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