| // 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 <ndnboost/math/special_functions/detail/round_fwd.hpp> |
| #include <ndnboost/math/tools/promotion.hpp> // for argument promotion. |
| #include <ndnboost/math/policies/policy.hpp> |
| #include <ndnboost/mpl/comparison.hpp> |
| #include <ndnboost/config/no_tr1/complex.hpp> |
| |
| #define BOOST_NO_MACRO_EXPAND /**/ |
| |
| namespace ndnboost |
| { |
| 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 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(unsigned m); |
| template <class T, class Policy> |
| T airy_ai_zero(unsigned m, const Policy&); |
| |
| template <class OutputIterator> |
| OutputIterator airy_ai_zero( |
| unsigned start_index, |
| unsigned number_of_zeros, |
| OutputIterator out_it); |
| template <class OutputIterator, class Policy> |
| OutputIterator airy_ai_zero( |
| unsigned start_index, |
| unsigned number_of_zeros, |
| OutputIterator out_it, |
| const Policy&); |
| |
| template <class T> |
| T airy_bi_zero(unsigned m); |
| template <class T, class Policy> |
| T airy_bi_zero(unsigned m, const Policy&); |
| |
| template <class OutputIterator> |
| OutputIterator airy_bi_zero( |
| unsigned start_index, |
| unsigned number_of_zeros, |
| OutputIterator out_it); |
| template <class OutputIterator, class Policy> |
| OutputIterator airy_bi_zero( |
| unsigned 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<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y); |
| |
| template <class T> |
| typename tools::promote_args<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); |
| |
| } // namespace math |
| } // namespace ndnboost |
| |
| #ifdef BOOST_HAS_LONG_LONG |
| #define BOOST_MATH_DETAIL_LL_FUNC(Policy)\ |
| \ |
| template <class T>\ |
| inline T modf(const T& v, ndnboost::long_long_type* ipart){ using ndnboost::math::modf; return modf(v, ipart, Policy()); }\ |
| \ |
| template <class T>\ |
| inline ndnboost::long_long_type lltrunc(const T& v){ using ndnboost::math::lltrunc; return lltrunc(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline ndnboost::long_long_type llround(const T& v){ using ndnboost::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 ndnboost::math::tools::promote_args<RT1, RT2>::type \ |
| beta(RT1 a, RT2 b) { return ::ndnboost::math::beta(a, b, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class A>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, A>::type \ |
| beta(RT1 a, RT2 b, A x){ return ::ndnboost::math::beta(a, b, x, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| betac(RT1 a, RT2 b, RT3 x) { return ::ndnboost::math::betac(a, b, x, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibeta(RT1 a, RT2 b, RT3 x){ return ::ndnboost::math::ibeta(a, b, x, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibetac(RT1 a, RT2 b, RT3 x){ return ::ndnboost::math::ibetac(a, b, x, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3, class T4>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3, T4>::type \ |
| ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::ndnboost::math::ibeta_inv(a, b, p, py, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::ndnboost::math::ibeta_inv(a, b, p, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3, class T4>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3, T4>::type \ |
| ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::ndnboost::math::ibetac_inv(a, b, q, py, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::ndnboost::math::ibeta_inva(a, b, p, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3>::type \ |
| ibetac_inva(T1 a, T2 b, T3 q){ return ::ndnboost::math::ibetac_inva(a, b, q, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::ndnboost::math::ibeta_invb(a, b, p, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3>::type \ |
| ibetac_invb(T1 a, T2 b, T3 q){ return ::ndnboost::math::ibetac_invb(a, b, q, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::ndnboost::math::ibetac_inv(a, b, q, Policy()); }\ |
| \ |
| template <class RT1, class RT2, class RT3>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2, RT3>::type \ |
| ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::ndnboost::math::ibeta_derivative(a, b, x, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type erf(RT z) { return ::ndnboost::math::erf(z, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type erfc(RT z){ return ::ndnboost::math::erfc(z, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::ndnboost::math::erf_inv(z, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::ndnboost::math::erfc_inv(z, Policy()); }\ |
| \ |
| using ndnboost::math::legendre_next;\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type \ |
| legendre_p(int l, T x){ return ::ndnboost::math::legendre_p(l, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type \ |
| legendre_q(unsigned l, T x){ return ::ndnboost::math::legendre_q(l, x, Policy()); }\ |
| \ |
| using ::ndnboost::math::legendre_next;\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type \ |
| legendre_p(int l, int m, T x){ return ::ndnboost::math::legendre_p(l, m, x, Policy()); }\ |
| \ |
| using ::ndnboost::math::laguerre_next;\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type \ |
| laguerre(unsigned n, T x){ return ::ndnboost::math::laguerre(n, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::laguerre_result<T1, T2>::type \ |
| laguerre(unsigned n, T1 m, T2 x) { return ::ndnboost::math::laguerre(n, m, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type \ |
| hermite(unsigned n, T x){ return ::ndnboost::math::hermite(n, x, Policy()); }\ |
| \ |
| using ndnboost::math::hermite_next;\ |
| \ |
| template <class T1, class T2>\ |
| inline std::complex<typename ndnboost::math::tools::promote_args<T1, T2>::type> \ |
| spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return ndnboost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type \ |
| spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::ndnboost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type \ |
| spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return ndnboost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\ |
| \ |
| template <class T1, class T2, class Policy>\ |
| inline typename ndnboost::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 ndnboost::math::tools::promote_args<T1, T2, T3>::type \ |
| ellint_rf(T1 x, T2 y, T3 z){ return ::ndnboost::math::ellint_rf(x, y, z, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3>::type \ |
| ellint_rd(T1 x, T2 y, T3 z){ return ::ndnboost::math::ellint_rd(x, y, z, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type \ |
| ellint_rc(T1 x, T2 y){ return ::ndnboost::math::ellint_rc(x, y, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3, class T4>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3, T4>::type \ |
| ellint_rj(T1 x, T2 y, T3 z, T4 p){ return ndnboost::math::ellint_rj(x, y, z, p, Policy()); }\ |
| \ |
| template <typename T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type ellint_2(T k){ return ndnboost::math::ellint_2(k, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return ndnboost::math::ellint_2(k, phi, Policy()); }\ |
| \ |
| template <typename T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type ellint_1(T k){ return ndnboost::math::ellint_1(k, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return ndnboost::math::ellint_1(k, phi, Policy()); }\ |
| \ |
| template <class T1, class T2, class T3>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return ndnboost::math::ellint_3(k, v, phi, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return ndnboost::math::ellint_3(k, v, Policy()); }\ |
| \ |
| using ndnboost::math::max_factorial;\ |
| template <class RT>\ |
| inline RT factorial(unsigned int i) { return ndnboost::math::factorial<RT>(i, Policy()); }\ |
| using ndnboost::math::unchecked_factorial;\ |
| template <class RT>\ |
| inline RT double_factorial(unsigned i){ return ndnboost::math::double_factorial<RT>(i, Policy()); }\ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return ndnboost::math::falling_factorial(x, n, Policy()); }\ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return ndnboost::math::rising_factorial(x, n, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type tgamma(RT z){ return ndnboost::math::tgamma(z, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return ndnboost::math::tgamma1pm1(z, Policy()); }\ |
| \ |
| template <class RT1, class RT2>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return ndnboost::math::tgamma(a, z, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return ndnboost::math::lgamma(z, sign, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type lgamma(RT x){ return ndnboost::math::lgamma(x, Policy()); }\ |
| \ |
| template <class RT1, class RT2>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return ndnboost::math::tgamma_lower(a, z, Policy()); }\ |
| \ |
| template <class RT1, class RT2>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return ndnboost::math::gamma_q(a, z, Policy()); }\ |
| \ |
| template <class RT1, class RT2>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return ndnboost::math::gamma_p(a, z, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return ndnboost::math::tgamma_delta_ratio(z, delta, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return ndnboost::math::tgamma_ratio(a, b, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return ndnboost::math::gamma_p_derivative(a, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return ndnboost::math::gamma_p_inv(a, p, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return ndnboost::math::gamma_p_inva(a, p, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return ndnboost::math::gamma_q_inv(a, q, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return ndnboost::math::gamma_q_inva(a, q, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type digamma(T x){ return ndnboost::math::digamma(x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type \ |
| hypot(T1 x, T2 y){ return ndnboost::math::hypot(x, y, Policy()); }\ |
| \ |
| template <class RT>\ |
| inline typename ndnboost::math::tools::promote_args<RT>::type cbrt(RT z){ return ndnboost::math::cbrt(z, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type log1p(T x){ return ndnboost::math::log1p(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type log1pmx(T x){ return ndnboost::math::log1pmx(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type expm1(T x){ return ndnboost::math::expm1(x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::tools::promote_args<T1, T2>::type \ |
| powm1(const T1 a, const T2 z){ return ndnboost::math::powm1(a, z, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return ndnboost::math::sqrt1pm1(val, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type sinc_pi(T x){ return ndnboost::math::sinc_pi(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type sinhc_pi(T x){ return ndnboost::math::sinhc_pi(x, Policy()); }\ |
| \ |
| template<typename T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type asinh(const T x){ return ndnboost::math::asinh(x, Policy()); }\ |
| \ |
| template<typename T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type acosh(const T x){ return ndnboost::math::acosh(x, Policy()); }\ |
| \ |
| template<typename T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type atanh(const T x){ return ndnboost::math::atanh(x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\ |
| { return ndnboost::math::cyl_bessel_j(v, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\ |
| { return ndnboost::math::sph_bessel(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ |
| cyl_bessel_i(T1 v, T2 x) { return ndnboost::math::cyl_bessel_i(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ |
| cyl_bessel_k(T1 v, T2 x) { return ndnboost::math::cyl_bessel_k(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type \ |
| cyl_neumann(T1 v, T2 x){ return ndnboost::math::cyl_neumann(v, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::detail::bessel_traits<T, T, Policy >::result_type \ |
| sph_neumann(unsigned v, T x){ return ndnboost::math::sph_neumann(v, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\ |
| { return ndnboost::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)\ |
| { ndnboost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\ |
| { return ndnboost::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)\ |
| { ndnboost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type sin_pi(T x){ return ndnboost::math::sin_pi(x); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type cos_pi(T x){ return ndnboost::math::cos_pi(x); }\ |
| \ |
| using ndnboost::math::fpclassify;\ |
| using ndnboost::math::isfinite;\ |
| using ndnboost::math::isinf;\ |
| using ndnboost::math::isnan;\ |
| using ndnboost::math::isnormal;\ |
| using ndnboost::math::signbit;\ |
| using ndnboost::math::sign;\ |
| using ndnboost::math::copysign;\ |
| using ndnboost::math::changesign;\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\ |
| { return ndnboost::math::expint(z, u, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type expint(T z){ return ndnboost::math::expint(z, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type zeta(T s){ return ndnboost::math::zeta(s, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T round(const T& v){ using ndnboost::math::round; return round(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline int iround(const T& v){ using ndnboost::math::iround; return iround(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline long lround(const T& v){ using ndnboost::math::lround; return lround(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T trunc(const T& v){ using ndnboost::math::trunc; return trunc(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline int itrunc(const T& v){ using ndnboost::math::itrunc; return itrunc(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline long ltrunc(const T& v){ using ndnboost::math::ltrunc; return ltrunc(v, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T modf(const T& v, T* ipart){ using ndnboost::math::modf; return modf(v, ipart, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T modf(const T& v, int* ipart){ using ndnboost::math::modf; return modf(v, ipart, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T modf(const T& v, long* ipart){ using ndnboost::math::modf; return modf(v, ipart, Policy()); }\ |
| \ |
| template <int N, class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type pow(T v){ return ndnboost::math::pow<N>(v, Policy()); }\ |
| \ |
| template <class T> T nextafter(const T& a, const T& b){ return ndnboost::math::nextafter(a, b, Policy()); }\ |
| template <class T> T float_next(const T& a){ return ndnboost::math::float_next(a, Policy()); }\ |
| template <class T> T float_prior(const T& a){ return ndnboost::math::float_prior(a, Policy()); }\ |
| template <class T> T float_distance(const T& a, const T& b){ return ndnboost::math::float_distance(a, b, Policy()); }\ |
| \ |
| template <class RT1, class RT2>\ |
| inline typename ndnboost::math::tools::promote_args<RT1, RT2>::type owens_t(RT1 a, RT2 z){ return ndnboost::math::owens_t(a, z, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline std::complex<typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\ |
| { return ndnboost::math::cyl_hankel_1(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline std::complex<typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\ |
| { return ndnboost::math::cyl_hankel_2(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline std::complex<typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\ |
| { return ndnboost::math::sph_hankel_1(v, x, Policy()); }\ |
| \ |
| template <class T1, class T2>\ |
| inline std::complex<typename ndnboost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\ |
| { return ndnboost::math::sph_hankel_2(v, x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\ |
| { return ndnboost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\ |
| \ |
| template <class U, class T>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_sn(U k, T theta)\ |
| { return ndnboost::math::jacobi_sn(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_cn(T k, U theta)\ |
| { return ndnboost::math::jacobi_cn(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_dn(T k, U theta)\ |
| { return ndnboost::math::jacobi_dn(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_cd(T k, U theta)\ |
| { return ndnboost::math::jacobi_cd(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_dc(T k, U theta)\ |
| { return ndnboost::math::jacobi_dc(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_ns(T k, U theta)\ |
| { return ndnboost::math::jacobi_ns(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_sd(T k, U theta)\ |
| { return ndnboost::math::jacobi_sd(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_ds(T k, U theta)\ |
| { return ndnboost::math::jacobi_ds(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_nc(T k, U theta)\ |
| { return ndnboost::math::jacobi_nc(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_nd(T k, U theta)\ |
| { return ndnboost::math::jacobi_nd(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_sc(T k, U theta)\ |
| { return ndnboost::math::jacobi_sc(k, theta, Policy()); }\ |
| \ |
| template <class T, class U>\ |
| inline typename ndnboost::math::tools::promote_args<T, U>::type jacobi_cs(T k, U theta)\ |
| { return ndnboost::math::jacobi_cs(k, theta, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type airy_ai(T x)\ |
| { return ndnboost::math::airy_ai(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type airy_bi(T x)\ |
| { return ndnboost::math::airy_bi(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type airy_ai_prime(T x)\ |
| { return ndnboost::math::airy_ai_prime(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline typename ndnboost::math::tools::promote_args<T>::type airy_bi_prime(T x)\ |
| { return ndnboost::math::airy_bi_prime(x, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T airy_ai_zero(int m)\ |
| { return ndnboost::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 ndnboost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\ |
| \ |
| template <class T>\ |
| inline T airy_bi_zero(int m)\ |
| { return ndnboost::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 ndnboost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\ |
| \ |
| |
| |
| |
| |
| |
| #endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP |
| |
| |