boost/math/special_functions/expm1.hpp
// (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, class Policy, class tag> struct expm1_initializer { struct init { init() { do_init(tag()); } template <int N> static void do_init(const mpl::int_<N>&){} static void do_init(const mpl::int_<64>&) { expm1(T(0.5)); } static void do_init(const mpl::int_<113>&) { expm1(T(0.5)); } void force_instantiate()const{} }; static const init initializer; static void force_instantiate() { initializer.force_instantiate(); } }; template <class T, class Policy, class tag> const typename expm1_initializer<T, Policy, tag>::init expm1_initializer<T, Policy, tag>::initializer; // // 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((boost::math::isnan)(a)) { return policies::raise_domain_error<T>("boost::math::expm1<%1%>(%1%)", "expm1 requires a finite argument, but got %1%", a, pol); } 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 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[] = { static_cast<T>(-0.28127670288085937e-1), static_cast<T>(0.51278186299064534e0), static_cast<T>(-0.6310029069350198e-1), static_cast<T>(0.11638457975729296e-1), static_cast<T>(-0.52143390687521003e-3), static_cast<T>(0.21491399776965688e-4) }; static const T d[] = { 1, static_cast<T>(-0.45442309511354755e0), static_cast<T>(0.90850389570911714e-1), static_cast<T>(-0.10088963629815502e-1), static_cast<T>(0.63003407478692265e-3), static_cast<T>(-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[] = { 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[] = { BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 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 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[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 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; detail::expm1_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); 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 static_cast<float>(::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