// (C) Copyright John Maddock 2006. | |
// Use, modification and distribution are subject to the | |
// Boost Software License, Version 1.0. (See accompanying file | |
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
#ifndef BOOST_MATH_EXPM1_INCLUDED | |
#define BOOST_MATH_EXPM1_INCLUDED | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/config/no_tr1/cmath.hpp> | |
#include <math.h> // platform's ::expm1 | |
#include <boost/limits.hpp> | |
#include <boost/math/tools/config.hpp> | |
#include <boost/math/tools/series.hpp> | |
#include <boost/math/tools/precision.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
#include <boost/math/tools/rational.hpp> | |
#include <boost/math/special_functions/math_fwd.hpp> | |
#include <boost/mpl/less_equal.hpp> | |
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS | |
# include <boost/static_assert.hpp> | |
#else | |
# include <boost/assert.hpp> | |
#endif | |
namespace boost{ namespace math{ | |
namespace detail | |
{ | |
// Functor expm1_series returns the next term in the Taylor series | |
// x^k / k! | |
// each time that operator() is invoked. | |
// | |
template <class T> | |
struct expm1_series | |
{ | |
typedef T result_type; | |
expm1_series(T x) | |
: k(0), m_x(x), m_term(1) {} | |
T operator()() | |
{ | |
++k; | |
m_term *= m_x; | |
m_term /= k; | |
return m_term; | |
} | |
int count()const | |
{ | |
return k; | |
} | |
private: | |
int k; | |
const T m_x; | |
T m_term; | |
expm1_series(const expm1_series&); | |
expm1_series& operator=(const expm1_series&); | |
}; | |
// | |
// Algorithm expm1 is part of C99, but is not yet provided by many compilers. | |
// | |
// This version uses a Taylor series expansion for 0.5 > |x| > epsilon. | |
// | |
template <class T, class Policy> | |
T expm1_imp(T x, const mpl::int_<0>&, const Policy& pol) | |
{ | |
BOOST_MATH_STD_USING | |
T a = fabs(x); | |
if(a > T(0.5f)) | |
{ | |
if(a >= tools::log_max_value<T>()) | |
{ | |
if(x > 0) | |
return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol); | |
return -1; | |
} | |
return exp(x) - T(1); | |
} | |
if(a < tools::epsilon<T>()) | |
return x; | |
detail::expm1_series<T> s(x); | |
boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); | |
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245) | |
T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter); | |
#else | |
T zero = 0; | |
T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero); | |
#endif | |
policies::check_series_iterations("boost::math::expm1<%1%>(%1%)", max_iter, pol); | |
return result; | |
} | |
template <class T, class P> | |
T expm1_imp(T x, const mpl::int_<53>&, const P& pol) | |
{ | |
BOOST_MATH_STD_USING | |
T a = fabs(x); | |
if(a > T(0.5L)) | |
{ | |
if(a >= tools::log_max_value<T>()) | |
{ | |
if(x > 0) | |
return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol); | |
return -1; | |
} | |
return exp(x) - T(1); | |
} | |
if(a < tools::epsilon<T>()) | |
return x; | |
static const float Y = 0.10281276702880859e1f; | |
static const T n[] = { -0.28127670288085937e-1, 0.51278186299064534e0, -0.6310029069350198e-1, 0.11638457975729296e-1, -0.52143390687521003e-3, 0.21491399776965688e-4 }; | |
static const T d[] = { 1, -0.45442309511354755e0, 0.90850389570911714e-1, -0.10088963629815502e-1, 0.63003407478692265e-3, -0.17976570003654402e-4 }; | |
T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x); | |
return result; | |
} | |
template <class T, class P> | |
T expm1_imp(T x, const mpl::int_<64>&, const P& pol) | |
{ | |
BOOST_MATH_STD_USING | |
T a = fabs(x); | |
if(a > T(0.5L)) | |
{ | |
if(a >= tools::log_max_value<T>()) | |
{ | |
if(x > 0) | |
return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol); | |
return -1; | |
} | |
return exp(x) - T(1); | |
} | |
if(a < tools::epsilon<T>()) | |
return x; | |
static const float Y = 0.10281276702880859375e1f; | |
static const T n[] = { | |
-0.281276702880859375e-1L, | |
0.512980290285154286358e0L, | |
-0.667758794592881019644e-1L, | |
0.131432469658444745835e-1L, | |
-0.72303795326880286965e-3L, | |
0.447441185192951335042e-4L, | |
-0.714539134024984593011e-6L | |
}; | |
static const T d[] = { | |
1, | |
-0.461477618025562520389e0L, | |
0.961237488025708540713e-1L, | |
-0.116483957658204450739e-1L, | |
0.873308008461557544458e-3L, | |
-0.387922804997682392562e-4L, | |
0.807473180049193557294e-6L | |
}; | |
T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x); | |
return result; | |
} | |
template <class T, class P> | |
T expm1_imp(T x, const mpl::int_<113>&, const P& pol) | |
{ | |
BOOST_MATH_STD_USING | |
T a = fabs(x); | |
if(a > T(0.5L)) | |
{ | |
if(a >= tools::log_max_value<T>()) | |
{ | |
if(x > 0) | |
return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol); | |
return -1; | |
} | |
return exp(x) - T(1); | |
} | |
if(a < tools::epsilon<T>()) | |
return x; | |
static const float Y = 0.10281276702880859375e1f; | |
static const T n[] = { | |
-0.28127670288085937499999999999999999854e-1L, | |
0.51278156911210477556524452177540792214e0L, | |
-0.63263178520747096729500254678819588223e-1L, | |
0.14703285606874250425508446801230572252e-1L, | |
-0.8675686051689527802425310407898459386e-3L, | |
0.88126359618291165384647080266133492399e-4L, | |
-0.25963087867706310844432390015463138953e-5L, | |
0.14226691087800461778631773363204081194e-6L, | |
-0.15995603306536496772374181066765665596e-8L, | |
0.45261820069007790520447958280473183582e-10L | |
}; | |
static const T d[] = { | |
1, | |
-0.45441264709074310514348137469214538853e0L, | |
0.96827131936192217313133611655555298106e-1L, | |
-0.12745248725908178612540554584374876219e-1L, | |
0.11473613871583259821612766907781095472e-2L, | |
-0.73704168477258911962046591907690764416e-4L, | |
0.34087499397791555759285503797256103259e-5L, | |
-0.11114024704296196166272091230695179724e-6L, | |
0.23987051614110848595909588343223896577e-8L, | |
-0.29477341859111589208776402638429026517e-10L, | |
0.13222065991022301420255904060628100924e-12L | |
}; | |
T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x); | |
return result; | |
} | |
} // namespace detail | |
template <class T, class Policy> | |
inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */) | |
{ | |
typedef typename tools::promote_args<T>::type result_type; | |
typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
typedef typename policies::precision<result_type, Policy>::type precision_type; | |
typedef typename policies::normalise< | |
Policy, | |
policies::promote_float<false>, | |
policies::promote_double<false>, | |
policies::discrete_quantile<>, | |
policies::assert_undefined<> >::type forwarding_policy; | |
typedef typename mpl::if_c< | |
::std::numeric_limits<result_type>::is_specialized == 0, | |
mpl::int_<0>, // no numeric_limits, use generic solution | |
typename mpl::if_< | |
typename mpl::less_equal<precision_type, mpl::int_<53> >::type, | |
mpl::int_<53>, // double | |
typename mpl::if_< | |
typename mpl::less_equal<precision_type, mpl::int_<64> >::type, | |
mpl::int_<64>, // 80-bit long double | |
typename mpl::if_< | |
typename mpl::less_equal<precision_type, mpl::int_<113> >::type, | |
mpl::int_<113>, // 128-bit long double | |
mpl::int_<0> // too many bits, use generic version. | |
>::type | |
>::type | |
>::type | |
>::type tag_type; | |
return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp( | |
static_cast<value_type>(x), | |
tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)"); | |
} | |
#ifdef expm1 | |
# ifndef BOOST_HAS_expm1 | |
# define BOOST_HAS_expm1 | |
# endif | |
# undef expm1 | |
#endif | |
#if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER)) | |
# ifdef BOOST_MATH_USE_C99 | |
inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); } | |
# ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS | |
inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); } | |
# endif | |
# else | |
inline float expm1(float x, const policies::policy<>&){ return ::expm1(x); } | |
# endif | |
inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); } | |
#endif | |
template <class T> | |
inline typename tools::promote_args<T>::type expm1(T x) | |
{ | |
return expm1(x, policies::policy<>()); | |
} | |
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564)) | |
inline float expm1(float z) | |
{ | |
return expm1<float>(z); | |
} | |
inline double expm1(double z) | |
{ | |
return expm1<double>(z); | |
} | |
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS | |
inline long double expm1(long double z) | |
{ | |
return expm1<long double>(z); | |
} | |
#endif | |
#endif | |
} // namespace math | |
} // namespace boost | |
#endif // BOOST_MATH_HYPOT_INCLUDED | |