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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