code:
//  (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

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 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

   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:                     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 mpl::int_<24>&)
{ // 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:                     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 mpl::int_<N>&){}
      static void do_init(const mpl::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 typename mpl::if_<
      mpl::less_equal<precision_type, mpl::int_<0> >,
      mpl::int_<0>,
      typename mpl::if_<
         mpl::less_equal<precision_type, mpl::int_<53> >,
         mpl::int_<53>,  // double
         typename mpl::if_<
            mpl::less_equal<precision_type, mpl::int_<64> >,
            mpl::int_<64>, // 80-bit long double
            mpl::int_<0> // too many bits, use generic version.
         >::type
      >::type
   >::type 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


code:
// math_fwd.hpp

// TODO revise completely for new distribution classes.

// Copyright Paul A. Bristow 2006.
// Copyright John Maddock 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)

// Omnibus list of forward declarations of math special functions.

// IT = Integer type.
// RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types
// AT = Integer or Real type

#ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP
#define BOOST_MATH_SPECIAL_MATH_FWD_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/detail/round_fwd.hpp>
#include <boost/math/tools/promotion.hpp> // for argument promotion.
#include <boost/math/policies/policy.hpp>
#include <boost/mpl/comparison.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/config/no_tr1/complex.hpp>

#define BOOST_NO_MACRO_EXPAND /**/

namespace boost
{
   namespace math
   { // Math functions (in roughly alphabetic order).

   // Beta functions.
   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type
         beta(RT1 a, RT2 b); // Beta function (2 arguments).

   template <class RT1, class RT2, class A>
   typename tools::promote_args<RT1, RT2, A>::type
         beta(RT1 a, RT2 b, A x); // Beta function (3 arguments).

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments).

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         betac(RT1 a, RT2 b, RT3 x);

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         betac(RT1 a, RT2 b, RT3 x, const Policy& pol);

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function.

   template <class T1, class T2, class T3, class T4>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ibeta_inv(T1 a, T2 b, T3 p, T4* py);

   template <class T1, class T2, class T3, class T4, class Policy>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol);

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.

   template <class T1, class T2, class T3, class T4>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ibetac_inv(T1 a, T2 b, T3 q, T4* py);

   template <class T1, class T2, class T3, class T4, class Policy>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol);

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.

   template <class RT1, class RT2, class RT3>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_derivative(RT1 a, RT2 b, RT3 x);  // derivative of incomplete beta

   template <class RT1, class RT2, class RT3, class Policy>
   typename tools::promote_args<RT1, RT2, RT3>::type
         ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol);  // derivative of incomplete beta

   // Binomial:
   template <class T, class Policy>
   T binomial_coefficient(unsigned n, unsigned k, const Policy& pol);
   template <class T>
   T binomial_coefficient(unsigned n, unsigned k);

   // erf & erfc error functions.
   template <class RT> // Error function.
   typename tools::promote_args<RT>::type erf(RT z);
   template <class RT, class Policy> // Error function.
   typename tools::promote_args<RT>::type erf(RT z, const Policy&);

   template <class RT>// Error function complement.
   typename tools::promote_args<RT>::type erfc(RT z);
   template <class RT, class Policy>// Error function complement.
   typename tools::promote_args<RT>::type erfc(RT z, const Policy&);

   template <class RT>// Error function inverse.
   typename tools::promote_args<RT>::type erf_inv(RT z);
   template <class RT, class Policy>// Error function inverse.
   typename tools::promote_args<RT>::type erf_inv(RT z, const Policy& pol);

   template <class RT>// Error function complement inverse.
   typename tools::promote_args<RT>::type erfc_inv(RT z);
   template <class RT, class Policy>// Error function complement inverse.
   typename tools::promote_args<RT>::type erfc_inv(RT z, const Policy& pol);

   // Polynomials:
   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
         legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);

   template <class T>
   typename tools::promote_args<T>::type
         legendre_p(int l, T x);
#if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
   template <class T, class Policy>
   typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
         legendre_p(int l, T x, const Policy& pol);
#endif
   template <class T>
   typename tools::promote_args<T>::type
         legendre_q(unsigned l, T x);
#if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
   template <class T, class Policy>
   typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
         legendre_q(unsigned l, T x, const Policy& pol);
#endif
   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
         legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1);

   template <class T>
   typename tools::promote_args<T>::type
         legendre_p(int l, int m, T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type
         legendre_p(int l, int m, T x, const Policy& pol);

   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
         laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1);

   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
      laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1);

   template <class T>
   typename tools::promote_args<T>::type
      laguerre(unsigned n, T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type
      laguerre(unsigned n, unsigned m, T x, const Policy& pol);

   template <class T1, class T2>
   struct laguerre_result
   {
      typedef typename mpl::if_<
         policies::is_policy<T2>,
         typename tools::promote_args<T1>::type,
         typename tools::promote_args<T2>::type
      >::type type;
   };

   template <class T1, class T2>
   typename laguerre_result<T1, T2>::type
      laguerre(unsigned n, T1 m, T2 x);

   template <class T>
   typename tools::promote_args<T>::type
      hermite(unsigned n, T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type
      hermite(unsigned n, T x, const Policy& pol);

   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
      hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1);

   template <class T1, class T2>
   std::complex<typename tools::promote_args<T1, T2>::type>
         spherical_harmonic(unsigned n, int m, T1 theta, T2 phi);

   template <class T1, class T2, class Policy>
   std::complex<typename tools::promote_args<T1, T2>::type>
      spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type
         spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type
      spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type
         spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type
      spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);

   // Elliptic integrals:
   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
         ellint_rf(T1 x, T2 y, T3 z);

   template <class T1, class T2, class T3, class Policy>
   typename tools::promote_args<T1, T2, T3>::type
         ellint_rf(T1 x, T2 y, T3 z, const Policy& pol);

   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
         ellint_rd(T1 x, T2 y, T3 z);

   template <class T1, class T2, class T3, class Policy>
   typename tools::promote_args<T1, T2, T3>::type
         ellint_rd(T1 x, T2 y, T3 z, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type
         ellint_rc(T1 x, T2 y);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type
         ellint_rc(T1 x, T2 y, const Policy& pol);

   template <class T1, class T2, class T3, class T4>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ellint_rj(T1 x, T2 y, T3 z, T4 p);

   template <class T1, class T2, class T3, class T4, class Policy>
   typename tools::promote_args<T1, T2, T3, T4>::type
         ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol);

   template <class T1, class T2, class T3>
   typename tools::promote_args<T1, T2, T3>::type
      ellint_rg(T1 x, T2 y, T3 z);

   template <class T1, class T2, class T3, class Policy>
   typename tools::promote_args<T1, T2, T3>::type
      ellint_rg(T1 x, T2 y, T3 z, const Policy& pol);

   template <typename T>
   typename tools::promote_args<T>::type ellint_2(T k);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi, const Policy& pol);

   template <typename T>
   typename tools::promote_args<T>::type ellint_1(T k);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol);

   template <typename T>
   typename tools::promote_args<T>::type ellint_d(T k);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol);

   namespace detail{

   template <class T, class U, class V>
   struct ellint_3_result
   {
      typedef typename mpl::if_<
         policies::is_policy<V>,
         typename tools::promote_args<T, U>::type,
         typename tools::promote_args<T, U, V>::type
      >::type type;
   };

   } // namespace detail

   template <class T1, class T2, class T3>
   typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi);

   template <class T1, class T2, class T3, class Policy>
   typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v);

   // Factorial functions.
   // Note: not for integral types, at present.
   template <class RT>
   struct max_factorial;
   template <class RT>
   RT factorial(unsigned int);
   template <class RT, class Policy>
   RT factorial(unsigned int, const Policy& pol);
   template <class RT>
   RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT));
   template <class RT>
   RT double_factorial(unsigned i);
   template <class RT, class Policy>
   RT double_factorial(unsigned i, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type rising_factorial(RT x, int n);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol);

   // Gamma functions.
   template <class RT>
   typename tools::promote_args<RT>::type tgamma(RT z);

   template <class RT>
   typename tools::promote_args<RT>::type tgamma1pm1(RT z);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type lgamma(RT z, int* sign);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type lgamma(RT x);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&);

   // gamma inverse.
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&);

   // digamma:
   template <class T>
   typename tools::promote_args<T>::type digamma(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type digamma(T x, const Policy&);

   // trigamma:
   template <class T>
   typename tools::promote_args<T>::type trigamma(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type trigamma(T x, const Policy&);

   // polygamma:
   template <class T>
   typename tools::promote_args<T>::type polygamma(int n, T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type polygamma(int n, T x, const Policy&);

   // Hypotenuse function sqrt(x ^ 2 + y ^ 2).
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type
         hypot(T1 x, T2 y);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type
         hypot(T1 x, T2 y, const Policy&);

   // cbrt - cube root.
   template <class RT>
   typename tools::promote_args<RT>::type cbrt(RT z);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type cbrt(RT z, const Policy&);

   // log1p is log(x + 1)
   template <class T>
   typename tools::promote_args<T>::type log1p(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type log1p(T, const Policy&);

   // log1pmx is log(x + 1) - x
   template <class T>
   typename tools::promote_args<T>::type log1pmx(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type log1pmx(T, const Policy&);

   // Exp (x) minus 1 functions.
   template <class T>
   typename tools::promote_args<T>::type expm1(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type expm1(T, const Policy&);

   // Power - 1
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type
         powm1(const T1 a, const T2 z);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type
         powm1(const T1 a, const T2 z, const Policy&);

   // sqrt(1+x) - 1
   template <class T>
   typename tools::promote_args<T>::type sqrt1pm1(const T& val);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&);

   // sinus cardinals:
   template <class T>
   typename tools::promote_args<T>::type sinc_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sinc_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type sinhc_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&);

   // inverse hyperbolics:
   template<typename T>
   typename tools::promote_args<T>::type asinh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type asinh(T x, const Policy&);

   template<typename T>
   typename tools::promote_args<T>::type acosh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type acosh(T x, const Policy&);

   template<typename T>
   typename tools::promote_args<T>::type atanh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type atanh(T x, const Policy&);

   namespace detail{

      typedef mpl::int_<0> bessel_no_int_tag;      // No integer optimisation possible.
      typedef mpl::int_<1> bessel_maybe_int_tag;   // Maybe integer optimisation.
      typedef mpl::int_<2> bessel_int_tag;         // Definite integer optimistaion.

      template <class T1, class T2, class Policy>
      struct bessel_traits
      {
         typedef typename mpl::if_<
            is_integral<T1>,
            typename tools::promote_args<T2>::type,
            typename tools::promote_args<T1, T2>::type
         >::type result_type;

         typedef typename policies::precision<result_type, Policy>::type precision_type;

         typedef typename mpl::if_<
            mpl::or_<
               mpl::less_equal<precision_type, mpl::int_<0> >,
               mpl::greater<precision_type, mpl::int_<64> > >,
            bessel_no_int_tag,
            typename mpl::if_<
               is_integral<T1>,
               bessel_int_tag,
               bessel_maybe_int_tag
            >::type
         >::type optimisation_tag;
      };
   } // detail

   // Bessel functions:
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol);
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x);
   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol);
   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x);
   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol);
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x);
   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol);
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x);
   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol);
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x);
   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol);
   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x);
   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m);

   template <class T, class OutputIterator>
   OutputIterator cyl_bessel_j_zero(T v,
                          int start_index,
                          unsigned number_of_zeros,
                          OutputIterator out_it);

   template <class T, class OutputIterator, class Policy>
   OutputIterator cyl_bessel_j_zero(T v,
                          int start_index,
                          unsigned number_of_zeros,
                          OutputIterator out_it,
                          const Policy&);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m);

   template <class T, class OutputIterator>
   OutputIterator cyl_neumann_zero(T v,
                         int start_index,
                         unsigned number_of_zeros,
                         OutputIterator out_it);

   template <class T, class OutputIterator, class Policy>
   OutputIterator cyl_neumann_zero(T v,
                         int start_index,
                         unsigned number_of_zeros,
                         OutputIterator out_it,
                         const Policy&);

   template <class T1, class T2>
   std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2, class Policy>
   std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type airy_ai(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type airy_ai(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type airy_bi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type airy_bi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type airy_ai_prime(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type airy_ai_prime(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type airy_bi_prime(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type airy_bi_prime(T x);

   template <class T>
   T airy_ai_zero(int m);
   template <class T, class Policy>
   T airy_ai_zero(int m, const Policy&);

   template <class OutputIterator>
   OutputIterator airy_ai_zero(
                     int start_index,
                     unsigned number_of_zeros,
                     OutputIterator out_it);
   template <class OutputIterator, class Policy>
   OutputIterator airy_ai_zero(
                     int start_index,
                     unsigned number_of_zeros,
                     OutputIterator out_it,
                     const Policy&);

   template <class T>
   T airy_bi_zero(int m);
   template <class T, class Policy>
   T airy_bi_zero(int m, const Policy&);

   template <class OutputIterator>
   OutputIterator airy_bi_zero(
                     int start_index,
                     unsigned number_of_zeros,
                     OutputIterator out_it);
   template <class OutputIterator, class Policy>
   OutputIterator airy_bi_zero(
                     int start_index,
                     unsigned number_of_zeros,
                     OutputIterator out_it,
                     const Policy&);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sin_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type sin_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type cos_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type cos_pi(T x);

   template <class T>
   int fpclassify BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isfinite BOOST_NO_MACRO_EXPAND(T z);

   template <class T>
   bool isinf BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isnan BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isnormal BOOST_NO_MACRO_EXPAND(T t);

   template<class T>
   int signbit BOOST_NO_MACRO_EXPAND(T x);

   template <class T>
   int sign BOOST_NO_MACRO_EXPAND(const T& z);

   template <class T, class U>
   typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y);

   template <class T>
   typename tools::promote_args_permissive<T>::type changesign BOOST_NO_MACRO_EXPAND(const T& z);

   // Exponential integrals:
   namespace detail{

   template <class T, class U>
   struct expint_result
   {
      typedef typename mpl::if_<
         policies::is_policy<U>,
         typename tools::promote_args<T>::type,
         typename tools::promote_args<U>::type
      >::type type;
   };

   } // namespace detail

   template <class T, class Policy>
   typename tools::promote_args<T>::type expint(unsigned n, T z, const Policy&);

   template <class T, class U>
   typename detail::expint_result<T, U>::type expint(T const z, U const u);

   template <class T>
   typename tools::promote_args<T>::type expint(T z);

   // Zeta:
   template <class T, class Policy>
   typename tools::promote_args<T>::type zeta(T s, const Policy&);

   // Owen's T function:
   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a, const Policy& pol);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a);

   // Jacobi Functions:
   template <class T, class U, class V, class Policy>
   typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&);

   template <class T, class U, class V>
   typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0);

   template <class U, class T, class Policy>
   typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta, const Policy& pol);

   template <class U, class T>
   typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta);

   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta, const Policy& pol);

   template <class T, class U>
   typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta);

   template <class T>
   typename tools::promote_args<T>::type zeta(T s);

   // pow:
   template <int N, typename T, class Policy>
   typename tools::promote_args<T>::type pow(T base, const Policy& policy);

   template <int N, typename T>
   typename tools::promote_args<T>::type pow(T base);

   // next:
   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type nextafter(const T&, const U&, const Policy&);
   template <class T, class U>
   typename tools::promote_args<T, U>::type nextafter(const T&, const U&);
   template <class T, class Policy>
   typename tools::promote_args<T>::type float_next(const T&, const Policy&);
   template <class T>
   typename tools::promote_args<T>::type float_next(const T&);
   template <class T, class Policy>
   typename tools::promote_args<T>::type float_prior(const T&, const Policy&);
   template <class T>
   typename tools::promote_args<T>::type float_prior(const T&);
   template <class T, class U, class Policy>
   typename tools::promote_args<T, U>::type float_distance(const T&, const U&, const Policy&);
   template <class T, class U>
   typename tools::promote_args<T, U>::type float_distance(const T&, const U&);
   template <class T, class Policy>
   typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol);
   template <class T>
   typename tools::promote_args<T>::type float_advance(const T& val, int distance);

   template <class T, class Policy>
   typename tools::promote_args<T>::type ulp(const T& val, const Policy& pol);
   template <class T>
   typename tools::promote_args<T>::type ulp(const T& val);

   template <class T, class U>
   typename tools::promote_args<T, U>::type relative_difference(const T&, const U&);
   template <class T, class U>
   typename tools::promote_args<T, U>::type epsilon_difference(const T&, const U&);

   template<class T>
   T unchecked_bernoulli_b2n(const std::size_t n);
   template <class T, class Policy>
   T bernoulli_b2n(const int i, const Policy &pol);
   template <class T>
   T bernoulli_b2n(const int i);
   template <class T, class OutputIterator, class Policy>
   OutputIterator bernoulli_b2n(const int start_index,
                                       const unsigned number_of_bernoullis_b2n,
                                       OutputIterator out_it,
                                       const Policy& pol);
   template <class T, class OutputIterator>
   OutputIterator bernoulli_b2n(const int start_index,
                                       const unsigned number_of_bernoullis_b2n,
                                       OutputIterator out_it);
   template <class T, class Policy>
   T tangent_t2n(const int i, const Policy &pol);
   template <class T>
   T tangent_t2n(const int i);
   template <class T, class OutputIterator, class Policy>
   OutputIterator tangent_t2n(const int start_index,
                                       const unsigned number_of_bernoullis_b2n,
                                       OutputIterator out_it,
                                       const Policy& pol);
   template <class T, class OutputIterator>
   OutputIterator tangent_t2n(const int start_index,
                                       const unsigned number_of_bernoullis_b2n,
                                       OutputIterator out_it);

    } // namespace math
} // namespace boost

#ifdef BOOST_HAS_LONG_LONG
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)\
   \
   template <class T>\
   inline T modf(const T& v, boost::long_long_type* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
   \
   template <class T>\
   inline boost::long_long_type lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\
   \
   template <class T>\
   inline boost::long_long_type llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\

#else
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)
#endif

#define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\
   \
   BOOST_MATH_DETAIL_LL_FUNC(Policy)\
   \
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type \
   beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\
\
   template <class RT1, class RT2, class A>\
   inline typename boost::math::tools::promote_args<RT1, RT2, A>::type \
   beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\
\
   template <class T1, class T2, class T3, class T4>\
   inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type  \
   ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\
\
   template <class T1, class T2, class T3, class T4>\
   inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
   ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
   ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
   ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\
\
   template <class RT1, class RT2, class RT3>\
   inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
   ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\
\
   template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\
\
   using boost::math::legendre_next;\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type \
   legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type \
   legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\
\
   using ::boost::math::legendre_next;\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type \
   legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\
\
   using ::boost::math::laguerre_next;\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type \
   laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::laguerre_result<T1, T2>::type \
   laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type \
   hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\
\
   using boost::math::hermite_next;\
\
   template <class T1, class T2>\
   inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \
   spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
   spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
   spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\
\
   template <class T1, class T2, class Policy>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
      spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
   ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
   ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
   ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\
\
   template <class T1, class T2, class T3, class T4>\
   inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
   ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
   ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\
   \
   template <typename T>\
   inline typename boost::math::tools::promote_args<T>::type ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\
\
   template <typename T>\
   inline typename boost::math::tools::promote_args<T>::type ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\
\
   template <typename T>\
   inline typename boost::math::tools::promote_args<T>::type ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\
\
   template <class T1, class T2, class T3>\
   inline typename boost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\
\
   using boost::math::max_factorial;\
   template <class RT>\
   inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\
   using boost::math::unchecked_factorial;\
   template <class RT>\
   inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\
\
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\
\
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\
\
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\
\
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type digamma(T x){ return boost::math::digamma(x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type trigamma(T x){ return boost::math::trigamma(x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\
   \
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
   hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\
\
   template <class RT>\
   inline typename boost::math::tools::promote_args<RT>::type cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type log1p(T x){ return boost::math::log1p(x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type expm1(T x){ return boost::math::expm1(x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::tools::promote_args<T1, T2>::type \
   powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\
\
   template<typename T>\
   inline typename boost::math::tools::promote_args<T>::type asinh(const T x){ return boost::math::asinh(x, Policy()); }\
\
   template<typename T>\
   inline typename boost::math::tools::promote_args<T>::type acosh(const T x){ return boost::math::acosh(x, Policy()); }\
\
   template<typename T>\
   inline typename boost::math::tools::promote_args<T>::type atanh(const T x){ return boost::math::atanh(x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\
   { return boost::math::cyl_bessel_j(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\
   { return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\
   { return boost::math::sph_bessel(v, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\
   { return boost::math::sph_bessel_prime(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\
\
   template <class T1, class T2>\
   inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
   cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
   sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
   sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\
   { return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\
\
template <class OutputIterator, class T>\
   inline void cyl_bessel_j_zero(T v,\
                                 int start_index,\
                                 unsigned number_of_zeros,\
                                 OutputIterator out_it)\
   { boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
\
   template <class T>\
   inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\
   { return boost::math::cyl_neumann_zero(v, m, Policy()); }\
\
template <class OutputIterator, class T>\
   inline void cyl_neumann_zero(T v,\
                                int start_index,\
                                unsigned number_of_zeros,\
                                OutputIterator out_it)\
   { boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type sin_pi(T x){ return boost::math::sin_pi(x); }\
\
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type cos_pi(T x){ return boost::math::cos_pi(x); }\
\
   using boost::math::fpclassify;\
   using boost::math::isfinite;\
   using boost::math::isinf;\
   using boost::math::isnan;\
   using boost::math::isnormal;\
   using boost::math::signbit;\
   using boost::math::sign;\
   using boost::math::copysign;\
   using boost::math::changesign;\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\
   { return boost::math::expint(z, u, Policy()); }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type expint(T z){ return boost::math::expint(z, Policy()); }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type zeta(T s){ return boost::math::zeta(s, Policy()); }\
   \
   template <class T>\
   inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\
   \
   template <class T>\
   inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\
   \
   template <class T>\
   inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\
   \
   template <class T>\
   inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\
   \
   template <class T>\
   inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\
   \
   template <class T>\
   inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\
   \
   template <class T>\
   inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
   \
   template <class T>\
   inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
   \
   template <class T>\
   inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
   \
   template <int N, class T>\
   inline typename boost::math::tools::promote_args<T>::type pow(T v){ return boost::math::pow<N>(v, Policy()); }\
   \
   template <class T> T nextafter(const T& a, const T& b){ return boost::math::nextafter(a, b, Policy()); }\
   template <class T> T float_next(const T& a){ return boost::math::float_next(a, Policy()); }\
   template <class T> T float_prior(const T& a){ return boost::math::float_prior(a, Policy()); }\
   template <class T> T float_distance(const T& a, const T& b){ return boost::math::float_distance(a, b, Policy()); }\
   template <class T> T ulp(const T& a){ return boost::math::ulp(a, Policy()); }\
   \
   template <class RT1, class RT2>\
   inline typename boost::math::tools::promote_args<RT1, RT2>::type owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\
   \
   template <class T1, class T2>\
   inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\
   {  return boost::math::cyl_hankel_1(v, x, Policy()); }\
   \
   template <class T1, class T2>\
   inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\
   { return boost::math::cyl_hankel_2(v, x, Policy()); }\
   \
   template <class T1, class T2>\
   inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\
   { return boost::math::sph_hankel_1(v, x, Policy()); }\
   \
   template <class T1, class T2>\
   inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\
   { return boost::math::sph_hankel_2(v, x, Policy()); }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\
   { return boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\
   \
   template <class U, class T>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_sn(U k, T theta)\
   { return boost::math::jacobi_sn(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_cn(T k, U theta)\
   { return boost::math::jacobi_cn(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_dn(T k, U theta)\
   { return boost::math::jacobi_dn(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_cd(T k, U theta)\
   { return boost::math::jacobi_cd(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_dc(T k, U theta)\
   { return boost::math::jacobi_dc(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_ns(T k, U theta)\
   { return boost::math::jacobi_ns(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_sd(T k, U theta)\
   { return boost::math::jacobi_sd(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_ds(T k, U theta)\
   { return boost::math::jacobi_ds(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_nc(T k, U theta)\
   { return boost::math::jacobi_nc(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_nd(T k, U theta)\
   { return boost::math::jacobi_nd(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_sc(T k, U theta)\
   { return boost::math::jacobi_sc(k, theta, Policy()); }\
   \
   template <class T, class U>\
   inline typename boost::math::tools::promote_args<T, U>::type jacobi_cs(T k, U theta)\
   { return boost::math::jacobi_cs(k, theta, Policy()); }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type airy_ai(T x)\
   {  return boost::math::airy_ai(x, Policy());  }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type airy_bi(T x)\
   {  return boost::math::airy_bi(x, Policy());  }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type airy_ai_prime(T x)\
   {  return boost::math::airy_ai_prime(x, Policy());  }\
   \
   template <class T>\
   inline typename boost::math::tools::promote_args<T>::type airy_bi_prime(T x)\
   {  return boost::math::airy_bi_prime(x, Policy());  }\
   \
   template <class T>\
   inline T airy_ai_zero(int m)\
   { return boost::math::airy_ai_zero<T>(m, Policy()); }\
   template <class T, class OutputIterator>\
   OutputIterator airy_ai_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
   { return boost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
   \
   template <class T>\
   inline T airy_bi_zero(int m)\
   { return boost::math::airy_bi_zero<T>(m, Policy()); }\
   template <class T, class OutputIterator>\
   OutputIterator airy_bi_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
   { return boost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
   \
   template <class T>\
   T bernoulli_b2n(const int i)\
   { return boost::math::bernoulli_b2n<T>(i, Policy()); }\
   template <class T, class OutputIterator>\
   OutputIterator bernoulli_b2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
   { return boost::math::bernoulli_b2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
   \
   template <class T>\
   T tangent_t2n(const int i)\
   { return boost::math::tangent_t2n<T>(i, Policy()); }\
   template <class T, class OutputIterator>\
   OutputIterator tangent_t2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
   { return boost::math::tangent_t2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
   \

#endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP

license: mit


code:
//  Copyright John Maddock 2007.
//  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_MODF_HPP
#define BOOST_MATH_MODF_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/special_functions/trunc.hpp>

namespace boost{ namespace math{

template <class T, class Policy>
inline T modf(const T& v, T* ipart, const Policy& pol)
{
   *ipart = trunc(v, pol);
   return v - *ipart;
}
template <class T>
inline T modf(const T& v, T* ipart)
{
   return modf(v, ipart, policies::policy<>());
}

template <class T, class Policy>
inline T modf(const T& v, int* ipart, const Policy& pol)
{
   *ipart = itrunc(v, pol);
   return v - *ipart;
}
template <class T>
inline T modf(const T& v, int* ipart)
{
   return modf(v, ipart, policies::policy<>());
}

template <class T, class Policy>
inline T modf(const T& v, long* ipart, const Policy& pol)
{
   *ipart = ltrunc(v, pol);
   return v - *ipart;
}
template <class T>
inline T modf(const T& v, long* ipart)
{
   return modf(v, ipart, policies::policy<>());
}

#ifdef BOOST_HAS_LONG_LONG
template <class T, class Policy>
inline T modf(const T& v, boost::long_long_type* ipart, const Policy& pol)
{
   *ipart = lltrunc(v, pol);
   return v - *ipart;
}
template <class T>
inline T modf(const T& v, boost::long_long_type* ipart)
{
   return modf(v, ipart, policies::policy<>());
}
#endif

}} // namespaces

#endif // BOOST_MATH_MODF_HPP