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src/boost/math/special_functions/log1p.hpp  view on Meta::CPAN

  //
  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&);
  };

// 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 many 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, class Policy>
T log1p_imp(T const & x, const Policy& pol, const mpl::int_<0>&)
{ // The function returns the natural logarithm of 1 + x.
   typedef typename tools::promote_args<T>::type result_type;
   BOOST_MATH_STD_USING

   static const char* function = "boost::math::log1p<%1%>(%1%)";

   if(x < -1)
      return policies::raise_domain_error<T>(
         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<T>(
         function, 0, pol);

   result_type a = abs(result_type(x));
   if(a > result_type(0.5f))
      return log(1 + result_type(x));
   // Note that without numeric_limits specialisation support, 
   // epsilon just returns zero, and our "optimisation" will always fail:
   if(a < tools::epsilon<result_type>())
      return x;
   detail::log1p_series<result_type> s(x);
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
   result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter);
#else
   result_type zero = 0;
   result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter, zero);
#endif
   policies::check_series_iterations<T>(function, max_iter, pol);
   return result;
}

template <class T, class Policy>
T log1p_imp(T const& x, const Policy& pol, const mpl::int_<53>&)
{ // The function returns the natural logarithm of 1 + x.
   BOOST_MATH_STD_USING

   static const char* function = "boost::math::log1p<%1%>(%1%)";

   if(x < -1)
      return policies::raise_domain_error<T>(
         function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<T>(
         function, 0, pol);

   T a = fabs(x);
   if(a > 0.5f)
      return log(1 + x);
   // Note that without numeric_limits specialisation support, 
   // epsilon just returns zero, and our "optimisation" will always fail:
   if(a < tools::epsilon<T>())
      return x;

   // Maximum Deviation Found:                     1.846e-017
   // Expected Error Term:                         1.843e-017
   // Maximum Relative Change in Control Points:   8.138e-004
   // Max Error found at double precision =        3.250766e-016
   static const T P[] = {    
       0.15141069795941984e-16L,
       0.35495104378055055e-15L,
       0.33333333333332835L,
       0.99249063543365859L,
       1.1143969784156509L,
       0.58052937949269651L,
       0.13703234928513215L,
       0.011294864812099712L
     };
   static const T Q[] = {    
       1L,
       3.7274719063011499L,
       5.5387948649720334L,
       4.159201143419005L,
       1.6423855110312755L,
       0.31706251443180914L,
       0.022665554431410243L,
       -0.29252538135177773e-5L
     };

   T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
   result *= x;

   return result;
}

template <class T, class Policy>
T log1p_imp(T const& x, const Policy& pol, const mpl::int_<64>&)
{ // The function returns the natural logarithm of 1 + x.
   BOOST_MATH_STD_USING

src/boost/math/special_functions/log1p.hpp  view on Meta::CPAN

template <class Policy>
inline float log1p(float x, const Policy& pol)
{
   return static_cast<float>(boost::math::log1p(static_cast<double>(x), pol));
}
#ifndef _WIN32_WCE
//
// For some reason this fails to compile under WinCE...
// Needs more investigation.
//
template <class Policy>
inline long double log1p(long double x, const Policy& pol)
{
   if(x < -1)
      return policies::raise_domain_error<long double>(
         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<long double>(
         "log1p<%1%>(%1%)", 0, pol);
   long double u = 1+x;
   if(u == 1.0) 
      return x; 
   else
      return ::logl(u)*(x/(u-1.0));
}
#endif
#endif

template <class T>
inline typename tools::promote_args<T>::type log1p(T x)
{
   return boost::math::log1p(x, policies::policy<>());
}
//
// Compute log(1+x)-x:
//
template <class T, class Policy>
inline typename tools::promote_args<T>::type 
   log1pmx(T x, const Policy& pol)
{
   typedef typename tools::promote_args<T>::type result_type;
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::log1pmx<%1%>(%1%)";

   if(x < -1)
      return policies::raise_domain_error<T>(
         function, "log1pmx(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<T>(
         function, 0, pol);

   result_type a = abs(result_type(x));
   if(a > result_type(0.95f))
      return log(1 + result_type(x)) - result_type(x);
   // Note that without numeric_limits specialisation support, 
   // epsilon just returns zero, and our "optimisation" will always fail:
   if(a < tools::epsilon<result_type>())
      return -x * x / 2;
   boost::math::detail::log1p_series<T> s(x);
   s();
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
   T zero = 0;
   T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
#else
   T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
#endif
   policies::check_series_iterations<T>(function, max_iter, pol);
   return result;
}

template <class T>
inline typename tools::promote_args<T>::type log1pmx(T x)
{
   return log1pmx(x, policies::policy<>());
}

} // namespace math
} // namespace boost

#endif // BOOST_MATH_LOG1P_INCLUDED