boost/math/special_functions/math_fwd.hpp
// math_fwd.hpp // TODO revise completely for new distribution classes. // Copyright Paul A. Bristow 2006. // Copyright John Maddock 2006. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt // or copy at http://www.boost.org/LICENSE_1_0.txt) // Omnibus list of forward declarations of math special functions. // IT = Integer type. // RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types // AT = Integer or Real type #ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP #define BOOST_MATH_SPECIAL_MATH_FWD_HPP #ifdef _MSC_VER #pragma once #endif #include <boost/math/special_functions/detail/round_fwd.hpp> #include <boost/math/tools/promotion.hpp> // for argument promotion. #include <boost/math/policies/policy.hpp> #include <boost/mpl/comparison.hpp> #include <boost/utility/enable_if.hpp> #include <boost/config/no_tr1/complex.hpp> #define BOOST_NO_MACRO_EXPAND /**/ namespace boost { namespace math { // Math functions (in roughly alphabetic order). // Beta functions. template <class RT1, class RT2> typename tools::promote_args<RT1, RT2>::type beta(RT1 a, RT2 b); // Beta function (2 arguments). template <class RT1, class RT2, class A> typename tools::promote_args<RT1, RT2, A>::type beta(RT1 a, RT2 b, A x); // Beta function (3 arguments). template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments). template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type betac(RT1 a, RT2 b, RT3 x); template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type betac(RT1 a, RT2 b, RT3 x, const Policy& pol); template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function. template <class T1, class T2, class T3, class T4> typename tools::promote_args<T1, T2, T3, T4>::type ibeta_inv(T1 a, T2 b, T3 p, T4* py); template <class T1, class T2, class T3, class T4, class Policy> typename tools::promote_args<T1, T2, T3, T4>::type ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol); template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class T1, class T2, class T3, class T4> typename tools::promote_args<T1, T2, T3, T4>::type ibetac_inv(T1 a, T2 b, T3 q, T4* py); template <class T1, class T2, class T3, class T4, class Policy> typename tools::promote_args<T1, T2, T3, T4>::type ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol); template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_derivative(RT1 a, RT2 b, RT3 x); // derivative of incomplete beta template <class RT1, class RT2, class RT3, class Policy> typename tools::promote_args<RT1, RT2, RT3>::type ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol); // derivative of incomplete beta // Binomial: template <class T, class Policy> T binomial_coefficient(unsigned n, unsigned k, const Policy& pol); template <class T> T binomial_coefficient(unsigned n, unsigned k); // erf & erfc error functions. template <class RT> // Error function. typename tools::promote_args<RT>::type erf(RT z); template <class RT, class Policy> // Error function. typename tools::promote_args<RT>::type erf(RT z, const Policy&); template <class RT>// Error function complement. typename tools::promote_args<RT>::type erfc(RT z); template <class RT, class Policy>// Error function complement. typename tools::promote_args<RT>::type erfc(RT z, const Policy&); template <class RT>// Error function inverse. typename tools::promote_args<RT>::type erf_inv(RT z); template <class RT, class Policy>// Error function inverse. typename tools::promote_args<RT>::type erf_inv(RT z, const Policy& pol); template <class RT>// Error function complement inverse. typename tools::promote_args<RT>::type erfc_inv(RT z); template <class RT, class Policy>// Error function complement inverse. typename tools::promote_args<RT>::type erfc_inv(RT z, const Policy& pol); // Polynomials: template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1); template <class T> typename tools::promote_args<T>::type legendre_p(int l, T x); 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> typename tools::promote_args<T>::type legendre_q(unsigned l, T x); 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); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1); template <class T> typename tools::promote_args<T>::type legendre_p(int l, int m, T x); template <class T, class Policy> typename tools::promote_args<T>::type legendre_p(int l, int m, T x, const Policy& pol); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1); template <class T> typename tools::promote_args<T>::type laguerre(unsigned n, T x); template <class T, class Policy> typename tools::promote_args<T>::type laguerre(unsigned n, unsigned m, T x, const Policy& pol); template <class T1, class T2> struct laguerre_result { typedef typename mpl::if_< policies::is_policy<T2>, typename tools::promote_args<T1>::type, typename tools::promote_args<T2>::type >::type type; }; template <class T1, class T2> typename laguerre_result<T1, T2>::type laguerre(unsigned n, T1 m, T2 x); template <class T> typename tools::promote_args<T>::type hermite(unsigned n, T x); template <class T, class Policy> typename tools::promote_args<T>::type hermite(unsigned n, T x, const Policy& pol); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1); template <class T1, class T2> std::complex<typename tools::promote_args<T1, T2>::type> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> std::complex<typename tools::promote_args<T1, T2>::type> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); // Elliptic integrals: template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type ellint_rf(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> typename tools::promote_args<T1, T2, T3>::type ellint_rf(T1 x, T2 y, T3 z, const Policy& pol); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type ellint_rd(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> typename tools::promote_args<T1, T2, T3>::type ellint_rd(T1 x, T2 y, T3 z, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type ellint_rc(T1 x, T2 y); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type ellint_rc(T1 x, T2 y, const Policy& pol); template <class T1, class T2, class T3, class T4> typename tools::promote_args<T1, T2, T3, T4>::type ellint_rj(T1 x, T2 y, T3 z, T4 p); template <class T1, class T2, class T3, class T4, class Policy> typename tools::promote_args<T1, T2, T3, T4>::type ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol); template <class T1, class T2, class T3> typename tools::promote_args<T1, T2, T3>::type ellint_rg(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> typename tools::promote_args<T1, T2, T3>::type ellint_rg(T1 x, T2 y, T3 z, const Policy& pol); template <typename T> typename tools::promote_args<T>::type ellint_2(T k); template <class T1, class T2> typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi, const Policy& pol); template <typename T> typename tools::promote_args<T>::type ellint_1(T k); template <class T1, class T2> typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol); template <typename T> typename tools::promote_args<T>::type ellint_d(T k); template <class T1, class T2> typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol); namespace detail{ template <class T, class U, class V> struct ellint_3_result { typedef typename mpl::if_< policies::is_policy<V>, typename tools::promote_args<T, U>::type, typename tools::promote_args<T, U, V>::type >::type type; }; } // namespace detail template <class T1, class T2, class T3> typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi); template <class T1, class T2, class T3, class Policy> typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol); template <class T1, class T2> typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v); // Factorial functions. // Note: not for integral types, at present. template <class RT> struct max_factorial; template <class RT> RT factorial(unsigned int); template <class RT, class Policy> RT factorial(unsigned int, const Policy& pol); template <class RT> RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT)); template <class RT> RT double_factorial(unsigned i); template <class RT, class Policy> RT double_factorial(unsigned i, const Policy& pol); template <class RT> typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n); template <class RT, class Policy> typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol); template <class RT> typename tools::promote_args<RT>::type rising_factorial(RT x, int n); template <class RT, class Policy> typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol); // Gamma functions. template <class RT> typename tools::promote_args<RT>::type tgamma(RT z); template <class RT> typename tools::promote_args<RT>::type tgamma1pm1(RT z); template <class RT, class Policy> typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol); template <class RT1, class RT2> typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol); template <class RT> typename tools::promote_args<RT>::type lgamma(RT z, int* sign); template <class RT, class Policy> typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol); template <class RT> typename tools::promote_args<RT>::type lgamma(RT x); template <class RT, class Policy> typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol); template <class RT1, class RT2> typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&); template <class RT1, class RT2> typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&); template <class RT1, class RT2> typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&); // gamma inverse. template <class T1, class T2> typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&); template <class T1, class T2> typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&); // digamma: template <class T> typename tools::promote_args<T>::type digamma(T x); template <class T, class Policy> typename tools::promote_args<T>::type digamma(T x, const Policy&); // trigamma: template <class T> typename tools::promote_args<T>::type trigamma(T x); template <class T, class Policy> typename tools::promote_args<T>::type trigamma(T x, const Policy&); // polygamma: template <class T> typename tools::promote_args<T>::type polygamma(int n, T x); template <class T, class Policy> typename tools::promote_args<T>::type polygamma(int n, T x, const Policy&); // Hypotenuse function sqrt(x ^ 2 + y ^ 2). template <class T1, class T2> typename tools::promote_args<T1, T2>::type hypot(T1 x, T2 y); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type hypot(T1 x, T2 y, const Policy&); // cbrt - cube root. template <class RT> typename tools::promote_args<RT>::type cbrt(RT z); template <class RT, class Policy> typename tools::promote_args<RT>::type cbrt(RT z, const Policy&); // log1p is log(x + 1) template <class T> typename tools::promote_args<T>::type log1p(T); template <class T, class Policy> typename tools::promote_args<T>::type log1p(T, const Policy&); // log1pmx is log(x + 1) - x template <class T> typename tools::promote_args<T>::type log1pmx(T); template <class T, class Policy> typename tools::promote_args<T>::type log1pmx(T, const Policy&); // Exp (x) minus 1 functions. template <class T> typename tools::promote_args<T>::type expm1(T); template <class T, class Policy> typename tools::promote_args<T>::type expm1(T, const Policy&); // Power - 1 template <class T1, class T2> typename tools::promote_args<T1, T2>::type powm1(const T1 a, const T2 z); template <class T1, class T2, class Policy> typename tools::promote_args<T1, T2>::type powm1(const T1 a, const T2 z, const Policy&); // sqrt(1+x) - 1 template <class T> typename tools::promote_args<T>::type sqrt1pm1(const T& val); template <class T, class Policy> typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&); // sinus cardinals: template <class T> typename tools::promote_args<T>::type sinc_pi(T x); template <class T, class Policy> typename tools::promote_args<T>::type sinc_pi(T x, const Policy&); template <class T> typename tools::promote_args<T>::type sinhc_pi(T x); template <class T, class Policy> typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&); // inverse hyperbolics: template<typename T> typename tools::promote_args<T>::type asinh(T x); template<typename T, class Policy> typename tools::promote_args<T>::type asinh(T x, const Policy&); template<typename T> typename tools::promote_args<T>::type acosh(T x); template<typename T, class Policy> typename tools::promote_args<T>::type acosh(T x, const Policy&); template<typename T> typename tools::promote_args<T>::type atanh(T x); template<typename T, class Policy> typename tools::promote_args<T>::type atanh(T x, const Policy&); namespace detail{ typedef mpl::int_<0> bessel_no_int_tag; // No integer optimisation possible. typedef mpl::int_<1> bessel_maybe_int_tag; // Maybe integer optimisation. typedef mpl::int_<2> bessel_int_tag; // Definite integer optimistaion. template <class T1, class T2, class Policy> struct bessel_traits { typedef typename 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, 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> T unchecked_bernoulli_b2n(const std::size_t n); template <class T, class Policy> T bernoulli_b2n(const int i, const Policy &pol); template <class T> T bernoulli_b2n(const int i); template <class T, class OutputIterator, class Policy> OutputIterator bernoulli_b2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it, const Policy& pol); template <class T, class OutputIterator> OutputIterator bernoulli_b2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it); template <class T, class Policy> T tangent_t2n(const int i, const Policy &pol); template <class T> T tangent_t2n(const int i); template <class T, class OutputIterator, class Policy> OutputIterator tangent_t2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it, const Policy& pol); template <class T, class OutputIterator> OutputIterator tangent_t2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it); } // namespace math } // namespace boost #ifdef BOOST_HAS_LONG_LONG #define BOOST_MATH_DETAIL_LL_FUNC(Policy)\ \ template <class T>\ inline T modf(const T& v, boost::long_long_type* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ inline boost::long_long_type lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\ \ template <class T>\ inline boost::long_long_type llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\ #else #define BOOST_MATH_DETAIL_LL_FUNC(Policy) #endif #define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\ \ BOOST_MATH_DETAIL_LL_FUNC(Policy)\ \ template <class RT1, class RT2>\ inline typename boost::math::tools::promote_args<RT1, RT2>::type \ beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\ \ template <class RT1, class RT2, class A>\ inline typename boost::math::tools::promote_args<RT1, RT2, A>::type \ beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\ \ template <class T1, class T2, class T3, class T4>\ inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\ \ template <class T1, class T2, class T3, class T4>\ inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \ ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\ \ template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\ \ using boost::math::legendre_next;\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type \ legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type \ legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\ \ using ::boost::math::legendre_next;\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type \ legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\ \ using ::boost::math::laguerre_next;\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type \ laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::laguerre_result<T1, T2>::type \ laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type \ hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\ \ using boost::math::hermite_next;\ \ template <class T1, class T2>\ inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \ spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\ \ template <class T1, class T2, class Policy>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\ \ template <class T1, class T2, class T3, class T4>\ inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \ ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type \ ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\ \ template <typename T>\ inline typename boost::math::tools::promote_args<T>::type ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\ \ template <typename T>\ inline typename boost::math::tools::promote_args<T>::type ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\ \ template <typename T>\ inline typename boost::math::tools::promote_args<T>::type ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\ \ template <class T1, class T2, class T3>\ inline typename boost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\ \ using boost::math::max_factorial;\ template <class RT>\ inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\ using boost::math::unchecked_factorial;\ template <class RT>\ inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\ \ template <class RT1, class RT2>\ inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\ \ template <class RT1, class RT2>\ inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\ \ template <class RT1, class RT2>\ inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\ \ template <class RT1, class RT2>\ inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type digamma(T x){ return boost::math::digamma(x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type trigamma(T x){ return boost::math::trigamma(x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\ \ template <class RT>\ inline typename boost::math::tools::promote_args<RT>::type cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type log1p(T x){ return boost::math::log1p(x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type expm1(T x){ return boost::math::expm1(x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::tools::promote_args<T1, T2>::type \ powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\ \ template<typename T>\ inline typename boost::math::tools::promote_args<T>::type asinh(const T x){ return boost::math::asinh(x, Policy()); }\ \ template<typename T>\ inline typename boost::math::tools::promote_args<T>::type acosh(const T x){ return boost::math::acosh(x, Policy()); }\ \ template<typename T>\ inline typename boost::math::tools::promote_args<T>::type atanh(const T x){ return boost::math::atanh(x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\ { return boost::math::cyl_bessel_j(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\ { return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\ { return boost::math::sph_bessel(v, x, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\ { return boost::math::sph_bessel_prime(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\ \ template <class T1, class T2>\ inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \ sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \ sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\ { return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\ \ template <class OutputIterator, class T>\ inline void cyl_bessel_j_zero(T v,\ int start_index,\ unsigned number_of_zeros,\ OutputIterator out_it)\ { boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ \ template <class T>\ inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\ { return boost::math::cyl_neumann_zero(v, m, Policy()); }\ \ template <class OutputIterator, class T>\ inline void cyl_neumann_zero(T v,\ int start_index,\ unsigned number_of_zeros,\ OutputIterator out_it)\ { boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type sin_pi(T x){ return boost::math::sin_pi(x); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type cos_pi(T x){ return boost::math::cos_pi(x); }\ \ using boost::math::fpclassify;\ using boost::math::isfinite;\ using boost::math::isinf;\ using boost::math::isnan;\ using boost::math::isnormal;\ using boost::math::signbit;\ using boost::math::sign;\ using boost::math::copysign;\ using boost::math::changesign;\ \ template <class T, class U>\ inline typename boost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\ { return boost::math::expint(z, u, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type expint(T z){ return boost::math::expint(z, Policy()); }\ \ template <class T>\ inline typename boost::math::tools::promote_args<T>::type zeta(T s){ return boost::math::zeta(s, Policy()); }\ \ template <class T>\ inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\ \ template <class T>\ inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\ \ template <class T>\ inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\ \ template <class T>\ inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\ \ template <class T>\ inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\ \ template <class T>\ inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\ \ template <class T>\ inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <int N, class T>\ inline typename boost::math::tools::promote_args<T>::type pow(T v){ return boost::math::pow<N>(v, Policy()); }\ \ template <class T> T nextafter(const T& a, const T& b){ return boost::math::nextafter(a, b, Policy()); }\ template <class T> T float_next(const T& a){ return boost::math::float_next(a, Policy()); }\ template <class T> T float_prior(const T& a){ return boost::math::float_prior(a, Policy()); }\ template <class T> T float_distance(const T& a, const T& b){ return boost::math::float_distance(a, b, Policy()); }\ \ template <class 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