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Diffstat (limited to '3rdParty/Boost/src/boost/math/special_functions/math_fwd.hpp')
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diff --git a/3rdParty/Boost/src/boost/math/special_functions/math_fwd.hpp b/3rdParty/Boost/src/boost/math/special_functions/math_fwd.hpp new file mode 100644 index 0000000..6669e3f --- /dev/null +++ b/3rdParty/Boost/src/boost/math/special_functions/math_fwd.hpp @@ -0,0 +1,1296 @@ +// 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)); + 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&); + + // 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 tools::promote_args< + T1, T2 + >::type result_type; + + typedef typename policies::precision<result_type, Policy>::type precision_type; + + typedef typename mpl::if_< + mpl::or_< + mpl::less_equal<precision_type, mpl::int_<0> >, + mpl::greater<precision_type, mpl::int_<64> > >, + bessel_no_int_tag, + typename mpl::if_< + is_integral<T1>, + bessel_int_tag, + bessel_maybe_int_tag + >::type + >::type optimisation_tag; + }; + } // detail + + // Bessel functions: + template <class T1, class T2, class Policy> + typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol); + + template <class T1, class T2> + typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(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> + typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(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> + typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(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> + typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(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> + typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(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> + typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T 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> + 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_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, 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> + T copysign BOOST_NO_MACRO_EXPAND(const T& x, const T& y); + + template <class T> + T 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 Policy> + typename tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn, const Policy&); + + template <class T> + typename tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn = 0, T* 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 Policy> + T nextafter(const T&, const T&, const Policy&); + template <class T> + T nextafter(const T&, const T&); + template <class T, class Policy> + T float_next(const T&, const Policy&); + template <class T> + T float_next(const T&); + template <class T, class Policy> + T float_prior(const T&, const Policy&); + template <class T> + T float_prior(const T&); + template <class T, class Policy> + T float_distance(const T&, const T&, const Policy&); + template <class T> + T float_distance(const T&, const T&); + + } // 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 RT>\ + inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\ +\ + template <class RT>\ + inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\ +\ + template <class RT>\ + inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\ +\ + template <class RT>\ + inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\ +\ + using boost::math::legendre_next;\ +\ + template <class T>\ + inline typename boost::math::tools::promote_args<T>::type \ + legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\ +\ + template <class T>\ + inline typename boost::math::tools::promote_args<T>::type \ + legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\ +\ + using ::boost::math::legendre_next;\ +\ + template <class T>\ + inline typename boost::math::tools::promote_args<T>::type \ + legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\ +\ + using ::boost::math::laguerre_next;\ +\ + template <class T>\ + inline typename boost::math::tools::promote_args<T>::type \ + laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\ +\ + template <class T1, class T2>\ + inline typename boost::math::laguerre_result<T1, T2>::type \ + laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\ +\ + template <class T>\ + inline typename boost::math::tools::promote_args<T>::type \ + hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\ +\ + using boost::math::hermite_next;\ +\ + template <class T1, class T2>\ + inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \ + spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\ +\ + template <class T1, class T2>\ + inline typename boost::math::tools::promote_args<T1, T2>::type \ + spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\ +\ + template <class T1, class T2>\ + inline typename boost::math::tools::promote_args<T1, T2>::type \ + spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\ +\ + template <class T1, class T2, class Policy>\ + inline typename boost::math::tools::promote_args<T1, T2>::type \ + spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\ +\ + template <class T1, class T2, class T3>\ + inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ + ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\ +\ + template <class T1, class T2, class T3>\ + inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ + ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\ +\ + template <class T1, class T2>\ + inline typename boost::math::tools::promote_args<T1, T2>::type \ + ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\ +\ + template <class T1, class T2, class T3, class T4>\ + inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ + ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\ +\ + template <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_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 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 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 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_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_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(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::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 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()); }\ + \ + + + + + +#endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP + + |