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344 lines
11 KiB
C++
344 lines
11 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_EXPM1_INCLUDED
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#define BOOST_MATH_EXPM1_INCLUDED
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/config/no_tr1/cmath.hpp>
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#include <math.h> // platform's ::expm1
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#include <boost/limits.hpp>
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#include <boost/math/tools/config.hpp>
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#include <boost/math/tools/series.hpp>
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#include <boost/math/tools/precision.hpp>
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#include <boost/math/tools/big_constant.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/mpl/less_equal.hpp>
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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# include <boost/static_assert.hpp>
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#else
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# include <boost/assert.hpp>
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#endif
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namespace boost{ namespace math{
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namespace detail
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{
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// Functor expm1_series returns the next term in the Taylor series
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// x^k / k!
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// each time that operator() is invoked.
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//
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template <class T>
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struct expm1_series
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{
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typedef T result_type;
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expm1_series(T x)
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: k(0), m_x(x), m_term(1) {}
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T operator()()
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{
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++k;
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m_term *= m_x;
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m_term /= k;
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return m_term;
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}
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int count()const
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{
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return k;
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}
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private:
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int k;
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const T m_x;
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T m_term;
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expm1_series(const expm1_series&);
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expm1_series& operator=(const expm1_series&);
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};
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template <class T, class Policy, class tag>
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struct expm1_initializer
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{
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struct init
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{
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init()
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{
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do_init(tag());
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}
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template <int N>
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static void do_init(const mpl::int_<N>&){}
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static void do_init(const mpl::int_<64>&)
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{
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expm1(T(0.5));
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}
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static void do_init(const mpl::int_<113>&)
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{
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expm1(T(0.5));
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}
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void force_instantiate()const{}
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};
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static const init initializer;
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static void force_instantiate()
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{
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initializer.force_instantiate();
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}
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};
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template <class T, class Policy, class tag>
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const typename expm1_initializer<T, Policy, tag>::init expm1_initializer<T, Policy, tag>::initializer;
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//
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// Algorithm expm1 is part of C99, but is not yet provided by many compilers.
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//
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// This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
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//
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template <class T, class Policy>
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T expm1_imp(T x, const mpl::int_<0>&, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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T a = fabs(x);
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if(a > T(0.5f))
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{
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if(a >= tools::log_max_value<T>())
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{
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if(x > 0)
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return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
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return -1;
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}
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return exp(x) - T(1);
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}
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if(a < tools::epsilon<T>())
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return x;
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detail::expm1_series<T> s(x);
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
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T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
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#else
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T zero = 0;
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T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
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#endif
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policies::check_series_iterations<T>("boost::math::expm1<%1%>(%1%)", max_iter, pol);
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return result;
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}
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template <class T, class P>
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T expm1_imp(T x, const mpl::int_<53>&, const P& pol)
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{
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BOOST_MATH_STD_USING
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T a = fabs(x);
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if(a > T(0.5L))
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{
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if(a >= tools::log_max_value<T>())
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{
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if(x > 0)
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return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
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return -1;
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}
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return exp(x) - T(1);
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}
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if(a < tools::epsilon<T>())
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return x;
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static const float Y = 0.10281276702880859e1f;
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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) };
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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) };
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T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
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return result;
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}
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template <class T, class P>
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T expm1_imp(T x, const mpl::int_<64>&, const P& pol)
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{
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BOOST_MATH_STD_USING
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T a = fabs(x);
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if(a > T(0.5L))
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{
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if(a >= tools::log_max_value<T>())
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{
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if(x > 0)
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return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
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return -1;
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}
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return exp(x) - T(1);
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}
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if(a < tools::epsilon<T>())
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return x;
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static const float Y = 0.10281276702880859375e1f;
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static const T n[] = {
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.512980290285154286358e0),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.667758794592881019644e-1),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.131432469658444745835e-1),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.72303795326880286965e-3),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.447441185192951335042e-4),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.714539134024984593011e-6)
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};
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static const T d[] = {
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.461477618025562520389e0),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.961237488025708540713e-1),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.116483957658204450739e-1),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.873308008461557544458e-3),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6)
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};
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T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
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return result;
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}
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template <class T, class P>
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T expm1_imp(T x, const mpl::int_<113>&, const P& pol)
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{
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BOOST_MATH_STD_USING
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T a = fabs(x);
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if(a > T(0.5L))
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{
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if(a >= tools::log_max_value<T>())
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{
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if(x > 0)
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return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
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return -1;
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}
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return exp(x) - T(1);
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}
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if(a < tools::epsilon<T>())
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return x;
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static const float Y = 0.10281276702880859375e1f;
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static const T n[] = {
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.51278156911210477556524452177540792214e0),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.63263178520747096729500254678819588223e-1),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.14703285606874250425508446801230572252e-1),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.8675686051689527802425310407898459386e-3),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.88126359618291165384647080266133492399e-4),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.25963087867706310844432390015463138953e-5),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.14226691087800461778631773363204081194e-6),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.15995603306536496772374181066765665596e-8),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.45261820069007790520447958280473183582e-10)
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};
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static const T d[] = {
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BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.45441264709074310514348137469214538853e0),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.96827131936192217313133611655555298106e-1),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.12745248725908178612540554584374876219e-1),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.11473613871583259821612766907781095472e-2),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.73704168477258911962046591907690764416e-4),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.34087499397791555759285503797256103259e-5),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.11114024704296196166272091230695179724e-6),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.23987051614110848595909588343223896577e-8),
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BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10),
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BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12)
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};
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T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
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return result;
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}
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} // namespace detail
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template <class T, class Policy>
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inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */)
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{
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typedef typename tools::promote_args<T>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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typedef typename policies::precision<result_type, Policy>::type precision_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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typedef typename mpl::if_c<
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::std::numeric_limits<result_type>::is_specialized == 0,
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mpl::int_<0>, // no numeric_limits, use generic solution
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typename mpl::if_<
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typename mpl::less_equal<precision_type, mpl::int_<53> >::type,
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mpl::int_<53>, // double
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typename mpl::if_<
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typename mpl::less_equal<precision_type, mpl::int_<64> >::type,
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mpl::int_<64>, // 80-bit long double
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typename mpl::if_<
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typename mpl::less_equal<precision_type, mpl::int_<113> >::type,
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mpl::int_<113>, // 128-bit long double
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mpl::int_<0> // too many bits, use generic version.
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>::type
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>::type
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>::type
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>::type tag_type;
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detail::expm1_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();
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return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp(
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static_cast<value_type>(x),
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tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)");
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}
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#ifdef expm1
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# ifndef BOOST_HAS_expm1
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# define BOOST_HAS_expm1
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# endif
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# undef expm1
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#endif
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#if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER))
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# ifdef BOOST_MATH_USE_C99
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inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); }
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# ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); }
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# endif
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# else
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inline float expm1(float x, const policies::policy<>&){ return static_cast<float>(::expm1(x)); }
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# endif
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inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); }
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#endif
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template <class T>
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inline typename tools::promote_args<T>::type expm1(T x)
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{
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return expm1(x, policies::policy<>());
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}
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#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
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inline float expm1(float z)
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{
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return expm1<float>(z);
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}
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inline double expm1(double z)
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{
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return expm1<double>(z);
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}
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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inline long double expm1(long double z)
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{
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return expm1<long double>(z);
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}
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#endif
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#endif
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} // namespace math
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} // namespace boost
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#endif // BOOST_MATH_HYPOT_INCLUDED
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