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">setprecision</span><span class="special">(</span><span class="number">50</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="special">}</span>
</pre>
<p>
Alternatively use with <code class="computeroutput"><span class="identifier">mpreal</span></code>
would look like:
</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">bindings</span><span class="special">/</span><span class="identifier">mpreal</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="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</span><span class="special">::</span><span class="identifier">set_precision</span><span class="special">(</span><span class="number">500</span><span class="special">);</span> <span class="comment">// 500 bit precision</span>
<span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</span> <span class="identifier">v</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">sqrt</span><span class="special">(</span><span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</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">setprecision</span><span class="special">(</span><span class="number">50</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="special">}</span>
</pre>
<p>
For those functions that are based upon the <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
approximation</a>, the bindings defines a series of approximations with
up to 61 terms and accuracy up to approximately 3e-113. This therefore sets
the upper limit for accuracy to the majority of functions defined this library
when used with either <code class="computeroutput"><span class="identifier">mpfr_class</span></code>
or <code class="computeroutput"><span class="identifier">mpreal</span></code>.
</p>
<p>
There is a concept checking test program for mpfr support <a href="../../../../../../../libs/math/test/mpfr_concept_check.cpp" target="_top">here</a>
and <a href="../../../../../../../libs/math/test/mpreal_concept_check.cpp" target="_top">here</a>.
</p>
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Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<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>)
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