boost/math/special_functions/expm1.hpp
// (C) Copyright John Maddock 2005.
// 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
#include <cmath>
#include <math.h> // platform's ::expm1
#include <boost/limits.hpp>
#include <boost/math/special_functions/detail/series.hpp>
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
# include <boost/static_assert.hpp>
#else
# include <boost/assert.hpp>
#endif
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::exp; using ::fabs; }
#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&);
};
} // namespace
//
// 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>
T expm1(T x)
{
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
BOOST_STATIC_ASSERT(::std::numeric_limits<T>::is_specialized);
#else
BOOST_ASSERT(std::numeric_limits<T>::is_specialized);
#endif
T a = std::fabs(x);
if(a > T(0.5L))
return std::exp(x) - T(1);
if(a < std::numeric_limits<T>::epsilon())
return x;
detail::expm1_series<T> s(x);
T result = detail::kahan_sum_series(s, std::numeric_limits<T>::digits + 2);
return result;
}
#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);
}
inline long double expm1(long double z)
{
return expm1<long double>(z);
}
#endif
#ifdef expm1
# ifndef BOOST_HAS_expm1
# define BOOST_HAS_expm1
# endif
# undef expm1
#endif
#ifdef BOOST_HAS_EXPM1
# if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901)
inline float expm1(float x){ return ::expm1f(x); }
inline long double expm1(long double x){ return ::expm1l(x); }
#else
inline float expm1(float x){ return ::expm1(x); }
#endif
inline double expm1(double x){ return ::expm1(x); }
#endif
} } // namespaces
#endif // BOOST_MATH_HYPOT_INCLUDED