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 <cmath>
#include <cstdint>
#include <limits>
#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/math/tools/assert.hpp>
#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic. Neither __extension__
// nor #pragma diagnostic ignored work :(
//
#pragma GCC system_header
#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 std::integral_constant<int, N>&){}
static void do_init(const std::integral_constant<int, 64>&)
{
expm1(T(0.5));
}
static void do_init(const std::integral_constant<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 std::integral_constant<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);
std::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
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 std::integral_constant<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 std::integral_constant<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 std::integral_constant<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 std::integral_constant<int,
precision_type::value <= 0 ? 0 :
precision_type::value <= 53 ? 53 :
precision_type::value <= 64 ? 64 :
precision_type::value <= 113 ? 113 : 0
> 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<>());
}
} // namespace math
} // namespace boost
#endif // BOOST_MATH_HYPOT_INCLUDED