math_fwd.hpp

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// 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/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

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

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

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

   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 <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);

   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));