// 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 <vector>
#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);
   template <class T>
   typename tools::promote_args<T>::type
          legendre_p_prime(int l, T x);

   template <class T, class Policy>
   inline std::vector<T> legendre_p_zeros(int l, const Policy& pol);

   template <class T>
   inline std::vector<T> legendre_p_zeros(int l);

#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);
   template <class T, class Policy>
   inline typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
      legendre_p_prime(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, class T3>
   typename tools::promote_args<T1, T2, T3>::type chebyshev_next(T1 const & x, T2 const & Tn, T3 const & Tn_1);

   template <class Real, class Policy>
   typename tools::promote_args<Real>::type
      chebyshev_t(unsigned n, Real const & x, const Policy&);
   template<class Real>
   typename tools::promote_args<Real>::type chebyshev_t(unsigned n, Real const & x);

   template <class Real, class Policy>
   typename tools::promote_args<Real>::type
      chebyshev_u(unsigned n, Real const & x, const Policy&);
   template<class Real>
   typename tools::promote_args<Real>::type chebyshev_u(unsigned n, Real const & x);

   template <class Real, class Policy>
   typename tools::promote_args<Real>::type
      chebyshev_t_prime(unsigned n, Real const & x, const Policy&);
   template<class Real>
   typename tools::promote_args<Real>::type chebyshev_t_prime(unsigned n, Real const & x);

   template<class Real, class T2>
   Real chebyshev_clenshaw_recurrence(const Real* const c, size_t length, const T2& x);

   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;
         typedef typename mpl::if_<
            mpl::or_<
               mpl::less_equal<precision_type, mpl::int_<0> >,
               mpl::greater<precision_type, mpl::int_<113> > >,
            bessel_no_int_tag,
            typename mpl::if_<
               is_integral<T1>,
               bessel_int_tag,
               bessel_maybe_int_tag
            >::type
         >::type optimisation_tag128;
      };
   } // 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>
   BOOST_MATH_CONSTEXPR_TABLE_FUNCTION 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_p_prime(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;\
\
   using boost::math::chebyshev_next;\
\
  template<class Real>\
  Real chebyshev_t(unsigned n, Real const & x){ return ::boost::math::chebyshev_t(n, x, Policy()); }\
\
  template<class Real>\
  Real chebyshev_u(unsigned n, Real const & x){ return ::boost::math::chebyshev_u(n, x, Policy()); }\
\
  template<class Real>\
  Real chebyshev_t_prime(unsigned n, Real const & x){ return ::boost::math::chebyshev_t_prime(n, x, Policy()); }\
\
  using ::boost::math::chebyshev_clenshaw_recurrence;\
\
   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


#include <boost/integer/static_log2.hpp>


#include "MPContext.hpp"
#include "fhe/NumbTh.h"
#include <set>
#include <NTL/ZZ.h>
#include <cmath>
#include <vector>
#include <thread>
#ifdef FHE_THREADS
const long WORKER_NR = 8;
#else
const long WORKER_NR = 1;
#endif

static long getSlots(long m, long p)
{
    return phi_N(m) / multOrd(p, m);
}

static long gcd(long a, long b) {
    if (a > b) std::swap(a, b);

    auto r = b % a;
    while (r > 0) {
        a = r;
        b = a;
        r = b % a;
    }
    return a;
}

bool checkSlots(long required, long check) {
    if (check < required) return false;
    return gcd(required, check) == required;
}

static std::set<long> FindPrimes(long m, long p, long parts)
{
    auto slots = getSlots(m, p);
    auto bits = static_cast<long>(std::ceil(std::log2(static_cast<double>(p))));
    std::set<long> primes;
	// {
	// 	std::vector<long> pprimes = {4139, 7321, 5381, 5783, 4231, 4937, 5279, 6679, 6323, 7459, 6791};
	// 	auto len = pprimes.size();
	// 	for (long pp = 0; pp < parts; pp++) primes.insert(pprimes[len - 1 - pp]);
	// 	return primes;
	// }
    primes.insert(p);
	long generated = 1;
	long trial = 0;
	while (generated < parts) {

		auto prime = NTL::RandomPrime_long(bits);
        auto s = getSlots(m, prime);
		if (checkSlots(slots, s)) {
			auto ok = primes.insert(prime);
			if (ok.second) {
				generated += 1;
			}
        }

		if (trial++ > 1000) {
			printf("Error: Can not find enough primes, only found %ld\n",
				   generated);
			break;
		}
	}

	return primes;
}

	MPContext::MPContext(long m, long p, long r, long parts)
: m_r(r)
{
	contexts.reserve(parts);
	auto primesSet = FindPrimes(m, p, parts);

	for (auto prime : primesSet) {
		m_plainSpace *= std::pow(prime, r);
		m_primes.push_back(prime);
	}

	std::vector<std::thread> worker;
	std::atomic<size_t> counter(0);
	const size_t num = m_primes.size();
	auto job = [this, &counter, &m, &r, &num]() {
		size_t i;
		while ((i = counter.fetch_add(1)) < num) {
			contexts[i] = std::make_shared<FHEcontext>(m, m_primes[i], r);
		}
	};

	contexts.resize(num);

	for (long wr = 0; wr < WORKER_NR; wr++) worker.push_back(std::thread(job));

	for (auto &&wr : worker) wr.join();
}

void MPContext::buildModChain(long L)
{
	std::vector<std::thread> worker;
	std::atomic<size_t> counter(0);
	const size_t num = contexts.size();
	auto job = [this, &counter, &num, &L]() {
		size_t i;
		while ((i = counter.fetch_add(1)) < num) {
			::buildModChain(*contexts[i], L);
		}
	};

	contexts.resize(num);

	for (long wr = 0; wr < WORKER_NR; wr++) worker.push_back(std::thread(job));

	for (auto &&wr : worker) wr.join();
}

double MPContext::precision() const
{
	return NTL::log(plainSpace()) / NTL::log(NTL::to_ZZ(2));
}


/*! \file boxplot_simple.cpp

    \brief An example to demonstrate simplest use of boxplot.\n
           See also boxplot_full.cpp for a wider range of use.

    \author Paul A Bristow

    \date 2009
*/

// Copyright Jacob Voytko 2007
// Copyright Paul A. Bristow 2008

// 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)

// This file is written to be included from a Quickbook .qbk document.
// It can be compiled by the C++ compiler, and run. Any output can
// also be added here as comment or included or pasted in elsewhere.

// Caution: this file contains Quickbook markup as well as code
// and comments: don't change any of the special comment markups!

//[boxplot_1d_1

/*`
Boxplot is a  convenient way of graphically depicting groups of numerical data
through their five-number summaries.
Show 1st quartile, median and 3rd quartile as a box, outliers and extreme outliers.

See [@http://en.wikipedia.org/wiki/Boxplot boxplot] and

Some Implementations of the Boxplot
Michael Frigge, David C. Hoaglin and Boris Iglewicz
The American Statistician, Vol. 43, No. 1 (Feb., 1989), pp. 50-54

First we need a few includes to use Boost.Plot.
*/

#include <vector>
using std::vector;
#include <cmath>
using ::sin;
#include <boost/svg_plot/svg_boxplot.hpp>

#include <iostream>
using std::cout;
using std::endl;

/*`Use two functions, 1/x and sin(x), to simulate distributions.
*/

double f(double x)
{ // Effectively 1/x.
  return 50 / x;
}

double g(double x)
{ // Effectively sin(x).
  return 40 + 25 * sin(x * 50);
}
//] [boxplot_1d_1]

int main()
{
  using namespace boost::svg;
  try
  {
//[boxplot_1d_2]
/*`10 values are computed and stored in two std:: vectors.
*/
  std::vector<double> data1;
  std::vector<double> data2;

  cout.precision(2);
  for(double i = 0.1; i < 10; i += 0.1)
  {   // Fill our vectors with 100 values:
    double fv = f(i);
    double gv = g(i);
    // cout << i << ' ' << fv << ' ' << gv << endl;
    data1.push_back(fv);
    data2.push_back(gv);
  }

/*`A new boxplot is contructed and a few settings added.
*/
  svg_boxplot my_boxplot;

  my_boxplot.background_border_color(darkblue);
  my_boxplot.background_color(azure);

  my_boxplot  // Title and axes labels.
    .title("Boxplots of 1/x and sin(x) Functions")
    .x_label("Functions")
    .y_label("Population Size");

  my_boxplot.y_range(0, 100)  // Axis information.
    //.y_minor_tick_length(20)
    .y_major_interval(20);

/*`Add the two data series containers, and their labels, to the plot.
*/

  my_boxplot.plot(data1, "[50 / x]");
  my_boxplot.plot(data2, "[40 + 25 * sin(x * 50)]");

/*  cout << "my_boxplot.title " << my_boxplot.title() << endl;
  cout << "my_boxplot.x_label_text "<< my_boxplot.x_label_text() << endl;
  cout << "my_boxplot.y_label_text " << my_boxplot.y_label_text() << endl;

  cout << "my_boxplot.background_color " << my_boxplot.background_color() << endl;
  cout << "my_boxplot.background_border_color " << my_boxplot.background_border_color() << endl;
  cout << "my_boxplot.plot_background_color " << my_boxplot.plot_background_color() << endl;
 */ cout << "my_boxplot.plot_border_color " << my_boxplot.plot_border_color() << endl;

/*`Finally write the SVG plot to a file.
*/
  my_boxplot.write("boxplot_simple.svg");
/*`You can view the plot at boxplot_simple.svg."
*/

//] [boxplot_1d_2]
  }
  catch(const std::exception& e)
  {
    std::cout <<
      "\n""Message from thrown exception was:\n  " << e.what() << std::endl;
  }
  return 0;
} // int main()

/*

Output:

*/


/* test_ranlux4.cpp
 *
 * Copyright Steven Watanabe 2011
 * Distributed under 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)
 *
 * $Id$
 *
 */

#include <boost/random/ranlux.hpp>

#define BOOST_RANDOM_URNG boost::random::ranlux4

#define BOOST_RANDOM_SEED_WORDS 24

// principal operation validated with CLHEP, values by experiment
#define BOOST_RANDOM_VALIDATION_VALUE 8587295U
#define BOOST_RANDOM_SEED_SEQ_VALIDATION_VALUE 10794046U
#define BOOST_RANDOM_ITERATOR_VALIDATION_VALUE 4515722U

#define BOOST_RANDOM_GENERATE_VALUES { 0x55E57B2CU, 0xF2DEF915U, 0x6D1A0CD9U, 0xCA0109F9U }

#include "test_generator.ipp"


/*
 * Copyright 2009-2020 The VOTCA Development Team (http://www.votca.org)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 */

#define BOOST_TEST_MAIN

#define BOOST_TEST_MODULE akimaspline_test

// Standard includes
#include <iostream>

// Third party includes
#include <boost/test/unit_test.hpp>

// Local VOTCA includes
#include "votca/tools/akimaspline.h"

using namespace votca::tools;

BOOST_AUTO_TEST_SUITE(akimaspline_test)

BOOST_AUTO_TEST_CASE(interpolate_test) {

  int size = 80;
  Eigen::VectorXd x = Eigen::VectorXd::Zero(size);
  Eigen::VectorXd y = Eigen::VectorXd::Zero(size);
  for (int i = 0; i < size; ++i) {
    x(i) = 0.25 * i;
    y(i) = std::sin(x(i));
  }
  AkimaSpline cspline;
  cspline.setBCInt(0);
  cspline.Interpolate(x, y);

  Eigen::VectorXd rs = Eigen::VectorXd::Zero(10);
  rs << 0.45, 0.47, 0.8, 0.75, 0.6, 0.4, 0.9, 0.55, 0, 0;
  Eigen::VectorXd values_ref = Eigen::VectorXd::Zero(10);
  values_ref << 0.434362, 0.452449, 0.717761, 0.681639, 0.564937, 0.388734,
      0.783279, 0.52316, 0, 0;
  Eigen::VectorXd derivatives_ref = Eigen::VectorXd::Zero(10);
  derivatives_ref << 0.906562, 0.902216, 0.698382, 0.747323, 0.818045, 0.918909,
      0.615268, 0.854075, 1.02038, 1.02038;
  Eigen::VectorXd values = cspline.Calculate(rs);
  Eigen::VectorXd derivatives = cspline.CalculateDerivative(rs);

  bool equal_val = values_ref.isApprox(values, 1e-5);

  if (!equal_val) {
    std::cout << "result value" << std::endl;
    std::cout << values.transpose() << std::endl;
    std::cout << "ref value" << std::endl;
    std::cout << values_ref.transpose() << std::endl;
  }
  BOOST_CHECK_EQUAL(equal_val, true);

  bool equal_derivative = derivatives_ref.isApprox(derivatives, 1e-5);

  if (!equal_derivative) {
    std::cout << "result value" << std::endl;
    std::cout << derivatives.transpose() << std::endl;
    std::cout << "ref value" << std::endl;
    std::cout << derivatives_ref.transpose() << std::endl;
  }
  BOOST_CHECK_EQUAL(equal_derivative, true);
}

BOOST_AUTO_TEST_SUITE_END()


#include <qlo/objects/obj_defaultbasket.hpp>

#include <ql/currencies/europe.hpp>
#include <ql/experimental/credit/basket.hpp>
#include <boost/make_shared.hpp>

QuantLibAddin::Basket::Basket(
    const boost::shared_ptr<reposit::ValueObject>& properties,
            // BEGIN typemap rp_tm_default
            std::vector< std::string > const &IssuerNames,
            std::vector< boost::shared_ptr< QuantLib::Issuer > > const &Issuers,
            std::vector< QuantLib::Real > const &Notionals,
            QuantLib::Date const &ReferenceDate,
            QuantLib::Real AttachmentRatio,
            QuantLib::Real DettachmentRatio,
            bool Amortizing,
            // END   typemap rp_tm_default
    bool permanent) : reposit::LibraryObject<QuantLib::Basket>(properties, permanent) {

        QL_REQUIRE(IssuerNames.size() == Issuers.size(),
            "Different number of names and issuers.");

        std::vector<QuantLib::DefaultProbKey> contractTriggers(
            IssuerNames.size(),
            QuantLib::NorthAmericaCorpDefaultKey(QuantLib::EURCurrency(),
                QuantLib::SeniorSec,
                QuantLib::Period(),
                1. // amount threshold
            ));

        boost::shared_ptr<QuantLib::Pool> pool(new QuantLib::Pool());
        for(QuantLib::Size i=0; i<IssuerNames.size(); i++)
                pool->add(IssuerNames[i], *Issuers[i], contractTriggers[i]);
        libraryObject_ =
            boost::make_shared<QuantLib::Basket>(
                QuantLib::Basket(ReferenceDate, IssuerNames, Notionals, pool,
                    AttachmentRatio, DettachmentRatio));
}


/*=============================================================================
    Copyright (c) 2017 Paul Fultz II
    rotate_lazy.cpp
    Distributed under 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)
==============================================================================*/
#include <boost/hof/lazy.hpp>
#include <boost/hof/placeholders.hpp>
#include <boost/hof/rotate.hpp>

int main() {
    auto i = (boost::hof::rotate(boost::hof::_1 - boost::hof::_2) * boost::hof::_1)(3, 6);
    (void)i;
}