williamr@2: //  (C) Copyright John Maddock 2005.
williamr@2: //  Use, modification and distribution are subject to the
williamr@2: //  Boost Software License, Version 1.0. (See accompanying file
williamr@2: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
williamr@2: 
williamr@2: #ifndef BOOST_MATH_EXPM1_INCLUDED
williamr@2: #define BOOST_MATH_EXPM1_INCLUDED
williamr@2: 
williamr@2: #include <cmath>
williamr@2: #include <math.h> // platform's ::expm1
williamr@2: #include <boost/limits.hpp>
williamr@2: #include <boost/math/special_functions/detail/series.hpp>
williamr@2: 
williamr@2: #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
williamr@2: #  include <boost/static_assert.hpp>
williamr@2: #else
williamr@2: #  include <boost/assert.hpp>
williamr@2: #endif
williamr@2: 
williamr@2: #ifdef BOOST_NO_STDC_NAMESPACE
williamr@2: namespace std{ using ::exp; using ::fabs; }
williamr@2: #endif
williamr@2: 
williamr@2: 
williamr@2: namespace boost{ namespace math{
williamr@2: 
williamr@2: namespace detail{
williamr@2: //
williamr@2: // Functor expm1_series returns the next term in the Taylor series
williamr@2: // x^k / k!
williamr@2: // each time that operator() is invoked.
williamr@2: //
williamr@2: template <class T>
williamr@2: struct expm1_series
williamr@2: {
williamr@2:    typedef T result_type;
williamr@2: 
williamr@2:    expm1_series(T x)
williamr@2:       : k(0), m_x(x), m_term(1) {}
williamr@2: 
williamr@2:    T operator()()
williamr@2:    {
williamr@2:       ++k;
williamr@2:       m_term *= m_x;
williamr@2:       m_term /= k;
williamr@2:       return m_term; 
williamr@2:    }
williamr@2: 
williamr@2:    int count()const
williamr@2:    {
williamr@2:       return k;
williamr@2:    }
williamr@2: 
williamr@2: private:
williamr@2:    int k;
williamr@2:    const T m_x;
williamr@2:    T m_term;
williamr@2:    expm1_series(const expm1_series&);
williamr@2:    expm1_series& operator=(const expm1_series&);
williamr@2: };
williamr@2: 
williamr@2: } // namespace
williamr@2: 
williamr@2: //
williamr@2: // Algorithm expm1 is part of C99, but is not yet provided by many compilers.
williamr@2: //
williamr@2: // This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
williamr@2: //
williamr@2: template <class T>
williamr@2: T expm1(T x)
williamr@2: {
williamr@2: #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
williamr@2:    BOOST_STATIC_ASSERT(::std::numeric_limits<T>::is_specialized);
williamr@2: #else
williamr@2:    BOOST_ASSERT(std::numeric_limits<T>::is_specialized);
williamr@2: #endif
williamr@2: 
williamr@2:    T a = std::fabs(x);
williamr@2:    if(a > T(0.5L))
williamr@2:       return std::exp(x) - T(1);
williamr@2:    if(a < std::numeric_limits<T>::epsilon())
williamr@2:       return x;
williamr@2:    detail::expm1_series<T> s(x);
williamr@2:    T result = detail::kahan_sum_series(s, std::numeric_limits<T>::digits + 2);
williamr@2:    return result;
williamr@2: }
williamr@2: #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
williamr@2: inline float expm1(float z)
williamr@2: {
williamr@2:    return expm1<float>(z);
williamr@2: }
williamr@2: inline double expm1(double z)
williamr@2: {
williamr@2:    return expm1<double>(z);
williamr@2: }
williamr@2: inline long double expm1(long double z)
williamr@2: {
williamr@2:    return expm1<long double>(z);
williamr@2: }
williamr@2: #endif
williamr@2: 
williamr@2: #ifdef expm1
williamr@2: #  ifndef BOOST_HAS_expm1
williamr@2: #     define BOOST_HAS_expm1
williamr@2: #  endif
williamr@2: #  undef expm1
williamr@2: #endif
williamr@2: 
williamr@2: #ifdef BOOST_HAS_EXPM1
williamr@2: #  if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901)
williamr@2: inline float expm1(float x){ return ::expm1f(x); }
williamr@2: inline long double expm1(long double x){ return ::expm1l(x); }
williamr@2: #else
williamr@2: inline float expm1(float x){ return ::expm1(x); }
williamr@2: #endif
williamr@2: inline double expm1(double x){ return ::expm1(x); }
williamr@2: #endif
williamr@2: 
williamr@2: } } // namespaces
williamr@2: 
williamr@2: #endif // BOOST_MATH_HYPOT_INCLUDED