diff options
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 /boost/multiprecision/cpp_dec_float.hpp | |
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 'boost/multiprecision/cpp_dec_float.hpp')
-rw-r--r-- | boost/multiprecision/cpp_dec_float.hpp | 3070 |
1 files changed, 3070 insertions, 0 deletions
diff --git a/boost/multiprecision/cpp_dec_float.hpp b/boost/multiprecision/cpp_dec_float.hpp new file mode 100644 index 0000000000..8fc97250a4 --- /dev/null +++ b/boost/multiprecision/cpp_dec_float.hpp @@ -0,0 +1,3070 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright Christopher Kormanyos 2002 - 2013. +// Copyright 2011 -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) +// +// 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 +// +// Note that there are no "noexcept" specifications on the functions in this file: there are too many +// calls to lexical_cast (and similar) to easily analyse the code for correctness. So until compilers +// can detect noexcept misuse at compile time, the only realistic option is to simply not use it here. +// + +#ifndef BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP +#define BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP + +#include <boost/config.hpp> +#include <boost/cstdint.hpp> +#include <limits> +#ifndef BOOST_NO_CXX11_HDR_ARRAY +#include <array> +#else +#include <boost/array.hpp> +#endif +#include <boost/cstdint.hpp> +#include <boost/multiprecision/number.hpp> +#include <boost/multiprecision/detail/big_lanczos.hpp> +#include <boost/multiprecision/detail/dynamic_array.hpp> + +// +// Headers required for Boost.Math integration: +// +#include <boost/math/policies/policy.hpp> + +namespace boost{ +namespace multiprecision{ +namespace backends{ + +template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void> +class cpp_dec_float; + +} // namespace + +template <unsigned Digits10, class ExponentType, class Allocator> +struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public mpl::int_<number_kind_floating_point>{}; + +namespace backends{ + +template <unsigned Digits10, class ExponentType, class Allocator> +class cpp_dec_float +{ +private: + static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; + + // We need at least 16-bits in the exponent type to do anything sensible: + BOOST_STATIC_ASSERT_MSG(boost::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type."); + BOOST_STATIC_ASSERT_MSG(sizeof(ExponentType) > 1, "ExponentType is too small."); + +public: + typedef mpl::list<long long> signed_types; + typedef mpl::list<unsigned long long> unsigned_types; + typedef mpl::list<long double> float_types; + typedef ExponentType exponent_type; + + static const boost::int32_t cpp_dec_float_radix = 10L; + static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L; + static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits<boost::int32_t>::const_max - 100; + static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting)); + static const ExponentType cpp_dec_float_max_exp10 = (static_cast<ExponentType>(1) << (std::numeric_limits<ExponentType>::digits - 5)); + static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10; + static const ExponentType cpp_dec_float_max_exp = cpp_dec_float_max_exp10; + static const ExponentType cpp_dec_float_min_exp = cpp_dec_float_min_exp10; + + BOOST_STATIC_ASSERT((cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10)); + +private: + static const boost::int32_t cpp_dec_float_elem_digits10 = 8L; + static const boost::int32_t cpp_dec_float_elem_mask = 100000000L; + + BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10); + + // There are three guard limbs. + // 1) The first limb has 'play' from 1...8 decimal digits. + // 2) The last limb also has 'play' from 1...8 decimal digits. + // 3) One limb can get lost when justifying after multiply, + // as only half of the triangle is multiplied and a carry + // from below is missing. + static const boost::int32_t cpp_dec_float_elem_number_request = static_cast<boost::int32_t>((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + (((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); + + // The number of elements needed (with a minimum of two) plus three added guard limbs. + static const boost::int32_t cpp_dec_float_elem_number = static_cast<boost::int32_t>(((cpp_dec_float_elem_number_request < 2L) ? 2L : cpp_dec_float_elem_number_request) + 3L); + +public: + static const boost::int32_t cpp_dec_float_total_digits10 = static_cast<boost::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10); + +private: + + typedef enum enum_fpclass_type + { + cpp_dec_float_finite, + cpp_dec_float_inf, + cpp_dec_float_NaN + } + fpclass_type; + +#ifndef BOOST_NO_CXX11_HDR_ARRAY + typedef typename mpl::if_<is_void<Allocator>, + std::array<boost::uint32_t, cpp_dec_float_elem_number>, + detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> + >::type array_type; +#else + typedef typename mpl::if_<is_void<Allocator>, + boost::array<boost::uint32_t, cpp_dec_float_elem_number>, + detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> + >::type array_type; +#endif + + array_type data; + ExponentType exp; + bool neg; + fpclass_type fpclass; + boost::int32_t prec_elem; + + // + // Special values constructor: + // + cpp_dec_float(fpclass_type c) : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (c), + prec_elem(cpp_dec_float_elem_number) { } + + // + // Static data initializer: + // + struct initializer + { + initializer() + { + cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); + cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); + (cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); + (cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); + cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); + cpp_dec_float<Digits10, ExponentType, Allocator>::one(); + cpp_dec_float<Digits10, ExponentType, Allocator>::two(); + cpp_dec_float<Digits10, ExponentType, Allocator>::half(); + cpp_dec_float<Digits10, ExponentType, Allocator>::double_min(); + cpp_dec_float<Digits10, ExponentType, Allocator>::double_max(); + cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max(); + cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min(); + cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_max(); + cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_min(); + cpp_dec_float<Digits10, ExponentType, Allocator>::ulong_long_max(); + cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); + cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(0); + } + void do_nothing(){} + }; + + static initializer init; + +public: + // Constructors + cpp_dec_float() : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) { } + + cpp_dec_float(const char* s) : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) + { + *this = s; + } + + template<class I> + cpp_dec_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) + { + from_unsigned_long_long(i); + } + + template <class I> + cpp_dec_float(I i, typename enable_if<is_signed<I> >::type* = 0) : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) + { + if(i < 0) + { + from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i)); + negate(); + } + else + from_unsigned_long_long(i); + } + + cpp_dec_float(const cpp_dec_float& f) : + data (f.data), + exp (f.exp), + neg (f.neg), + fpclass (f.fpclass), + prec_elem(f.prec_elem) { } + + template <unsigned D, class ET, class A> + cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename enable_if_c<D <= Digits10>::type* = 0) : + data(), + exp (f.exp), + neg (f.neg), + fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))), + prec_elem(cpp_dec_float_elem_number) + { + std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin()); + } + template <unsigned D, class ET, class A> + explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename disable_if_c<D <= Digits10>::type* = 0) : + data(), + exp (f.exp), + neg (f.neg), + fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))), + prec_elem(cpp_dec_float_elem_number) + { + // TODO: this doesn't round! + std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin()); + } + + template <class F> + cpp_dec_float(const F val, typename enable_if<is_floating_point<F> >::type* = 0) : + data(), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) + { + *this = val; + } + + cpp_dec_float(const double mantissa, const ExponentType exponent); + + // Specific special values. + static const cpp_dec_float& nan() + { + static const cpp_dec_float val(cpp_dec_float_NaN); + init.do_nothing(); + return val; + } + + static const cpp_dec_float& inf() + { + static const cpp_dec_float val(cpp_dec_float_inf); + init.do_nothing(); + return val; + } + + static const cpp_dec_float& (max)() + { + init.do_nothing(); + static cpp_dec_float val_max = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_max_exp10)).c_str(); + return val_max; + } + + static const cpp_dec_float& (min)() + { + init.do_nothing(); + static cpp_dec_float val_min = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_min_exp10)).c_str(); + return val_min; + } + + static const cpp_dec_float& zero() + { + init.do_nothing(); + static cpp_dec_float val(static_cast<unsigned long long>(0u)); + return val; + } + + static const cpp_dec_float& one() + { + init.do_nothing(); + static cpp_dec_float val(static_cast<unsigned long long>(1u)); + return val; + } + + static const cpp_dec_float& two() + { + init.do_nothing(); + static cpp_dec_float val(static_cast<unsigned long long>(2u)); + return val; + } + + static const cpp_dec_float& half() + { + init.do_nothing(); + static cpp_dec_float val(0.5L); + return val; + } + + static const cpp_dec_float& double_min() + { + init.do_nothing(); + static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); + return val; + } + + static const cpp_dec_float& double_max() + { + init.do_nothing(); + static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); + return val; + } + + static const cpp_dec_float& long_double_min() + { + init.do_nothing(); + static cpp_dec_float val((std::numeric_limits<long double>::min)()); + return val; + } + + static const cpp_dec_float& long_double_max() + { + init.do_nothing(); + static cpp_dec_float val((std::numeric_limits<long double>::max)()); + return val; + } + + static const cpp_dec_float& long_long_max() + { + init.do_nothing(); + static cpp_dec_float val((std::numeric_limits<long long>::max)()); + return val; + } + + static const cpp_dec_float& long_long_min() + { + init.do_nothing(); + static cpp_dec_float val((std::numeric_limits<long long>::min)()); + return val; + } + + static const cpp_dec_float& ulong_long_max() + { + init.do_nothing(); + static cpp_dec_float val((std::numeric_limits<unsigned long long>::max)()); + return val; + } + + static const cpp_dec_float& eps() + { + init.do_nothing(); + static cpp_dec_float val(1.0, 1 - static_cast<int>(cpp_dec_float_digits10)); + return val; + } + + // Basic operations. + cpp_dec_float& operator=(const cpp_dec_float& v) + { + data = v.data; + exp = v.exp; + neg = v.neg; + fpclass = v.fpclass; + prec_elem = v.prec_elem; + return *this; + } + + template <unsigned D> + cpp_dec_float& operator=(const cpp_dec_float<D>& f) + { + exp = f.exp; + neg = f.neg; + fpclass = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass)); + unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number); + std::copy(f.data.begin(), f.data.begin() + elems, data.begin()); + std::fill(data.begin() + elems, data.end(), 0); + prec_elem = cpp_dec_float_elem_number; + return *this; + } + + cpp_dec_float& operator=(long long v) + { + if(v < 0) + { + from_unsigned_long_long(-v); + negate(); + } + else + from_unsigned_long_long(v); + return *this; + } + + cpp_dec_float& operator=(unsigned long long v) + { + from_unsigned_long_long(v); + return *this; + } + + cpp_dec_float& operator=(long double v); + + cpp_dec_float& operator=(const char* v) + { + rd_string(v); + return *this; + } + + cpp_dec_float& operator+=(const cpp_dec_float& v); + cpp_dec_float& operator-=(const cpp_dec_float& v); + cpp_dec_float& operator*=(const cpp_dec_float& v); + cpp_dec_float& operator/=(const cpp_dec_float& v); + + cpp_dec_float& add_unsigned_long_long(const unsigned long long n) + { + cpp_dec_float t; + t.from_unsigned_long_long(n); + return *this += t; + } + + cpp_dec_float& sub_unsigned_long_long(const unsigned long long n) + { + cpp_dec_float t; + t.from_unsigned_long_long(n); + return *this -= t; + } + + cpp_dec_float& mul_unsigned_long_long(const unsigned long long n); + cpp_dec_float& div_unsigned_long_long(const unsigned long long n); + + // Elementary primitives. + cpp_dec_float& calculate_inv (); + cpp_dec_float& calculate_sqrt(); + + void negate() + { + if(!iszero()) + neg = !neg; + } + + // Comparison functions + bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); } + bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); } + bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); } + + bool iszero () const + { + return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u)); + } + + bool isone () const; + bool isint () const; + bool isneg () const { return neg; } + + // Operators pre-increment and pre-decrement + cpp_dec_float& operator++() + { + return *this += one(); + } + + cpp_dec_float& operator--() + { + return *this -= one(); + } + + std::string str(boost::intmax_t digits, std::ios_base::fmtflags f)const; + + int compare(const cpp_dec_float& v)const; + + template <class V> + int compare(const V& v)const + { + cpp_dec_float<Digits10, ExponentType, Allocator> t; + t = v; + return compare(t); + } + + void swap(cpp_dec_float& v) + { + data.swap(v.data); + std::swap(exp, v.exp); + std::swap(neg, v.neg); + std::swap(fpclass, v.fpclass); + std::swap(prec_elem, v.prec_elem); + } + + double extract_double() const; + long double extract_long_double() const; + signed long long extract_signed_long_long() const; + unsigned long long extract_unsigned_long_long() const; + void extract_parts(double& mantissa, ExponentType& exponent) const; + cpp_dec_float extract_integer_part() const; + + void precision(const boost::int32_t prec_digits) + { + if(prec_digits >= cpp_dec_float_total_digits10) + { + prec_elem = cpp_dec_float_elem_number; + } + else + { + const boost::int32_t elems = static_cast<boost::int32_t>( static_cast<boost::int32_t>( (prec_digits + (cpp_dec_float_elem_digits10 / 2)) / cpp_dec_float_elem_digits10) + + static_cast<boost::int32_t>(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); + + prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2))); + } + } + static cpp_dec_float pow2(long long i); + ExponentType order()const + { + const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<boost::uint32_t>(0u))); + // + // Binary search to find the order of the leading term: + // + ExponentType prefix = 0; + + if(data[0] >= 100000UL) + { + if(data[0] >= 10000000UL) + { + if(data[0] >= 100000000UL) + { + if(data[0] >= 1000000000UL) + prefix = 9; + else + prefix = 8; + } + else + prefix = 7; + } + else + { + if(data[0] >= 1000000UL) + prefix = 6; + else + prefix = 5; + } + } + else + { + if(data[0] >= 1000UL) + { + if(data[0] >= 10000UL) + prefix = 4; + else + prefix = 3; + } + else + { + if(data[0] >= 100) + prefix = 2; + else if(data[0] >= 10) + prefix = 1; + } + } + + return (bo_order_is_zero ? static_cast<ExponentType>(0) : static_cast<ExponentType>(exp + prefix)); + } + + template<class Archive> + void serialize(Archive & ar, const unsigned int /*version*/) + { + for(unsigned i = 0; i < data.size(); ++i) + ar & data[i]; + ar & exp; + ar & neg; + ar & fpclass; + ar & prec_elem; + } + +private: + static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); } + static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } + static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); } + + void from_unsigned_long_long(const unsigned long long u); + + int cmp_data(const array_type& vd) const; + + + static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p); + static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); + + bool rd_string(const char* const s); + + template <unsigned D, class ET, class A> + friend class cpp_dec_float; +}; + +template <unsigned Digits10, class ExponentType, class Allocator> +typename cpp_dec_float<Digits10, ExponentType, Allocator>::initializer cpp_dec_float<Digits10, ExponentType, Allocator>::init; + +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_setting; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; +template <unsigned Digits10, class ExponentType, class Allocator> +const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; +template <unsigned Digits10, class ExponentType, class Allocator> +const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; +template <unsigned Digits10, class ExponentType, class Allocator> +const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; +template <unsigned Digits10, class ExponentType, class Allocator> +const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number_request; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number; +template <unsigned Digits10, class ExponentType, class Allocator> +const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask; + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) +{ + if((isnan)()) + { + return *this; + } + + if((isinf)()) + { + if((v.isinf)() && (isneg() != v.isneg())) + { + *this = nan(); + } + return *this; + } + + if(iszero()) + { + return operator=(v); + } + + // Get the offset for the add/sub operation. + static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); + + const ExponentType ofs_exp = static_cast<ExponentType>(exp - v.exp); + + // Check if the operation is out of range, requiring special handling. + if(v.iszero() || (ofs_exp > max_delta_exp)) + { + // Result is *this unchanged since v is negligible compared to *this. + return *this; + } + else if(ofs_exp < -max_delta_exp) + { + // Result is *this = v since *this is negligible compared to v. + return operator=(v); + } + + // Do the add/sub operation. + + typename array_type::iterator p_u = data.begin(); + typename array_type::const_iterator p_v = v.data.begin(); + bool b_copy = false; + const boost::int32_t ofs = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10); + array_type n_data; + + if(neg == v.neg) + { + // Add v to *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + // The result is stored in *this. The data are added one element + // at a time, each element with carry. + if(ofs >= static_cast<boost::int32_t>(0)) + { + std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); + p_v = n_data.begin(); + } + else + { + std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); + p_u = n_data.begin(); + b_copy = true; + } + + // Addition algorithm + boost::uint32_t carry = static_cast<boost::uint32_t>(0u); + + for(boost::int32_t j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) + { + boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry); + carry = t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask); + p_u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint32_t>(carry * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + } + + // There needs to be a carry into the element -1 of the array data + if(carry != static_cast<boost::uint32_t>(0u)) + { + std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end()); + data[0] = carry; + exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); + } + } + else + { + // Subtract v from *this, where the data array of either *this or v + // might have to be treated with a positive, negative or zero offset. + if((ofs > static_cast<boost::int32_t>(0)) + || ( (ofs == static_cast<boost::int32_t>(0)) + && (cmp_data(v.data) > static_cast<boost::int32_t>(0))) + ) + { + // In this case, |u| > |v| and ofs is positive. + // Copy the data of v, shifted down to a lower value + // into the data array m_n. Set the operand pointer p_v + // to point to the copied, shifted data m_n. + std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); + std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); + p_v = n_data.begin(); + } + else + { + if(ofs != static_cast<boost::int32_t>(0)) + { + // In this case, |u| < |v| and ofs is negative. + // Shift the data of u down to a lower value. + std::copy_backward(data.begin(), data.end() - static_cast<size_t>(-ofs), data.end()); + std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); + } + + // Copy the data of v into the data array n_data. + // Set the u-pointer p_u to point to m_n and the + // operand pointer p_v to point to the shifted + // data m_data. + n_data = v.data; + p_u = n_data.begin(); + p_v = data.begin(); + b_copy = true; + } + + boost::int32_t j; + + // Subtraction algorithm + boost::int32_t borrow = static_cast<boost::int32_t>(0); + + for(j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) + { + boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>( static_cast<boost::int32_t>(p_u[j]) + - static_cast<boost::int32_t>(p_v[j])) - borrow); + + // Underflow? Borrow? + if(t < static_cast<boost::int32_t>(0)) + { + // Yes, underflow and borrow + t += static_cast<boost::int32_t>(cpp_dec_float_elem_mask); + borrow = static_cast<boost::int32_t>(1); + } + else + { + borrow = static_cast<boost::int32_t>(0); + } + + p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); + } + + if(b_copy) + { + data = n_data; + exp = v.exp; + neg = v.neg; + } + + // Is it necessary to justify the data? + const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + + if(first_nonzero_elem != data.begin()) + { + if(first_nonzero_elem == data.end()) + { + // This result of the subtraction is exactly zero. + // Reset the sign and the exponent. + neg = false; + exp = static_cast<ExponentType>(0); + } + else + { + // Justify the data + const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem)); + + std::copy(data.begin() + static_cast<std::size_t>(sj), data.end(), data.begin()); + std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u)); + + exp -= static_cast<ExponentType>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); + } + } + } + + // Handle underflow. + if(iszero()) + return (*this = zero()); + + // Check for potential overflow. + const bool b_result_might_overflow = (exp >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); + + // Handle overflow. + if(b_result_might_overflow) + { + const bool b_result_is_neg = neg; + neg = false; + + if(compare((cpp_dec_float::max)()) > 0) + *this = inf(); + + neg = b_result_is_neg; + } + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) +{ + // Use *this - v = -(-*this + v). + negate(); + *this += v; + negate(); + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) +{ + // Evaluate the sign of the result. + const bool b_result_is_neg = (neg != v.neg); + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = (isinf)(); + const bool b_v_is_inf = (v.isinf)(); + const bool b_u_is_zero = iszero(); + const bool b_v_is_zero = v.iszero(); + + if( ((isnan)() || (v.isnan)()) + || (b_u_is_inf && b_v_is_zero) + || (b_v_is_inf && b_u_is_zero) + ) + { + *this = nan(); + return *this; + } + + if(b_u_is_inf || b_v_is_inf) + { + *this = inf(); + if(b_result_is_neg) + negate(); + return *this; + } + + if(b_u_is_zero || b_v_is_zero) + { + return *this = zero(); + } + + // Check for potential overflow or underflow. + const bool b_result_might_overflow = ((exp + v.exp) >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); + const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<ExponentType>(cpp_dec_float_min_exp10)); + + // Set the exponent of the result. + exp += v.exp; + + const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); + + const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul); + + // Handle a potential carry. + if(carry != static_cast<boost::uint32_t>(0u)) + { + exp += cpp_dec_float_elem_digits10; + + // Shift the result of the multiplication one element to the right... + std::copy_backward(data.begin(), + data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), + data.begin() + static_cast<std::size_t>(prec_elem)); + + // ... And insert the carry. + data.front() = carry; + } + + // Handle overflow. + if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) + { + *this = inf(); + } + + // Handle underflow. + if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) + { + *this = zero(); + + return *this; + } + + // Set the sign of the result. + neg = b_result_is_neg; + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) +{ + const bool u_and_v_are_finite_and_identical = ( (isfinite)() + && (fpclass == v.fpclass) + && (exp == v.exp) + && (cmp_data(v.data) == static_cast<boost::int32_t>(0))); + + if(u_and_v_are_finite_and_identical) + { + if(neg != v.neg) + { + *this = one(); + negate(); + } + else + *this = one(); + return *this; + } + else + { + if(iszero()) + { + if((v.isnan)() || v.iszero()) + { + return *this = v; + } + return *this; + } + cpp_dec_float t(v); + t.calculate_inv(); + return operator*=(t); + } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const unsigned long long n) +{ + // Multiply *this with a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + const bool b_u_is_inf = (isinf)(); + const bool b_n_is_zero = (n == static_cast<boost::int32_t>(0)); + + if((isnan)() || (b_u_is_inf && b_n_is_zero)) + { + return (*this = nan()); + } + + if(b_u_is_inf) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(iszero() || b_n_is_zero) + { + // Multiplication by zero. + return *this = zero(); + } + + if(n >= static_cast<unsigned long long>(cpp_dec_float_elem_mask)) + { + neg = b_neg; + cpp_dec_float t; + t = n; + return operator*=(t); + } + + if(n == static_cast<unsigned long long>(1u)) + { + neg = b_neg; + return *this; + } + + // Set up the multiplication loop. + const boost::uint32_t nn = static_cast<boost::uint32_t>(n); + const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); + + // Handle the carry and adjust the exponent. + if(carry != static_cast<boost::uint32_t>(0u)) + { + exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); + + // Shift the result of the multiplication one element to the right. + std::copy_backward(data.begin(), + data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), + data.begin() + static_cast<std::size_t>(prec_elem)); + + data.front() = static_cast<boost::uint32_t>(carry); + } + + // Check for potential overflow. + const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10); + + // Handle overflow. + if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) + { + *this = inf(); + } + + // Set the sign. + neg = b_neg; + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const unsigned long long n) +{ + // Divide *this by a constant unsigned long long. + + // Evaluate the sign of the result. + const bool b_neg = neg; + + // Artificially set the sign of the result to be positive. + neg = false; + + // Handle special cases like zero, inf and NaN. + if((isnan)()) + { + return *this; + } + + if((isinf)()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if(n == static_cast<unsigned long long>(0u)) + { + // Divide by 0. + if(iszero()) + { + *this = nan(); + return *this; + } + else + { + *this = inf(); + if(isneg()) + negate(); + return *this; + } + } + + if(iszero()) + { + return *this; + } + + if(n >= static_cast<unsigned long long>(cpp_dec_float_elem_mask)) + { + neg = b_neg; + cpp_dec_float t; + t = n; + return operator/=(t); + } + + const boost::uint32_t nn = static_cast<boost::uint32_t>(n); + + if(nn > static_cast<boost::uint32_t>(1u)) + { + // Do the division loop. + const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); + + // Determine if one leading zero is in the result data. + if(data[0] == static_cast<boost::uint32_t>(0u)) + { + // Adjust the exponent + exp -= static_cast<ExponentType>(cpp_dec_float_elem_digits10); + + // Shift result of the division one element to the left. + std::copy(data.begin() + static_cast<std::size_t>(1u), + data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), + data.begin()); + + data[prec_elem - static_cast<boost::int32_t>(1)] = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(prev * static_cast<boost::uint64_t>(cpp_dec_float_elem_mask)) / nn); + } + } + + // Check for potential underflow. + const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10); + + // Handle underflow. + if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) + return (*this = zero()); + + // Set the sign of the result. + neg = b_neg; + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv() +{ + // Compute the inverse of *this. + const bool b_neg = neg; + + neg = false; + + // Handle special cases like zero, inf and NaN. + if(iszero()) + { + *this = inf(); + if(b_neg) + negate(); + return *this; + } + + if((isnan)()) + { + return *this; + } + + if((isinf)()) + { + return *this = zero(); + } + + if(isone()) + { + if(b_neg) + negate(); + return *this; + } + + // Save the original *this. + cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + ExponentType ne; + x.extract_parts(dd, ne); + + // Do the inverse estimate using double precision estimates of mantissa and exponent. + operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne)); + + // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration + // is used. During the iterative steps, the precision of the calculation is limited + // to the minimum required in order to minimize the run-time. + + static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; + + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast<boost::int32_t>(2)) + { + // Adjust precision of the terms. + precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); + x.precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); + + // Next iteration. + cpp_dec_float t(*this); + t *= x; + t -= two(); + t.negate(); + *this *= t; + } + + neg = b_neg; + + prec_elem = cpp_dec_float_elem_number; + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt() +{ + // Compute the square root of *this. + + if(isneg() || (!(isfinite)())) + { + *this = nan(); + return *this; + } + + if(iszero() || isone()) + { + return *this; + } + + // Save the original *this. + cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); + + // Generate the initial estimate using division. + // Extract the mantissa and exponent for a "manual" + // computation of the estimate. + double dd; + ExponentType ne; + extract_parts(dd, ne); + + // Force the exponent to be an even multiple of two. + if((ne % static_cast<ExponentType>(2)) != static_cast<ExponentType>(0)) + { + ++ne; + dd /= 10.0; + } + + // Setup the iteration. + // Estimate the square root using simple manipulations. + const double sqd = std::sqrt(dd); + + *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2))); + + // Estimate 1.0 / (2.0 * x0) using simple manipulations. + cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2))); + + // Compute the square root of x. Coupled Newton iteration + // as described in "Pi Unleashed" is used. During the + // iterative steps, the precision of the calculation is + // limited to the minimum required in order to minimize + // the run-time. + // + // Book references: + // http://www.jjj.de/pibook/pibook.html + // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 + + static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; + + for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u) + { + // Adjust precision of the terms. + precision((digits + 10) * 2); + vi.precision((digits + 10) * 2); + + // Next iteration of vi + cpp_dec_float t(*this); + t *= vi; + t.negate(); + t.mul_unsigned_long_long(2u); + t += one(); + t *= vi; + vi += t; + + // Next iteration of *this + t = *this; + t *= *this; + t.negate(); + t += x; + t *= vi; + *this += t; + } + + prec_elem = cpp_dec_float_elem_number; + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +int cpp_dec_float<Digits10, ExponentType, Allocator>::cmp_data(const array_type& vd) const +{ + // Compare the data of *this with those of v. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); + + const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); + + if(is_equal) + { + return 0; + } + else + { + return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); + } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const +{ + // Compare v with *this. + // Return +1 for *this > v + // 0 for *this = v + // -1 for *this < v + + // Handle all non-finite cases. + if((!(isfinite)()) || (!(v.isfinite)())) + { + // NaN can never equal NaN. Return an implementation-dependent + // signed result. Also note that comparison of NaN with NaN + // using operators greater-than or less-than is undefined. + if((isnan)() || (v.isnan)()) { return ((isnan)() ? 1 : -1); } + + if((isinf)() && (v.isinf)()) + { + // Both *this and v are infinite. They are equal if they have the same sign. + // Otherwise, *this is less than v if and only if *this is negative. + return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); + } + + if((isinf)()) + { + // *this is infinite, but v is finite. + // So negative infinite *this is less than any finite v. + // Whereas positive infinite *this is greater than any finite v. + return (isneg() ? -1 : 1); + } + else + { + // *this is finite, and v is infinite. + // So any finite *this is greater than negative infinite v. + // Whereas any finite *this is less than positive infinite v. + return (v.neg ? 1 : -1); + } + } + + // And now handle all *finite* cases. + if(iszero()) + { + // The value of *this is zero and v is either zero or non-zero. + return (v.iszero() ? 0 + : (v.neg ? 1 : -1)); + } + else if(v.iszero()) + { + // The value of v is zero and *this is non-zero. + return (neg ? -1 : 1); + } + else + { + // Both *this and v are non-zero. + + if(neg != v.neg) + { + // The signs are different. + return (neg ? -1 : 1); + } + else if(exp != v.exp) + { + // The signs are the same and the exponents are different. + const int val_cexpression = ((exp < v.exp) ? 1 : -1); + + return (neg ? val_cexpression : -val_cexpression); + } + else + { + // The signs are the same and the exponents are the same. + // Compare the data. + const int val_cmp_data = cmp_data(v.data); + + return ((!neg) ? val_cmp_data : -val_cmp_data); + } + } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const +{ + // Check if the value of *this is identically 1 or very close to 1. + + const bool not_negative_and_is_finite = ((!neg) && (isfinite)()); + + if(not_negative_and_is_finite) + { + if((data[0u] == static_cast<boost::uint32_t>(1u)) && (exp == static_cast<ExponentType>(0))) + { + const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); + return (it_non_zero == data.end()); + } + else if((data[0u] == static_cast<boost::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<ExponentType>(-cpp_dec_float_elem_digits10))) + { + const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); + return (it_non_nine == data.end()); + } + } + + return false; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const +{ + if(fpclass != cpp_dec_float_finite) { return false; } + + if(iszero()) { return true; } + + if(exp < static_cast<ExponentType>(0)) { return false; } // |*this| < 1. + + const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u; + + if(offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number)) + { + // The number is too large to resolve the integer part. + // It considered to be a pure integer. + return true; + } + + typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); + + return (it_non_zero == data.end()); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const +{ + // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x. + + // Extracts the mantissa and exponent. + exponent = exp; + + boost::uint32_t p10 = static_cast<boost::uint32_t>(1u); + boost::uint32_t test = data[0u]; + + for(;;) + { + test /= static_cast<boost::uint32_t>(10u); + + if(test == static_cast<boost::uint32_t>(0u)) + { + break; + } + + p10 *= static_cast<boost::uint32_t>(10u); + ++exponent; + } + + // Establish the upper bound of limbs for extracting the double. + const int max_elem_in_double_count = static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10) + + (static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0) + + 1; + + // And make sure this upper bound stays within bounds of the elems. + const std::size_t max_elem_extract_count = static_cast<std::size_t>((std::min)(static_cast<boost::int32_t>(max_elem_in_double_count), cpp_dec_float_elem_number)); + + // Extract into the mantissa the first limb, extracted as a double. + mantissa = static_cast<double>(data[0]); + double scale = 1.0; + + // Extract the rest of the mantissa piecewise from the limbs. + for(std::size_t i = 1u; i < max_elem_extract_count; i++) + { + scale /= static_cast<double>(cpp_dec_float_elem_mask); + mantissa += (static_cast<double>(data[i]) * scale); + } + + mantissa /= static_cast<double>(p10); + + if(neg) { mantissa = -mantissa; } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const +{ + // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. + + // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>. + if(!(isfinite)()) + { + if((isnan)()) + { + return std::numeric_limits<double>::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits<double>::infinity() + : -std::numeric_limits<double>::infinity()); + } + } + + cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. + if(iszero() || (xx.compare(double_min()) < 0)) + { + return 0.0; + } + + // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. + if(xx.compare(double_max()) > 0) + { + return ((!neg) ? std::numeric_limits<double>::infinity() + : -std::numeric_limits<double>::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific); + + double d; + ss >> d; + + return d; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const +{ + // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. + + // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal. + if(!(isfinite)()) + { + if((isnan)()) + { + return std::numeric_limits<long double>::quiet_NaN(); + } + else + { + return ((!neg) ? std::numeric_limits<long double>::infinity() + : -std::numeric_limits<long double>::infinity()); + } + } + + cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); + if(xx.isneg()) + xx.negate(); + + // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. + if(iszero() || (xx.compare(long_double_min()) < 0)) + { + return static_cast<long double>(0.0); + } + + // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. + if(xx.compare(long_double_max()) > 0) + { + return ((!neg) ? std::numeric_limits<long double>::infinity() + : -std::numeric_limits<long double>::infinity()); + } + + std::stringstream ss; + + ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific); + + long double ld; + ss >> ld; + + return ld; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +signed long long cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const +{ + // Extracts a signed long long from *this. + // If (x > maximum of signed long long) or (x < minimum of signed long long), + // then the maximum or minimum of signed long long is returned accordingly. + + if(exp < static_cast<ExponentType>(0)) + { + return static_cast<signed long long>(0); + } + + const bool b_neg = isneg(); + + unsigned long long val; + + if((!b_neg) && (compare(long_long_max()) > 0)) + { + return (std::numeric_limits<signed long long>::max)(); + } + else if(b_neg && (compare(long_long_min()) < 0)) + { + return (std::numeric_limits<signed long long>::min)(); + } + else + { + // Extract the data into an unsigned long long value. + cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); + if(xn.isneg()) + xn.negate(); + + val = static_cast<unsigned long long>(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); + + for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) + { + val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask); + val += static_cast<unsigned long long>(xn.data[i]); + } + } + + if (!b_neg) + { + return static_cast<signed long long>(val); + } + else + { + // This strange expression avoids a hardware trap in the corner case + // that val is the most negative value permitted in long long. + // See https://svn.boost.org/trac/boost/ticket/9740. + // + signed long long sval = static_cast<signed long long>(val - 1); + sval = -sval; + --sval; + return sval; + } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +unsigned long long cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const +{ + // Extracts an unsigned long long from *this. + // If x exceeds the maximum of unsigned long long, + // then the maximum of unsigned long long is returned. + // If x is negative, then the unsigned long long cast of + // the signed long long extracted value is returned. + + if(isneg()) + { + return static_cast<unsigned long long>(extract_signed_long_long()); + } + + if(exp < static_cast<ExponentType>(0)) + { + return static_cast<unsigned long long>(0u); + } + + const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); + + unsigned long long val; + + if(xn.compare(ulong_long_max()) > 0) + { + return (std::numeric_limits<unsigned long long>::max)(); + } + else + { + // Extract the data into an unsigned long long value. + val = static_cast<unsigned long long>(xn.data[0]); + + const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); + + for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) + { + val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask); + val += static_cast<unsigned long long>(xn.data[i]); + } + } + + return val; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const +{ + // Compute the signed integer part of x. + + if(!(isfinite)()) + { + return *this; + } + + if(exp < static_cast<ExponentType>(0)) + { + // The absolute value of the number is smaller than 1. + // Thus the integer part is zero. + return zero(); + } + + // Truncate the digits from the decimal part, including guard digits + // that do not belong to the integer part. + + // Make a local copy. + cpp_dec_float<Digits10, ExponentType, Allocator> x = *this; + + // Clear out the decimal portion + const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(cpp_dec_float_elem_digits10)) + 1u; + const size_t last_clear = static_cast<size_t>(cpp_dec_float_elem_number); + + if(first_clear < last_clear) + std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u)); + + return x; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const +{ + if((this->isinf)()) + { + if(this->isneg()) + return "-inf"; + else if(f & std::ios_base::showpos) + return "+inf"; + else + return "inf"; + } + else if((this->isnan)()) + { + return "nan"; + } + + std::string str; + boost::intmax_t org_digits(number_of_digits); + ExponentType my_exp = order(); + + if(number_of_digits == 0) + number_of_digits = cpp_dec_float_total_digits10; + + if(f & std::ios_base::fixed) + { + number_of_digits += my_exp + 1; + } + else if(f & std::ios_base::scientific) + ++number_of_digits; + // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>. + const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>((number_of_digits / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 2u), + static_cast<std::size_t>(cpp_dec_float_elem_number)); + + // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point. + str = boost::lexical_cast<std::string>(data[0]); + + // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element. + for(std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++) + { + std::stringstream ss; + + ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10)) + << std::setfill(static_cast<char>('0')) + << data[i]; + + str += ss.str(); + } + + bool have_leading_zeros = false; + + if(number_of_digits == 0) + { + // We only get here if the output format is "fixed" and we just need to + // round the first non-zero digit. + number_of_digits -= my_exp + 1; // reset to original value + str.insert(0, std::string::size_type(number_of_digits), '0'); + have_leading_zeros = true; + } + + if(number_of_digits < 0) + { + str = "0"; + if(isneg()) + str.insert(0, 1, '-'); + boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero()); + return str; + } + else + { + // Cut the output to the size of the precision. + if(str.length() > static_cast<std::string::size_type>(number_of_digits)) + { + // Get the digit after the last needed digit for rounding + const boost::uint32_t round = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<boost::uint32_t>('0')); + + bool need_round_up = round >= 5u; + + if(round == 5u) + { + const boost::uint32_t ix = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<boost::uint32_t>('0')); + if((ix & 1u) == 0) + { + // We have an even digit followed by a 5, so we might not actually need to round up + // if all the remaining digits are zero: + if(str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos) + { + bool all_zeros = true; + // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string: + for(std::size_t i = number_of_elements; i < data.size(); i++) + { + if(data[i]) + { + all_zeros = false; + break; + } + } + if(all_zeros) + need_round_up = false; // tie break - round to even. + } + } + } + + // Truncate the string + str.erase(static_cast<std::string::size_type>(number_of_digits)); + + if(need_round_up) + { + std::size_t ix = static_cast<std::size_t>(str.length() - 1u); + + // Every trailing 9 must be rounded up + while(ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9))) + { + str.at(ix) = static_cast<char>('0'); + --ix; + } + + if(!ix) + { + // There were nothing but trailing nines. + if(static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>(0x30)) == static_cast<boost::int32_t>(9)) + { + // Increment up to the next order and adjust exponent. + str.at(ix) = static_cast<char>('1'); + ++my_exp; + } + else + { + // Round up this digit. + ++str.at(ix); + } + } + else + { + // Round up the last digit. + ++str[ix]; + } + } + } + } + + if(have_leading_zeros) + { + // We need to take the zeros back out again, and correct the exponent + // if we rounded up: + if(str[std::string::size_type(number_of_digits - 1)] != '0') + { + ++my_exp; + str.erase(0, std::string::size_type(number_of_digits - 1)); + } + else + str.erase(0, std::string::size_type(number_of_digits)); + } + + if(isneg()) + str.insert(0, 1, '-'); + + boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero()); + return str; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s) +{ + try{ + + std::string str(s); + + // TBD: Using several regular expressions may significantly reduce + // the code complexity (and perhaps the run-time) of rd_string(). + + // Get a possible exponent and remove it. + exp = static_cast<ExponentType>(0); + + std::size_t pos; + + if( ((pos = str.find('e')) != std::string::npos) + || ((pos = str.find('E')) != std::string::npos) + ) + { + // Remove the exponent part from the string. + exp = boost::lexical_cast<ExponentType>(static_cast<const char*>(str.c_str() + (pos + 1u))); + str = str.substr(static_cast<std::size_t>(0u), pos); + } + + // Get a possible +/- sign and remove it. + neg = false; + + if(str.size()) + { + if(str[0] == '-') + { + neg = true; + str.erase(0, 1); + } + else if(str[0] == '+') + { + str.erase(0, 1); + } + } + // + // Special cases for infinities and NaN's: + // + if((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY")) + { + if(neg) + { + *this = this->inf(); + this->negate(); + } + else + *this = this->inf(); + return true; + } + if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN"))) + { + *this = this->nan(); + return true; + } + + // Remove the leading zeros for all input types. + const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); + + if(fwd_it_leading_zero != str.begin()) + { + if(fwd_it_leading_zero == str.end()) + { + // The string contains nothing but leading zeros. + // This string represents zero. + operator=(zero()); + return true; + } + else + { + str.erase(str.begin(), fwd_it_leading_zero); + } + } + + // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form + // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an + // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded + // on the right-end, and n is a signed 64-bit integer which is an + // even multiple of cpp_dec_float_elem_digits10. + + // Find a possible decimal point. + pos = str.find(static_cast<char>('.')); + + if(pos != std::string::npos) + { + // Remove all trailing insignificant zeros. + const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); + + if(rit_non_zero != str.rbegin()) + { + const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero); + str.erase(str.begin() + ofs, str.end()); + } + + // Check if the input is identically zero. + if(str == std::string(".")) + { + operator=(zero()); + return true; + } + + // Remove leading significant zeros just after the decimal point + // and adjust the exponent accordingly. + // Note that the while-loop operates only on strings of the form ".000abcd..." + // and peels away the zeros just after the decimal point. + if(str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.')) + { + const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); + + std::size_t delta_exp = static_cast<std::size_t>(0u); + + if(str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0')) + { + delta_exp = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero); + } + + // Bring one single digit into the mantissa and adjust the exponent accordingly. + str.erase(str.begin(), it_non_zero); + str.insert(static_cast<std::size_t>(1u), "."); + exp -= static_cast<ExponentType>(delta_exp + 1u); + } + } + else + { + // Input string has no decimal point: Append decimal point. + str.append("."); + } + + // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10. + std::size_t n_shift = static_cast<std::size_t>(0u); + const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)); + + if((exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)) != static_cast<ExponentType>(0)) + { + n_shift = ((exp < static_cast<ExponentType>(0)) + ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + : static_cast<std::size_t>(n_exp_rem)); + } + + // Make sure that there are enough digits for the decimal point shift. + pos = str.find(static_cast<char>('.')); + + std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u); + + if((str.length() - pos_plus_one) < n_shift) + { + const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one)); + + str.append(std::string(sz, static_cast<char>('0'))); + } + + // Do the decimal point shift. + if(n_shift != static_cast<std::size_t>(0u)) + { + str.insert(static_cast<std::size_t>(pos_plus_one + n_shift), "."); + + str.erase(pos, static_cast<std::size_t>(1u)); + + exp -= static_cast<ExponentType>(n_shift); + } + + // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10. + pos = str.find(static_cast<char>('.')); + pos_plus_one = static_cast<std::size_t>(pos + 1u); + + if(pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + { + const boost::int32_t n_pos = static_cast<boost::int32_t>(pos); + const boost::int32_t n_rem_is_zero = ((static_cast<boost::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(1) : static_cast<boost::int32_t>(0)); + const boost::int32_t n = static_cast<boost::int32_t>(static_cast<boost::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero); + + str.insert(static_cast<std::size_t>(static_cast<boost::int32_t>(n_pos - static_cast<boost::int32_t>(n * cpp_dec_float_elem_digits10))), "."); + + str.erase(pos_plus_one, static_cast<std::size_t>(1u)); + + exp += static_cast<ExponentType>(static_cast<ExponentType>(n) * static_cast<ExponentType>(cpp_dec_float_elem_digits10)); + } + + // Pad the decimal part such that its value is an even + // multiple of cpp_dec_float_elem_digits10. + pos = str.find(static_cast<char>('.')); + pos_plus_one = static_cast<std::size_t>(pos + 1u); + + const boost::int32_t n_dec = static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.length() - 1u) - static_cast<boost::int32_t>(pos)); + const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % cpp_dec_float_elem_digits10); + + boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0)) + ? static_cast<boost::int32_t>(cpp_dec_float_elem_digits10 - n_rem) + : static_cast<boost::int32_t>(0)); + + if(n_cnt != static_cast<boost::int32_t>(0)) + { + str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0')); + } + + // Truncate decimal part if it is too long. + const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); + + if(static_cast<std::size_t>(str.length() - pos) > max_dec) + { + str = str.substr(static_cast<std::size_t>(0u), + static_cast<std::size_t>(pos_plus_one + max_dec)); + } + + // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form. + // (See the comment above.) + + // Set all the data elements to 0. + std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); + + // Extract the data. + + // First get the digits to the left of the decimal point... + data[0u] = boost::lexical_cast<boost::uint32_t>(str.substr(static_cast<std::size_t>(0u), pos)); + + // ...then get the remaining digits to the right of the decimal point. + const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); + + for(std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++) + { + const std::string::const_iterator it = str.begin() + + pos_plus_one + + (i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); + + data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10))); + } + + // Check for overflow... + if(exp > cpp_dec_float_max_exp10) + { + const bool b_result_is_neg = neg; + + *this = inf(); + if(b_result_is_neg) + negate(); + } + + // ...and check for underflow. + if(exp <= cpp_dec_float_min_exp10) + { + if(exp == cpp_dec_float_min_exp10) + { + // Check for identity with the minimum value. + cpp_dec_float<Digits10, ExponentType, Allocator> test = *this; + + test.exp = static_cast<ExponentType>(0); + + if(test.isone()) + { + *this = zero(); + } + } + else + { + *this = zero(); + } + } + + } + catch(const bad_lexical_cast&) + { + // Rethrow with better error message: + std::string msg = "Unable to parse the string \""; + msg += s; + msg += "\" as a floating point value."; + throw std::runtime_error(msg); + } + + return true; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent) + : data (), + exp (static_cast<ExponentType>(0)), + neg (false), + fpclass (cpp_dec_float_finite), + prec_elem(cpp_dec_float_elem_number) +{ + // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent. + // Note: This constructor does not maintain the full precision of double. + + const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon()))); + + if(mantissa_is_iszero) + { + std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); + return; + } + + const bool b_neg = (mantissa < 0.0); + + double d = ((!b_neg) ? mantissa : -mantissa); + ExponentType e = exponent; + + while(d > 10.0) { d /= 10.0; ++e; } + while(d < 1.0) { d *= 10.0; --e; } + + boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); + + while(static_cast<boost::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<boost::int32_t>(0)) + { + d *= 10.0; + --e; + } + + exp = e; + neg = b_neg; + + std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); + + static const boost::int32_t digit_ratio = static_cast<boost::int32_t>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); + static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2)); + + for(boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++) + { + boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d)); + data[i] = static_cast<boost::uint32_t>(n); + d -= static_cast<double>(n); + d *= static_cast<double>(cpp_dec_float_elem_mask); + } +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator= (long double a) +{ + // Christopher Kormanyos's original code used a cast to long long here, but that fails + // when long double has more digits than a long long. + using std::frexp; + using std::ldexp; + using std::floor; + + if(a == 0) + return *this = zero(); + + if(a == 1) + return *this = one(); + + if((boost::math::isinf)(a)) + return *this = inf(); + + if((boost::math::isnan)(a)) + return *this = nan(); + + int e; + long double f, term; + *this = zero(); + + f = frexp(a, &e); + + static const int shift = std::numeric_limits<int>::digits - 1; + + while(f) + { + // extract int sized bits from f: + f = ldexp(f, shift); + term = floor(f); + e -= shift; + *this *= pow2(shift); + if(term > 0) + add_unsigned_long_long(static_cast<unsigned>(term)); + else + sub_unsigned_long_long(static_cast<unsigned>(-term)); + f -= term; + } + + if(e != 0) + *this *= pow2(e); + + return *this; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const unsigned long long u) +{ + std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); + + exp = static_cast<ExponentType>(0); + neg = false; + fpclass = cpp_dec_float_finite; + prec_elem = cpp_dec_float_elem_number; + + std::size_t i =static_cast<std::size_t>(0u); + + unsigned long long uu = u; + + boost::uint32_t temp[(std::numeric_limits<unsigned long long>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = { static_cast<boost::uint32_t>(0u) }; + + while(uu != static_cast<unsigned long long>(0u)) + { + temp[i] = static_cast<boost::uint32_t>(uu % static_cast<unsigned long long>(cpp_dec_float_elem_mask)); + uu = static_cast<unsigned long long>(uu / static_cast<unsigned long long>(cpp_dec_float_elem_mask)); + ++i; + } + + if(i > static_cast<std::size_t>(1u)) + { + exp += static_cast<ExponentType>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); + } + + std::reverse(temp, temp + i); + std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin()); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) +{ + // + // There is a limit on how many limbs this algorithm can handle without dropping digits + // due to overflow in the carry, it is: + // + // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844 + // + BOOST_STATIC_ASSERT_MSG(cpp_dec_float_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); + + boost::uint64_t carry = static_cast<boost::uint64_t>(0u); + + for(boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--) + { + boost::uint64_t sum = carry; + + for(boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--) + { + sum += static_cast<boost::uint64_t>(u[j - i] * static_cast<boost::uint64_t>(v[i])); + } + + u[j] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); + carry = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); + } + + return static_cast<boost::uint32_t>(carry); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t carry = static_cast<boost::uint64_t>(0u); + + // Multiplication loop. + for(boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--) + { + const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n))); + carry = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); + u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint64_t>(static_cast<boost::uint32_t>(cpp_dec_float_elem_mask) * static_cast<boost::uint64_t>(carry))); + } + + return static_cast<boost::uint32_t>(carry); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) +{ + boost::uint64_t prev = static_cast<boost::uint64_t>(0u); + + for(boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++) + { + const boost::uint64_t t = static_cast<boost::uint64_t>(u[j] + static_cast<boost::uint64_t>(prev * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); + u[j] = static_cast<boost::uint32_t>(t / n); + prev = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j]))); + } + + return static_cast<boost::uint32_t>(prev); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const long long p) +{ + // Create a static const table of p^2 for -128 < p < +128. + // Note: The size of this table must be odd-numbered and + // symmetric about 0. + init.do_nothing(); + static const boost::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 255u> p2_data = + {{ + cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), + cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), + cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), + cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), + cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), + cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), + cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), + cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), + cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), + cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), + cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), + cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), + cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), + cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), + cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), + cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), + cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), + cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), + cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), + cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"), + cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"), + cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"), + cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"), + cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"), + cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"), + cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"), + cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"), + cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"), + cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"), + cpp_dec_float("3.155443620884047221646914261131144918692825740436092019081115722656250000000000000000000000000000000e-30"), + cpp_dec_float("6.310887241768094443293828522262289837385651480872184038162231445312500000000000000000000000000000000e-30"), + cpp_dec_float("1.262177448353618888658765704452457967477130296174436807632446289062500000000000000000000000000000000e-29"), + cpp_dec_float("2.524354896707237777317531408904915934954260592348873615264892578125000000000000000000000000000000000e-29"), + cpp_dec_float("5.048709793414475554635062817809831869908521184697747230529785156250000000000000000000000000000000000e-29"), + cpp_dec_float("1.009741958682895110927012563561966373981704236939549446105957031250000000000000000000000000000000000e-28"), + cpp_dec_float("2.019483917365790221854025127123932747963408473879098892211914062500000000000000000000000000000000000e-28"), + cpp_dec_float("4.038967834731580443708050254247865495926816947758197784423828125000000000000000000000000000000000000e-28"), + cpp_dec_float("8.077935669463160887416100508495730991853633895516395568847656250000000000000000000000000000000000000e-28"), + cpp_dec_float("1.615587133892632177483220101699146198370726779103279113769531250000000000000000000000000000000000000e-27"), + cpp_dec_float("3.231174267785264354966440203398292396741453558206558227539062500000000000000000000000000000000000000e-27"), + cpp_dec_float("6.462348535570528709932880406796584793482907116413116455078125000000000000000000000000000000000000000e-27"), + cpp_dec_float("1.292469707114105741986576081359316958696581423282623291015625000000000000000000000000000000000000000e-26"), + cpp_dec_float("2.584939414228211483973152162718633917393162846565246582031250000000000000000000000000000000000000000e-26"), + cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"), + cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"), + cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"), + cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"), + cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"), + cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"), + cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"), + cpp_dec_float("6.617444900424221398971269536559702828526496887207031250000000000000000000000000000000000000000000000e-24"), + cpp_dec_float("1.323488980084844279794253907311940565705299377441406250000000000000000000000000000000000000000000000e-23"), + cpp_dec_float("2.646977960169688559588507814623881131410598754882812500000000000000000000000000000000000000000000000e-23"), + cpp_dec_float("5.293955920339377119177015629247762262821197509765625000000000000000000000000000000000000000000000000e-23"), + cpp_dec_float("1.058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000e-22"), + cpp_dec_float("2.117582368135750847670806251699104905128479003906250000000000000000000000000000000000000000000000000e-22"), + cpp_dec_float("4.235164736271501695341612503398209810256958007812500000000000000000000000000000000000000000000000000e-22"), + cpp_dec_float("8.470329472543003390683225006796419620513916015625000000000000000000000000000000000000000000000000000e-22"), + cpp_dec_float("1.694065894508600678136645001359283924102783203125000000000000000000000000000000000000000000000000000e-21"), + cpp_dec_float("3.388131789017201356273290002718567848205566406250000000000000000000000000000000000000000000000000000e-21"), + cpp_dec_float("6.776263578034402712546580005437135696411132812500000000000000000000000000000000000000000000000000000e-21"), + cpp_dec_float("1.355252715606880542509316001087427139282226562500000000000000000000000000000000000000000000000000000e-20"), + cpp_dec_float("2.710505431213761085018632002174854278564453125000000000000000000000000000000000000000000000000000000e-20"), + cpp_dec_float("5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20"), + cpp_dec_float("1.084202172485504434007452800869941711425781250000000000000000000000000000000000000000000000000000000e-19"), + cpp_dec_float("2.168404344971008868014905601739883422851562500000000000000000000000000000000000000000000000000000000e-19"), + cpp_dec_float("4.336808689942017736029811203479766845703125000000000000000000000000000000000000000000000000000000000e-19"), + cpp_dec_float("8.673617379884035472059622406959533691406250000000000000000000000000000000000000000000000000000000000e-19"), + cpp_dec_float("1.734723475976807094411924481391906738281250000000000000000000000000000000000000000000000000000000000e-18"), + cpp_dec_float("3.469446951953614188823848962783813476562500000000000000000000000000000000000000000000000000000000000e-18"), + cpp_dec_float("6.938893903907228377647697925567626953125000000000000000000000000000000000000000000000000000000000000e-18"), + cpp_dec_float("1.387778780781445675529539585113525390625000000000000000000000000000000000000000000000000000000000000e-17"), + cpp_dec_float("2.775557561562891351059079170227050781250000000000000000000000000000000000000000000000000000000000000e-17"), + cpp_dec_float("5.551115123125782702118158340454101562500000000000000000000000000000000000000000000000000000000000000e-17"), + cpp_dec_float("1.110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000000000e-16"), + cpp_dec_float("2.220446049250313080847263336181640625000000000000000000000000000000000000000000000000000000000000000e-16"), + cpp_dec_float("4.440892098500626161694526672363281250000000000000000000000000000000000000000000000000000000000000000e-16"), + cpp_dec_float("8.881784197001252323389053344726562500000000000000000000000000000000000000000000000000000000000000000e-16"), + cpp_dec_float("1.776356839400250464677810668945312500000000000000000000000000000000000000000000000000000000000000000e-15"), + cpp_dec_float("3.552713678800500929355621337890625000000000000000000000000000000000000000000000000000000000000000000e-15"), + cpp_dec_float("7.105427357601001858711242675781250000000000000000000000000000000000000000000000000000000000000000000e-15"), + cpp_dec_float("1.421085471520200371742248535156250000000000000000000000000000000000000000000000000000000000000000000e-14"), + cpp_dec_float("2.842170943040400743484497070312500000000000000000000000000000000000000000000000000000000000000000000e-14"), + cpp_dec_float("5.684341886080801486968994140625000000000000000000000000000000000000000000000000000000000000000000000e-14"), + cpp_dec_float("1.136868377216160297393798828125000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"), + cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"), + cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), + cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), + cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), + cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), + cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), + cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), + cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), + cpp_dec_float("0.125"), + cpp_dec_float("0.25"), + cpp_dec_float("0.5"), + one(), + two(), + cpp_dec_float(static_cast<unsigned long long>(4)), + cpp_dec_float(static_cast<unsigned long long>(8)), + cpp_dec_float(static_cast<unsigned long long>(16)), + cpp_dec_float(static_cast<unsigned long long>(32)), + cpp_dec_float(static_cast<unsigned long long>(64)), + cpp_dec_float(static_cast<unsigned long long>(128)), + cpp_dec_float(static_cast<unsigned long long>(256)), + cpp_dec_float(static_cast<unsigned long long>(512)), + cpp_dec_float(static_cast<unsigned long long>(1024)), + cpp_dec_float(static_cast<unsigned long long>(2048)), + cpp_dec_float(static_cast<unsigned long long>(4096)), + cpp_dec_float(static_cast<unsigned long long>(8192)), + cpp_dec_float(static_cast<unsigned long long>(16384)), + cpp_dec_float(static_cast<unsigned long long>(32768)), + cpp_dec_float(static_cast<unsigned long long>(65536)), + cpp_dec_float(static_cast<unsigned long long>(131072)), + cpp_dec_float(static_cast<unsigned long long>(262144)), + cpp_dec_float(static_cast<unsigned long long>(524288)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 20u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 21u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 22u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 23u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 24u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 25u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 26u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 27u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 28u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 29u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 30u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uL << 31u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 32u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 33u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 34u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 35u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 36u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 37u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 38u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 39u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 40u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 41u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 42u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 43u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 44u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 45u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 46u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 47u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 48u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 49u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 50u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 51u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 52u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 53u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 54u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 55u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 56u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 57u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 58u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 59u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 60u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 61u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 62u)), + cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 63u)), + cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), + cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), + cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), + cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"), + cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"), + cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"), + cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"), + cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"), + cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"), + cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"), + cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"), + cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"), + cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"), + cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"), + cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"), + cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"), + cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"), + cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"), + cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), + cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") + }}; + + if((p > static_cast<long long>(-128)) && (p < static_cast<long long>(+128))) + { + return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))]; + } + else + { + // Compute and return 2^p. + if(p < static_cast<long long>(0)) + { + return pow2(static_cast<long long>(-p)).calculate_inv(); + } + else + { + cpp_dec_float<Digits10, ExponentType, Allocator> t; + default_ops::detail::pow_imp(t, two(), p, mpl::true_()); + return t; + } + } +} + + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) +{ + result += o; +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) +{ + result -= o; +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) +{ + result *= o; +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) +{ + result /= o; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o) +{ + result.add_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o) +{ + result.sub_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o) +{ + result.mul_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const unsigned long long& o) +{ + result.div_unsigned_long_long(o); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) +{ + if(o < 0) + result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); + else + result.add_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) +{ + if(o < 0) + result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); + else + result.sub_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) +{ + if(o < 0) + { + result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); + result.negate(); + } + else + result.mul_unsigned_long_long(o); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) +{ + if(o < 0) + { + result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); + result.negate(); + } + else + result.div_unsigned_long_long(o); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_convert_to(unsigned long long* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + *result = val.extract_unsigned_long_long(); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_convert_to(long long* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + *result = val.extract_signed_long_long(); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_convert_to(long double* result, cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + *result = val.extract_long_double(); +} + +// +// Non member function support: +// +template <unsigned Digits10, class ExponentType, class Allocator> +inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + if((x.isinf)()) + return FP_INFINITE; + if((x.isnan)()) + return FP_NAN; + if(x.iszero()) + return FP_ZERO; + return FP_NORMAL; +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + result = x; + if(x.isneg()) + result.negate(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + result = x; + result.calculate_sqrt(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + result = x; + if(!(x.isfinite)() || x.isint()) + { + return; + } + + if(x.isneg()) + result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one(); + result = result.extract_integer_part(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + result = x; + if(!(x.isfinite)() || x.isint()) + { + return; + } + + if(!x.isneg()) + result += cpp_dec_float<Digits10, ExponentType, Allocator>::one(); + result = result.extract_integer_part(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) +{ + if(!(x.isfinite)()) + { + result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number<cpp_dec_float<Digits10, ExponentType, Allocator> >(x), number<cpp_dec_float<Digits10, ExponentType, Allocator> >(x), boost::math::policies::policy<>()).backend(); + return; + } + else if(x.isint()) + { + result = x; + return; + } + result = x.extract_integer_part(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + // Set result, to the exponent of val: + return val.order(); +} +template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> +inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_) +{ + using default_ops::eval_multiply; + const ExponentType e = e_; + cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e); + eval_multiply(result, val, t); +} + +template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> +inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e) +{ + const long long the_exp = static_cast<long long>(e); + + if((the_exp > (std::numeric_limits<ExponentType>::max)()) || (the_exp < (std::numeric_limits<ExponentType>::min)())) + BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range."))); + + result = x; + + if ((the_exp > static_cast<long long>(-std::numeric_limits<long long>::digits)) && (the_exp < static_cast<long long>(0))) + result.div_unsigned_long_long(1ULL << static_cast<long long>(-the_exp)); + else if((the_exp < static_cast<long long>( std::numeric_limits<long long>::digits)) && (the_exp > static_cast<long long>(0))) + result.mul_unsigned_long_long(1ULL << the_exp); + else if(the_exp != static_cast<long long>(0)) + result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e) +{ + result = x; + if(result.isneg()) + result.negate(); + + if(result.iszero()) + { + *e = 0; + return; + } + + ExponentType t = result.order(); + BOOST_MP_USING_ABS + if(abs(t) < ((std::numeric_limits<ExponentType>::max)() / 1000)) + { + t *= 1000; + t /= 301; + } + else + { + t /= 301; + t *= 1000; + } + + result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); + + if(result.iszero() || (result.isinf)() || (result.isnan)()) + { + // pow2 overflowed, slip the calculation up: + result = x; + if(result.isneg()) + result.negate(); + t /= 2; + result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); + } + BOOST_MP_USING_ABS + if(abs(result.order()) > 5) + { + // If our first estimate doesn't get close enough then try recursion until we do: + ExponentType e2; + cpp_dec_float<Digits10, ExponentType, Allocator> r2; + eval_frexp(r2, result, &e2); + // overflow protection: + if((t > 0) && (e2 > 0) && (t > (std::numeric_limits<ExponentType>::max)() - e2)) + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); + if((t < 0) && (e2 < 0) && (t < (std::numeric_limits<ExponentType>::min)() - e2)) + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); + t += e2; + result = r2; + } + + while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0) + { + result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); + ++t; + } + while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0) + { + result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); + --t; + } + *e = t; + if(x.isneg()) + result.negate(); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline typename disable_if<is_same<ExponentType, int> >::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e) +{ + ExponentType t; + eval_frexp(result, x, &t); + if((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)())) + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int")); + *e = static_cast<int>(t); +} + +template <unsigned Digits10, class ExponentType, class Allocator> +inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + return val.iszero(); +} +template <unsigned Digits10, class ExponentType, class Allocator> +inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) +{ + return val.iszero() ? 0 : val.isneg() ? -1 : 1; +} + +} // namespace backends + +using boost::multiprecision::backends::cpp_dec_float; + + +typedef number<cpp_dec_float<50> > cpp_dec_float_50; +typedef number<cpp_dec_float<100> > cpp_dec_float_100; + +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template<unsigned D1, class E1, class A1, unsigned D2, class E2, class A2> +struct is_explicitly_convertible<cpp_dec_float<D1, E1, A1>, cpp_dec_float<D2, E2, A2> > : public mpl::true_ {}; + +} + +#endif + + +}} + +namespace std +{ + template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> + class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> > + { + public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; + BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_total_digits10; + BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int. + BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int. + BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; + BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_indeterminate; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + BOOST_STATIC_CONSTEXPR bool traps = false; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (min) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (max) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> lowest () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> epsilon () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error () { return 0.5L; } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> infinity () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> quiet_NaN () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> signaling_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } + BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> denorm_min () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } + }; + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before; +template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style; + +#endif +} + +namespace boost{ namespace math{ + +namespace policies{ + +template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates> +struct precision< boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy> +{ + // Define a local copy of cpp_dec_float_digits10 because it might differ + // from the template parameter Digits10 for small or large digit counts. + static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; + + typedef typename Policy::precision_type precision_type; + typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2; + typedef typename mpl::if_c< + ((digits_2::value <= precision_type::value) + || (Policy::precision_type::value <= 0)), + // Default case, full precision for RealType: + digits_2, + // User customized precision: + precision_type + >::type type; +}; + +} // namespace policies + +}} // namespaces boost::math + +#endif |