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Diffstat (limited to 'boost/math/bindings/e_float.hpp')
-rw-r--r-- | boost/math/bindings/e_float.hpp | 803 |
1 files changed, 803 insertions, 0 deletions
diff --git a/boost/math/bindings/e_float.hpp b/boost/math/bindings/e_float.hpp new file mode 100644 index 0000000000..959bff109b --- /dev/null +++ b/boost/math/bindings/e_float.hpp @@ -0,0 +1,803 @@ +// Copyright John Maddock 2008. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Wrapper that works with mpfr_class defined in gmpfrxx.h +// See http://math.berkeley.edu/~wilken/code/gmpfrxx/ +// Also requires the gmp and mpfr libraries. +// + +#ifndef BOOST_MATH_E_FLOAT_BINDINGS_HPP +#define BOOST_MATH_E_FLOAT_BINDINGS_HPP + +#include <boost/config.hpp> + + +#include <e_float/e_float.h> +#include <functions/functions.h> + +#include <boost/math/tools/precision.hpp> +#include <boost/math/tools/real_cast.hpp> +#include <boost/math/policies/policy.hpp> +#include <boost/math/distributions/fwd.hpp> +#include <boost/math/special_functions/math_fwd.hpp> +#include <boost/math/special_functions/fpclassify.hpp> +#include <boost/math/bindings/detail/big_digamma.hpp> +#include <boost/math/bindings/detail/big_lanczos.hpp> + + +namespace boost{ namespace math{ namespace ef{ + +class e_float +{ +public: + // Constructors: + e_float() {} + e_float(const ::e_float& c) : m_value(c){} + e_float(char c) + { + m_value = ::e_float(c); + } +#ifndef BOOST_NO_INTRINSIC_WCHAR_T + e_float(wchar_t c) + { + m_value = ::e_float(c); + } +#endif + e_float(unsigned char c) + { + m_value = ::e_float(c); + } + e_float(signed char c) + { + m_value = ::e_float(c); + } + e_float(unsigned short c) + { + m_value = ::e_float(c); + } + e_float(short c) + { + m_value = ::e_float(c); + } + e_float(unsigned int c) + { + m_value = ::e_float(c); + } + e_float(int c) + { + m_value = ::e_float(c); + } + e_float(unsigned long c) + { + m_value = ::e_float((UINT64)c); + } + e_float(long c) + { + m_value = ::e_float((INT64)c); + } +#ifdef BOOST_HAS_LONG_LONG + e_float(boost::ulong_long_type c) + { + m_value = ::e_float(c); + } + e_float(boost::long_long_type c) + { + m_value = ::e_float(c); + } +#endif + e_float(float c) + { + assign_large_real(c); + } + e_float(double c) + { + assign_large_real(c); + } + e_float(long double c) + { + assign_large_real(c); + } + + // Assignment: + e_float& operator=(char c) { m_value = ::e_float(c); return *this; } + e_float& operator=(unsigned char c) { m_value = ::e_float(c); return *this; } + e_float& operator=(signed char c) { m_value = ::e_float(c); return *this; } +#ifndef BOOST_NO_INTRINSIC_WCHAR_T + e_float& operator=(wchar_t c) { m_value = ::e_float(c); return *this; } +#endif + e_float& operator=(short c) { m_value = ::e_float(c); return *this; } + e_float& operator=(unsigned short c) { m_value = ::e_float(c); return *this; } + e_float& operator=(int c) { m_value = ::e_float(c); return *this; } + e_float& operator=(unsigned int c) { m_value = ::e_float(c); return *this; } + e_float& operator=(long c) { m_value = ::e_float((INT64)c); return *this; } + e_float& operator=(unsigned long c) { m_value = ::e_float((UINT64)c); return *this; } +#ifdef BOOST_HAS_LONG_LONG + e_float& operator=(boost::long_long_type c) { m_value = ::e_float(c); return *this; } + e_float& operator=(boost::ulong_long_type c) { m_value = ::e_float(c); return *this; } +#endif + e_float& operator=(float c) { assign_large_real(c); return *this; } + e_float& operator=(double c) { assign_large_real(c); return *this; } + e_float& operator=(long double c) { assign_large_real(c); return *this; } + + // Access: + ::e_float& value(){ return m_value; } + ::e_float const& value()const{ return m_value; } + + // Member arithmetic: + e_float& operator+=(const e_float& other) + { m_value += other.value(); return *this; } + e_float& operator-=(const e_float& other) + { m_value -= other.value(); return *this; } + e_float& operator*=(const e_float& other) + { m_value *= other.value(); return *this; } + e_float& operator/=(const e_float& other) + { m_value /= other.value(); return *this; } + e_float operator-()const + { return -m_value; } + e_float const& operator+()const + { return *this; } + +private: + ::e_float m_value; + + template <class V> + void assign_large_real(const V& a) + { + using std::frexp; + using std::ldexp; + using std::floor; + if (a == 0) { + m_value = ::ef::zero(); + return; + } + + if (a == 1) { + m_value = ::ef::one(); + return; + } + + if ((boost::math::isinf)(a)) + { + m_value = a > 0 ? m_value.my_value_inf() : -m_value.my_value_inf(); + return; + } + if((boost::math::isnan)(a)) + { + m_value = m_value.my_value_nan(); + return; + } + + int e; + long double f, term; + ::e_float t; + m_value = ::ef::zero(); + + f = frexp(a, &e); + + ::e_float shift = ::ef::pow2(30); + + while(f) + { + // extract 30 bits from f: + f = ldexp(f, 30); + term = floor(f); + e -= 30; + m_value *= shift; + m_value += ::e_float(static_cast<INT64>(term)); + f -= term; + } + m_value *= ::ef::pow2(e); + } +}; + + +// Non-member arithmetic: +inline e_float operator+(const e_float& a, const e_float& b) +{ + e_float result(a); + result += b; + return result; +} +inline e_float operator-(const e_float& a, const e_float& b) +{ + e_float result(a); + result -= b; + return result; +} +inline e_float operator*(const e_float& a, const e_float& b) +{ + e_float result(a); + result *= b; + return result; +} +inline e_float operator/(const e_float& a, const e_float& b) +{ + e_float result(a); + result /= b; + return result; +} + +// Comparison: +inline bool operator == (const e_float& a, const e_float& b) +{ return a.value() == b.value() ? true : false; } +inline bool operator != (const e_float& a, const e_float& b) +{ return a.value() != b.value() ? true : false;} +inline bool operator < (const e_float& a, const e_float& b) +{ return a.value() < b.value() ? true : false; } +inline bool operator <= (const e_float& a, const e_float& b) +{ return a.value() <= b.value() ? true : false; } +inline bool operator > (const e_float& a, const e_float& b) +{ return a.value() > b.value() ? true : false; } +inline bool operator >= (const e_float& a, const e_float& b) +{ return a.value() >= b.value() ? true : false; } + +std::istream& operator >> (std::istream& is, e_float& f) +{ + return is >> f.value(); +} + +std::ostream& operator << (std::ostream& os, const e_float& f) +{ + return os << f.value(); +} + +inline e_float fabs(const e_float& v) +{ + return ::ef::fabs(v.value()); +} + +inline e_float abs(const e_float& v) +{ + return ::ef::fabs(v.value()); +} + +inline e_float floor(const e_float& v) +{ + return ::ef::floor(v.value()); +} + +inline e_float ceil(const e_float& v) +{ + return ::ef::ceil(v.value()); +} + +inline e_float pow(const e_float& v, const e_float& w) +{ + return ::ef::pow(v.value(), w.value()); +} + +inline e_float pow(const e_float& v, int i) +{ + return ::ef::pow(v.value(), ::e_float(i)); +} + +inline e_float exp(const e_float& v) +{ + return ::ef::exp(v.value()); +} + +inline e_float log(const e_float& v) +{ + return ::ef::log(v.value()); +} + +inline e_float sqrt(const e_float& v) +{ + return ::ef::sqrt(v.value()); +} + +inline e_float sin(const e_float& v) +{ + return ::ef::sin(v.value()); +} + +inline e_float cos(const e_float& v) +{ + return ::ef::cos(v.value()); +} + +inline e_float tan(const e_float& v) +{ + return ::ef::tan(v.value()); +} + +inline e_float acos(const e_float& v) +{ + return ::ef::acos(v.value()); +} + +inline e_float asin(const e_float& v) +{ + return ::ef::asin(v.value()); +} + +inline e_float atan(const e_float& v) +{ + return ::ef::atan(v.value()); +} + +inline e_float ldexp(const e_float& v, int e) +{ + return v.value() * ::ef::pow2(e); +} + +inline e_float frexp(const e_float& v, int* expon) +{ + double d; + INT64 i; + v.value().extract_parts(d, i); + *expon = static_cast<int>(i); + return v.value() * ::ef::pow2(-i); +} + +inline e_float sinh (const e_float& x) +{ + return ::ef::sinh(x.value()); +} + +inline e_float cosh (const e_float& x) +{ + return ::ef::cosh(x.value()); +} + +inline e_float tanh (const e_float& x) +{ + return ::ef::tanh(x.value()); +} + +inline e_float asinh (const e_float& x) +{ + return ::ef::asinh(x.value()); +} + +inline e_float acosh (const e_float& x) +{ + return ::ef::acosh(x.value()); +} + +inline e_float atanh (const e_float& x) +{ + return ::ef::atanh(x.value()); +} + +e_float fmod(const e_float& v1, const e_float& v2) +{ + e_float n; + if(v1 < 0) + n = ceil(v1 / v2); + else + n = floor(v1 / v2); + return v1 - n * v2; +} + +} namespace detail{ + +template <> +inline int fpclassify_imp< boost::math::ef::e_float> BOOST_NO_MACRO_EXPAND(boost::math::ef::e_float x, const generic_tag<true>&) +{ + if(x.value().isnan()) + return FP_NAN; + if(x.value().isinf()) + return FP_INFINITE; + if(x == 0) + return FP_ZERO; + return FP_NORMAL; +} + +} namespace ef{ + +template <class Policy> +inline int itrunc(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::trunc(v, pol); + if(fabs(r) > (std::numeric_limits<int>::max)()) + return static_cast<int>(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, 0, v, pol)); + return static_cast<int>(r.value().extract_int64()); +} + +template <class Policy> +inline long ltrunc(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::trunc(v, pol); + if(fabs(r) > (std::numeric_limits<long>::max)()) + return static_cast<long>(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, 0L, v, pol)); + return static_cast<long>(r.value().extract_int64()); +} + +#ifdef BOOST_HAS_LONG_LONG +template <class Policy> +inline boost::long_long_type lltrunc(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::trunc(v, pol); + if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)()) + return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64()); + return static_cast<boost::long_long_type>(r.value().extract_int64()); +} +#endif + +template <class Policy> +inline int iround(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::round(v, pol); + if(fabs(r) > (std::numeric_limits<int>::max)()) + return static_cast<int>(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).value().extract_int64()); + return static_cast<int>(r.value().extract_int64()); +} + +template <class Policy> +inline long lround(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::round(v, pol); + if(fabs(r) > (std::numeric_limits<long>::max)()) + return static_cast<long int>(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).value().extract_int64()); + return static_cast<long int>(r.value().extract_int64()); +} + +#ifdef BOOST_HAS_LONG_LONG +template <class Policy> +inline boost::long_long_type llround(const e_float& v, const Policy& pol) +{ + BOOST_MATH_STD_USING + e_float r = boost::math::round(v, pol); + if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)()) + return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64()); + return static_cast<boost::long_long_type>(r.value().extract_int64()); +} +#endif + +}}} + +namespace std{ + + template<> + class numeric_limits< ::boost::math::ef::e_float> : public numeric_limits< ::e_float> + { + public: + static const ::boost::math::ef::e_float (min) (void) + { + return (numeric_limits< ::e_float>::min)(); + } + static const ::boost::math::ef::e_float (max) (void) + { + return (numeric_limits< ::e_float>::max)(); + } + static const ::boost::math::ef::e_float epsilon (void) + { + return (numeric_limits< ::e_float>::epsilon)(); + } + static const ::boost::math::ef::e_float round_error(void) + { + return (numeric_limits< ::e_float>::round_error)(); + } + static const ::boost::math::ef::e_float infinity (void) + { + return (numeric_limits< ::e_float>::infinity)(); + } + static const ::boost::math::ef::e_float quiet_NaN (void) + { + return (numeric_limits< ::e_float>::quiet_NaN)(); + } + // + // e_float's supplied digits member is wrong + // - it should be same the same as digits 10 + // - given that radix is 10. + // + static const int digits = digits10; + }; + +} // namespace std + +namespace boost{ namespace math{ + +namespace policies{ + +template <class Policy> +struct precision< ::boost::math::ef::e_float, Policy> +{ + typedef typename Policy::precision_type precision_type; + typedef digits2<((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L> 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 customised precision: + precision_type + >::type type; +}; + +} + +namespace tools{ + +template <> +inline int digits< ::boost::math::ef::e_float>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC( ::boost::math::ef::e_float)) +{ + return ((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L; +} + +template <> +inline ::boost::math::ef::e_float root_epsilon< ::boost::math::ef::e_float>() +{ + return detail::root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>()); +} + +template <> +inline ::boost::math::ef::e_float forth_root_epsilon< ::boost::math::ef::e_float>() +{ + return detail::forth_root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>()); +} + +} + +namespace lanczos{ + +template<class Policy> +struct lanczos<boost::math::ef::e_float, Policy> +{ + typedef typename mpl::if_c< + std::numeric_limits< ::e_float>::digits10 < 22, + lanczos13UDT, + typename mpl::if_c< + std::numeric_limits< ::e_float>::digits10 < 36, + lanczos22UDT, + typename mpl::if_c< + std::numeric_limits< ::e_float>::digits10 < 50, + lanczos31UDT, + typename mpl::if_c< + std::numeric_limits< ::e_float>::digits10 < 110, + lanczos61UDT, + undefined_lanczos + >::type + >::type + >::type + >::type type; +}; + +} // namespace lanczos + +template <class Policy> +inline boost::math::ef::e_float skewness(const extreme_value_distribution<boost::math::ef::e_float, Policy>& /*dist*/) +{ + // + // This is 12 * sqrt(6) * zeta(3) / pi^3: + // See http://mathworld.wolfram.com/ExtremeValueDistribution.html + // + return boost::lexical_cast<boost::math::ef::e_float>("1.1395470994046486574927930193898461120875997958366"); +} + +template <class Policy> +inline boost::math::ef::e_float skewness(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/) +{ + // using namespace boost::math::constants; + return boost::lexical_cast<boost::math::ef::e_float>("0.63111065781893713819189935154422777984404221106391"); + // Computed using NTL at 150 bit, about 50 decimal digits. + // return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>(); +} + +template <class Policy> +inline boost::math::ef::e_float kurtosis(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/) +{ + // using namespace boost::math::constants; + return boost::lexical_cast<boost::math::ef::e_float>("3.2450893006876380628486604106197544154170667057995"); + // Computed using NTL at 150 bit, about 50 decimal digits. + // return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) / + // (four_minus_pi<RealType>() * four_minus_pi<RealType>()); +} + +template <class Policy> +inline boost::math::ef::e_float kurtosis_excess(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/) +{ + //using namespace boost::math::constants; + // Computed using NTL at 150 bit, about 50 decimal digits. + return boost::lexical_cast<boost::math::ef::e_float>("0.2450893006876380628486604106197544154170667057995"); + // return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) / + // (four_minus_pi<RealType>() * four_minus_pi<RealType>()); +} // kurtosis + +namespace detail{ + +// +// Version of Digamma accurate to ~100 decimal digits. +// +template <class Policy> +boost::math::ef::e_float digamma_imp(boost::math::ef::e_float x, const mpl::int_<0>* , const Policy& pol) +{ + // + // This handles reflection of negative arguments, and all our + // eboost::math::ef::e_floator handling, then forwards to the T-specific approximation. + // + BOOST_MATH_STD_USING // ADL of std functions. + + boost::math::ef::e_float result = 0; + // + // Check for negative arguments and use reflection: + // + if(x < 0) + { + // Reflect: + x = 1 - x; + // Argument reduction for tan: + boost::math::ef::e_float remainder = x - floor(x); + // Shift to negative if > 0.5: + if(remainder > 0.5) + { + remainder -= 1; + } + // + // check for evaluation at a negative pole: + // + if(remainder == 0) + { + return policies::raise_pole_error<boost::math::ef::e_float>("boost::math::digamma<%1%>(%1%)", 0, (1-x), pol); + } + result = constants::pi<boost::math::ef::e_float>() / tan(constants::pi<boost::math::ef::e_float>() * remainder); + } + result += big_digamma(x); + return result; +} +boost::math::ef::e_float bessel_i0(boost::math::ef::e_float x) +{ + static const boost::math::ef::e_float P1[] = { + boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375249e+15"), + boost::lexical_cast<boost::math::ef::e_float>("-5.5050369673018427753e+14"), + boost::lexical_cast<boost::math::ef::e_float>("-3.2940087627407749166e+13"), + boost::lexical_cast<boost::math::ef::e_float>("-8.4925101247114157499e+11"), + boost::lexical_cast<boost::math::ef::e_float>("-1.1912746104985237192e+10"), + boost::lexical_cast<boost::math::ef::e_float>("-1.0313066708737980747e+08"), + boost::lexical_cast<boost::math::ef::e_float>("-5.9545626019847898221e+05"), + boost::lexical_cast<boost::math::ef::e_float>("-2.4125195876041896775e+03"), + boost::lexical_cast<boost::math::ef::e_float>("-7.0935347449210549190e+00"), + boost::lexical_cast<boost::math::ef::e_float>("-1.5453977791786851041e-02"), + boost::lexical_cast<boost::math::ef::e_float>("-2.5172644670688975051e-05"), + boost::lexical_cast<boost::math::ef::e_float>("-3.0517226450451067446e-08"), + boost::lexical_cast<boost::math::ef::e_float>("-2.6843448573468483278e-11"), + boost::lexical_cast<boost::math::ef::e_float>("-1.5982226675653184646e-14"), + boost::lexical_cast<boost::math::ef::e_float>("-5.2487866627945699800e-18"), + }; + static const boost::math::ef::e_float Q1[] = { + boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375245e+15"), + boost::lexical_cast<boost::math::ef::e_float>("7.8858692566751002988e+12"), + boost::lexical_cast<boost::math::ef::e_float>("-1.2207067397808979846e+10"), + boost::lexical_cast<boost::math::ef::e_float>("1.0377081058062166144e+07"), + boost::lexical_cast<boost::math::ef::e_float>("-4.8527560179962773045e+03"), + boost::lexical_cast<boost::math::ef::e_float>("1.0"), + }; + static const boost::math::ef::e_float P2[] = { + boost::lexical_cast<boost::math::ef::e_float>("-2.2210262233306573296e-04"), + boost::lexical_cast<boost::math::ef::e_float>("1.3067392038106924055e-02"), + boost::lexical_cast<boost::math::ef::e_float>("-4.4700805721174453923e-01"), + boost::lexical_cast<boost::math::ef::e_float>("5.5674518371240761397e+00"), + boost::lexical_cast<boost::math::ef::e_float>("-2.3517945679239481621e+01"), + boost::lexical_cast<boost::math::ef::e_float>("3.1611322818701131207e+01"), + boost::lexical_cast<boost::math::ef::e_float>("-9.6090021968656180000e+00"), + }; + static const boost::math::ef::e_float Q2[] = { + boost::lexical_cast<boost::math::ef::e_float>("-5.5194330231005480228e-04"), + boost::lexical_cast<boost::math::ef::e_float>("3.2547697594819615062e-02"), + boost::lexical_cast<boost::math::ef::e_float>("-1.1151759188741312645e+00"), + boost::lexical_cast<boost::math::ef::e_float>("1.3982595353892851542e+01"), + boost::lexical_cast<boost::math::ef::e_float>("-6.0228002066743340583e+01"), + boost::lexical_cast<boost::math::ef::e_float>("8.5539563258012929600e+01"), + boost::lexical_cast<boost::math::ef::e_float>("-3.1446690275135491500e+01"), + boost::lexical_cast<boost::math::ef::e_float>("1.0"), + }; + boost::math::ef::e_float value, factor, r; + + BOOST_MATH_STD_USING + using namespace boost::math::tools; + + if (x < 0) + { + x = -x; // even function + } + if (x == 0) + { + return static_cast<boost::math::ef::e_float>(1); + } + if (x <= 15) // x in (0, 15] + { + boost::math::ef::e_float y = x * x; + value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); + } + else // x in (15, \infty) + { + boost::math::ef::e_float y = 1 / x - 1 / 15; + r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); + factor = exp(x) / sqrt(x); + value = factor * r; + } + + return value; +} + +boost::math::ef::e_float bessel_i1(boost::math::ef::e_float x) +{ + static const boost::math::ef::e_float P1[] = { + lexical_cast<boost::math::ef::e_float>("-1.4577180278143463643e+15"), + lexical_cast<boost::math::ef::e_float>("-1.7732037840791591320e+14"), + lexical_cast<boost::math::ef::e_float>("-6.9876779648010090070e+12"), + lexical_cast<boost::math::ef::e_float>("-1.3357437682275493024e+11"), + lexical_cast<boost::math::ef::e_float>("-1.4828267606612366099e+09"), + lexical_cast<boost::math::ef::e_float>("-1.0588550724769347106e+07"), + lexical_cast<boost::math::ef::e_float>("-5.1894091982308017540e+04"), + lexical_cast<boost::math::ef::e_float>("-1.8225946631657315931e+02"), + lexical_cast<boost::math::ef::e_float>("-4.7207090827310162436e-01"), + lexical_cast<boost::math::ef::e_float>("-9.1746443287817501309e-04"), + lexical_cast<boost::math::ef::e_float>("-1.3466829827635152875e-06"), + lexical_cast<boost::math::ef::e_float>("-1.4831904935994647675e-09"), + lexical_cast<boost::math::ef::e_float>("-1.1928788903603238754e-12"), + lexical_cast<boost::math::ef::e_float>("-6.5245515583151902910e-16"), + lexical_cast<boost::math::ef::e_float>("-1.9705291802535139930e-19"), + }; + static const boost::math::ef::e_float Q1[] = { + lexical_cast<boost::math::ef::e_float>("-2.9154360556286927285e+15"), + lexical_cast<boost::math::ef::e_float>("9.7887501377547640438e+12"), + lexical_cast<boost::math::ef::e_float>("-1.4386907088588283434e+10"), + lexical_cast<boost::math::ef::e_float>("1.1594225856856884006e+07"), + lexical_cast<boost::math::ef::e_float>("-5.1326864679904189920e+03"), + lexical_cast<boost::math::ef::e_float>("1.0"), + }; + static const boost::math::ef::e_float P2[] = { + lexical_cast<boost::math::ef::e_float>("1.4582087408985668208e-05"), + lexical_cast<boost::math::ef::e_float>("-8.9359825138577646443e-04"), + lexical_cast<boost::math::ef::e_float>("2.9204895411257790122e-02"), + lexical_cast<boost::math::ef::e_float>("-3.4198728018058047439e-01"), + lexical_cast<boost::math::ef::e_float>("1.3960118277609544334e+00"), + lexical_cast<boost::math::ef::e_float>("-1.9746376087200685843e+00"), + lexical_cast<boost::math::ef::e_float>("8.5591872901933459000e-01"), + lexical_cast<boost::math::ef::e_float>("-6.0437159056137599999e-02"), + }; + static const boost::math::ef::e_float Q2[] = { + lexical_cast<boost::math::ef::e_float>("3.7510433111922824643e-05"), + lexical_cast<boost::math::ef::e_float>("-2.2835624489492512649e-03"), + lexical_cast<boost::math::ef::e_float>("7.4212010813186530069e-02"), + lexical_cast<boost::math::ef::e_float>("-8.5017476463217924408e-01"), + lexical_cast<boost::math::ef::e_float>("3.2593714889036996297e+00"), + lexical_cast<boost::math::ef::e_float>("-3.8806586721556593450e+00"), + lexical_cast<boost::math::ef::e_float>("1.0"), + }; + boost::math::ef::e_float value, factor, r, w; + + BOOST_MATH_STD_USING + using namespace boost::math::tools; + + w = abs(x); + if (x == 0) + { + return static_cast<boost::math::ef::e_float>(0); + } + if (w <= 15) // w in (0, 15] + { + boost::math::ef::e_float y = x * x; + r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); + factor = w; + value = factor * r; + } + else // w in (15, \infty) + { + boost::math::ef::e_float y = 1 / w - boost::math::ef::e_float(1) / 15; + r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); + factor = exp(w) / sqrt(w); + value = factor * r; + } + + if (x < 0) + { + value *= -value; // odd function + } + return value; +} + +} // namespace detail + +}} +#endif // BOOST_MATH_E_FLOAT_BINDINGS_HPP + |