FM / special_functions

/usr/include/boost/math/special_functions/

/usr/include/boost/math/special_functions

Name	Size	Mode	Actions
detail/	-	0755	rm
acosh.hpp	3693	0644	edit dl rm
airy.hpp	16270	0644	edit dl rm
asinh.hpp	3935	0644	edit dl rm
atanh.hpp	4104	0644	edit dl rm
bernoulli.hpp	5389	0644	edit dl rm
bessel.hpp	28405	0644	edit dl rm
bessel_iterators.hpp	6893	0644	edit dl rm
bessel_prime.hpp	13238	0644	edit dl rm
beta.hpp	52594	0644	edit dl rm
binomial.hpp	2508	0644	edit dl rm
cardinal_b_spline.hpp	4796	0644	edit dl rm
cbrt.hpp	5200	0644	edit dl rm
chebyshev.hpp	4760	0644	edit dl rm
chebyshev_transform.hpp	6209	0644	edit dl rm
cos_pi.hpp	2328	0644	edit dl rm
daubechies_scaling.hpp	15036	0644	edit dl rm
daubechies_wavelet.hpp	9671	0644	edit dl rm
digamma.hpp	22318	0644	edit dl rm
ellint_1.hpp	6700	0644	edit dl rm
ellint_2.hpp	6377	0644	edit dl rm
ellint_3.hpp	12048	0644	edit dl rm
ellint_d.hpp	5965	0644	edit dl rm
ellint_rc.hpp	3135	0644	edit dl rm
ellint_rd.hpp	6280	0644	edit dl rm
ellint_rf.hpp	5255	0644	edit dl rm
ellint_rg.hpp	4125	0644	edit dl rm
ellint_rj.hpp	8862	0644	edit dl rm
erf.hpp	56660	0644	edit dl rm
expint.hpp	75066	0644	edit dl rm
expm1.hpp	11335	0644	edit dl rm
factorials.hpp	8054	0644	edit dl rm
fpclassify.hpp	19871	0644	edit dl rm
gamma.hpp	70488	0644	edit dl rm
gegenbauer.hpp	2015	0644	edit dl rm
hankel.hpp	6994	0644	edit dl rm
hermite.hpp	1778	0644	edit dl rm
heuman_lambda.hpp	2891	0644	edit dl rm
hypergeometric_0F1.hpp	4283	0644	edit dl rm
hypergeometric_1F0.hpp	2383	0644	edit dl rm
hypergeometric_1F1.hpp	31854	0644	edit dl rm
hypergeometric_2F0.hpp	6127	0644	edit dl rm
hypergeometric_pFq.hpp	8518	0644	edit dl rm
hypot.hpp	2246	0644	edit dl rm
jacobi.hpp	1884	0644	edit dl rm
jacobi_elliptic.hpp	10190	0644	edit dl rm
jacobi_zeta.hpp	2273	0644	edit dl rm
laguerre.hpp	3651	0644	edit dl rm
lambert_w.hpp	95998	0644	edit dl rm
lanczos.hpp	312974	0644	edit dl rm
legendre.hpp	11275	0644	edit dl rm
legendre_stieltjes.hpp	6901	0644	edit dl rm
log1p.hpp	16271	0644	edit dl rm
math_fwd.hpp	73671	0644	edit dl rm
modf.hpp	1628	0644	edit dl rm
next.hpp	28961	0644	edit dl rm
nonfinite_num_facets.hpp	18572	0644	edit dl rm
owens_t.hpp	49887	0644	edit dl rm
polygamma.hpp	3209	0644	edit dl rm
pow.hpp	3426	0644	edit dl rm
powm1.hpp	2442	0644	edit dl rm
prime.hpp	91594	0644	edit dl rm
relative_difference.hpp	5455	0644	edit dl rm
round.hpp	4361	0644	edit dl rm
sign.hpp	5648	0644	edit dl rm
sinc.hpp	3409	0644	edit dl rm
sinhc.hpp	4643	0644	edit dl rm
sin_pi.hpp	2311	0644	edit dl rm
spherical_harmonic.hpp	6358	0644	edit dl rm
sqrt1pm1.hpp	1149	0644	edit dl rm
trigamma.hpp	21411	0644	edit dl rm
trunc.hpp	5450	0644	edit dl rm
ulp.hpp	3324	0644	edit dl rm
zeta.hpp	53776	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/log1p.hpp (16271B)

//  (C) Copyright John Maddock 2005-2006.
//  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

#ifdef _MSC_VER
#pragma once
#pragma warning(push)
#pragma warning(disable:4702) // Unreachable code (release mode only warning)
#endif

#include <boost/config/no_tr1/cmath.hpp>
#include <math.h> // platform's ::log1p
#include <boost/limits.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/series.hpp>
#include <boost/math/tools/rational.hpp>
#include <boost/math/tools/big_constant.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/special_functions/math_fwd.hpp>

#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
#  include <boost/static_assert.hpp>
#else
#  include <boost/assert.hpp>
#endif

#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic.  Neither __extension__
// nor #pragma diagnostic ignored work :(
//
#pragma GCC system_header
#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&);
  };

// 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 boost::integral_constant<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) || (boost::math::isnan)(x))
      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 boost::integral_constant<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 boost::integral_constant<int, 64>&)
{ // The function returns the natural logarithm of 1 + x.
   BOOST_MATH_STD_USING

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

// Maximum Deviation Found:                     8.089e-20
   // Expected Error Term:                         8.088e-20
   // Maximum Relative Change in Control Points:   9.648e-05
   // Max Error found at long double precision =   2.242324e-19
   static const T P[] = {    
      BOOST_MATH_BIG_CONSTANT(T, 64, -0.807533446680736736712e-19),
      BOOST_MATH_BIG_CONSTANT(T, 64, -0.490881544804798926426e-18),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.333333333333333373941),
      BOOST_MATH_BIG_CONSTANT(T, 64, 1.17141290782087994162),
      BOOST_MATH_BIG_CONSTANT(T, 64, 1.62790522814926264694),
      BOOST_MATH_BIG_CONSTANT(T, 64, 1.13156411870766876113),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.408087379932853785336),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.0706537026422828914622),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.00441709903782239229447)
   };
   static const T Q[] = {    
      BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 64, 4.26423872346263928361),
      BOOST_MATH_BIG_CONSTANT(T, 64, 7.48189472704477708962),
      BOOST_MATH_BIG_CONSTANT(T, 64, 6.94757016732904280913),
      BOOST_MATH_BIG_CONSTANT(T, 64, 3.6493508622280767304),
      BOOST_MATH_BIG_CONSTANT(T, 64, 1.06884863623790638317),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.158292216998514145947),
      BOOST_MATH_BIG_CONSTANT(T, 64, 0.00885295524069924328658),
      BOOST_MATH_BIG_CONSTANT(T, 64, -0.560026216133415663808e-6)
   };

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 boost::integral_constant<int, 24>&)
{ // The function returns the natural logarithm of 1 + x.
   BOOST_MATH_STD_USING

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

// Maximum Deviation Found:                     6.910e-08
   // Expected Error Term:                         6.910e-08
   // Maximum Relative Change in Control Points:   2.509e-04
   // Max Error found at double precision =        6.910422e-08
   // Max Error found at float precision =         8.357242e-08
   static const T P[] = {    
      -0.671192866803148236519e-7L,
      0.119670999140731844725e-6L,
      0.333339469182083148598L,
      0.237827183019664122066L
   };
   static const T Q[] = {    
      1L,
      1.46348272586988539733L,
      0.497859871350117338894L,
      -0.00471666268910169651936L
   };

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

return result;
}

template <class T, class Policy, class tag>
struct log1p_initializer
{
   struct init
   {
      init()
      {
         do_init(tag());
      }
      template <int N>
      static void do_init(const boost::integral_constant<int, N>&){}
      static void do_init(const boost::integral_constant<int, 64>&)
      {
         boost::math::log1p(static_cast<T>(0.25), Policy());
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T, class Policy, class tag>
const typename log1p_initializer<T, Policy, tag>::init log1p_initializer<T, Policy, tag>::initializer;

} // namespace detail

template <class T, class Policy>
inline typename tools::promote_args<T>::type log1p(T x, const Policy&)
{ 
   typedef typename tools::promote_args<T>::type result_type;
   typedef typename policies::evaluation<result_type, Policy>::type value_type;
   typedef typename policies::precision<result_type, Policy>::type precision_type;
   typedef typename policies::normalise<
      Policy, 
      policies::promote_float<false>, 
      policies::promote_double<false>, 
      policies::discrete_quantile<>,
      policies::assert_undefined<> >::type forwarding_policy;

typedef boost::integral_constant<int,
      precision_type::value <= 0 ? 0 :
      precision_type::value <= 53 ? 53 :
      precision_type::value <= 64 ? 64 : 0
   > tag_type;

detail::log1p_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();

return policies::checked_narrowing_cast<result_type, forwarding_policy>(
      detail::log1p_imp(static_cast<value_type>(x), forwarding_policy(), tag_type()), "boost::math::log1p<%1%>(%1%)");
}

#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);
}
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
inline long double log1p(long double z)
{
   return log1p<long double>(z);
}
#endif
#endif

#ifdef log1p
#  ifndef BOOST_HAS_LOG1P
#     define BOOST_HAS_LOG1P
#  endif
#  undef log1p
#endif

#if defined(BOOST_HAS_LOG1P) && !(defined(__osf__) && defined(__DECCXX_VER))
#  ifdef BOOST_MATH_USE_C99
template <class Policy>
inline float log1p(float x, const Policy& pol)
{ 
   if(x < -1)
      return policies::raise_domain_error<float>(
         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<float>(
         "log1p<%1%>(%1%)", 0, pol);
   return ::log1pf(x); 
}
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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);
   return ::log1pl(x); 
}
#endif
#else
template <class Policy>
inline float log1p(float x, const Policy& pol)
{ 
   if(x < -1)
      return policies::raise_domain_error<float>(
         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<float>(
         "log1p<%1%>(%1%)", 0, pol);
   return ::log1p(x); 
}
#endif
template <class Policy>
inline double log1p(double x, const Policy& pol)
{ 
   if(x < -1)
      return policies::raise_domain_error<double>(
         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<double>(
         "log1p<%1%>(%1%)", 0, pol);
   return ::log1p(x); 
}
#elif defined(_MSC_VER) && (BOOST_MSVC >= 1400)
//
// You should only enable this branch if you are absolutely sure
// that your compilers optimizer won't mess this code up!!
// Currently tested with VC8 and Intel 9.1.
//
template <class Policy>
inline double log1p(double x, const Policy& pol)
{
   if(x < -1)
      return policies::raise_domain_error<double>(
         "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
   if(x == -1)
      return -policies::raise_overflow_error<double>(
         "log1p<%1%>(%1%)", 0, pol);
   double u = 1+x;
   if(u == 1.0) 
      return x; 
   else
      return ::log(u)*(x/(u-1.0));
}
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

#ifdef _MSC_VER
#pragma warning(pop)
#endif

#endif // BOOST_MATH_LOG1P_INCLUDED

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