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Diffstat (limited to 'boost/math/special_functions/expm1.hpp')
-rw-r--r-- | boost/math/special_functions/expm1.hpp | 344 |
1 files changed, 344 insertions, 0 deletions
diff --git a/boost/math/special_functions/expm1.hpp b/boost/math/special_functions/expm1.hpp new file mode 100644 index 0000000000..345220fcee --- /dev/null +++ b/boost/math/special_functions/expm1.hpp @@ -0,0 +1,344 @@ +// (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/tools/big_constant.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&); + }; + +template <class T, bool b = boost::is_pod<T>::value> +struct expm1_init_on_startup +{ + struct init + { + init() + { + boost::math::expm1(T(0.5f)); + } + void do_nothing()const{} + }; + + static void do_nothing() + { + initializer.do_nothing(); + } + + static const init initializer; +}; + +template <class T, bool b> +const typename expm1_init_on_startup<T, b>::init expm1_init_on_startup<T, b>::initializer; + +template <class T> +struct expm1_init_on_startup<T, true> +{ + static void do_nothing(){} +}; +// +// 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<T>("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 + + expm1_init_on_startup<T>::do_nothing(); + + 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 + + expm1_init_on_startup<T>::do_nothing(); + + 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[] = { + BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.512980290285154286358e0), + BOOST_MATH_BIG_CONSTANT(T, 64, -0.667758794592881019644e-1), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.131432469658444745835e-1), + BOOST_MATH_BIG_CONSTANT(T, 64, -0.72303795326880286965e-3), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.447441185192951335042e-4), + BOOST_MATH_BIG_CONSTANT(T, 64, -0.714539134024984593011e-6) + }; + static const T d[] = { + 1, + BOOST_MATH_BIG_CONSTANT(T, 64, -0.461477618025562520389e0), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.961237488025708540713e-1), + BOOST_MATH_BIG_CONSTANT(T, 64, -0.116483957658204450739e-1), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.873308008461557544458e-3), + BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4), + BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6) + }; + + 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 + + expm1_init_on_startup<T>::do_nothing(); + + 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[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.51278156911210477556524452177540792214e0), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.63263178520747096729500254678819588223e-1), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.14703285606874250425508446801230572252e-1), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.8675686051689527802425310407898459386e-3), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.88126359618291165384647080266133492399e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.25963087867706310844432390015463138953e-5), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.14226691087800461778631773363204081194e-6), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.15995603306536496772374181066765665596e-8), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.45261820069007790520447958280473183582e-10) + }; + static const T d[] = { + 1, + BOOST_MATH_BIG_CONSTANT(T, 113, -0.45441264709074310514348137469214538853e0), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.96827131936192217313133611655555298106e-1), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.12745248725908178612540554584374876219e-1), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.11473613871583259821612766907781095472e-2), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.73704168477258911962046591907690764416e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.34087499397791555759285503797256103259e-5), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.11114024704296196166272091230695179724e-6), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.23987051614110848595909588343223896577e-8), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12) + }; + + 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 + + + + |