| // (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 |
| |
| |
| |
| |