boost/math/special_functions/log1p.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_LOG1P_INCLUDED
#define BOOST_MATH_LOG1P_INCLUDED
#include <cmath>
#include <math.h> // platform's ::log1p
#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 ::fabs; using ::log; }
#endif
namespace boost{ namespace math{
namespace detail{
//
// Functor log1p_series returns the next term in the Taylor series
// pow(-1, k-1)*pow(x, k) / k
// each time that operator() is invoked.
//
template <class T>
struct log1p_series
{
typedef T result_type;
log1p_series(T x)
: k(0), m_mult(-x), m_prod(-1){}
T operator()()
{
m_prod *= m_mult;
return m_prod / ++k;
}
int count()const
{
return k;
}
private:
int k;
const T m_mult;
T m_prod;
log1p_series(const log1p_series&);
log1p_series& operator=(const log1p_series&);
};
} // namespace
//
// Algorithm log1p is part of C99, but is not yet provided by many compilers.
//
// This version uses a Taylor series expansion for 0.5 > x > epsilon, which may
// require up to std::numeric_limits<T>::digits+1 terms to be calculated. It would
// be much more efficient to use the equivalence:
// log(1+x) == (log(1+x) * x) / ((1-x) - 1)
// Unfortunately optimizing compilers make such a mess of this, that it performs
// no better than log(1+x): which is to say not very well at all.
//
template <class T>
T log1p(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::log(T(1.0) + x);
if(a < std::numeric_limits<T>::epsilon())
return x;
detail::log1p_series<T> s(x);
return detail::kahan_sum_series(s, std::numeric_limits<T>::digits + 2);
}
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
// these overloads work around a type deduction bug:
inline float log1p(float z)
{
return log1p<float>(z);
}
inline double log1p(double z)
{
return log1p<double>(z);
}
inline long double log1p(long double z)
{
return log1p<long double>(z);
}
#endif
#ifdef log1p
# ifndef BOOST_HAS_LOG1P
# define BOOST_HAS_LOG1P
# endif
# undef log1p
#endif
#ifdef BOOST_HAS_LOG1P
# if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901)
inline float log1p(float x){ return ::log1pf(x); }
inline long double log1p(long double x){ return ::log1pl(x); }
#else
inline float log1p(float x){ return ::log1p(x); }
#endif
inline double log1p(double x){ return ::log1p(x); }
#endif
} } // namespaces
#endif // BOOST_MATH_HYPOT_INCLUDED