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. // Copyright Matt Borland 2024 // 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/tools/config.hpp> #include <boost/math/tools/promotion.hpp> // for argument promotion. #include <boost/math/tools/type_traits.hpp> #include <boost/math/tools/complex.hpp> #include <boost/math/policies/policy.hpp> #ifdef BOOST_MATH_HAS_NVRTC namespace boost { namespace math { template <class RT1, class RT2, class A> BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<RT1, RT2, A>::type beta(RT1 a, RT2 b, A arg); namespace detail{ template <class T, class U, class V> struct ellint_3_result { using type = typename boost::math::conditional< policies::is_policy<V>::value, tools::promote_args_t<T, U>, tools::promote_args_t<T, U, V> >::type; }; template <class T, class U> struct expint_result { using type = typename boost::math::conditional< policies::is_policy<U>::value, tools::promote_args_t<T>, typename tools::promote_args<U>::type >::type; }; typedef boost::math::integral_constant<int, 0> bessel_no_int_tag; // No integer optimisation possible. typedef boost::math::integral_constant<int, 1> bessel_maybe_int_tag; // Maybe integer optimisation. typedef boost::math::integral_constant<int, 2> bessel_int_tag; // Definite integer optimisation. template <class T1, class T2, class Policy> struct bessel_traits { using result_type = typename boost::math::conditional< boost::math::is_integral<T1>::value, typename tools::promote_args<T2>::type, tools::promote_args_t<T1, T2> >::type; typedef typename policies::precision<result_type, Policy>::type precision_type; using optimisation_tag = typename boost::math::conditional< (precision_type::value <= 0 || precision_type::value > 64), bessel_no_int_tag, typename boost::math::conditional< boost::math::is_integral<T1>::value, bessel_int_tag, bessel_maybe_int_tag >::type >::type; using optimisation_tag128 = typename boost::math::conditional< (precision_type::value <= 0 || precision_type::value > 113), bessel_no_int_tag, typename boost::math::conditional< boost::math::is_integral<T1>::value, bessel_int_tag, bessel_maybe_int_tag >::type >::type; }; } // namespace detail } // namespace math } // namespace boost #else #include <vector> #include <complex> #include <type_traits> #include <boost/math/special_functions/detail/round_fwd.hpp> #include <boost/math/tools/type_traits.hpp> #include <boost/math/policies/policy.hpp> #define BOOST_NO_MACRO_EXPAND /**/ namespace boost { namespace math { // Math functions (in roughly alphabetic order). // Beta functions. template <class RT1, class RT2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> beta(RT1 a, RT2 b); // Beta function (2 arguments). template <class RT1, class RT2, class A> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, A> beta(RT1 a, RT2 b, A x); // Beta function (3 arguments). template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments). template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> betac(RT1 a, RT2 b, RT3 x); template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> betac(RT1 a, RT2 b, RT3 x, const Policy& pol); template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function. template <class T1, class T2, class T3, class T4> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ibeta_inv(T1 a, T2 b, T3 p, T4* py); template <class T1, class T2, class T3, class T4, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol); template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function. template <class T1, class T2, class T3, class T4> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ibetac_inv(T1 a, T2 b, T3 q, T4* py); template <class T1, class T2, class T3, class T4, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol); template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function. template <class RT1, class RT2, class RT3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_derivative(RT1 a, RT2 b, RT3 x); // derivative of incomplete beta template <class RT1, class RT2, class RT3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2, RT3> ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol); // derivative of incomplete beta // Binomial: template <class T, class Policy> BOOST_MATH_GPU_ENABLED T binomial_coefficient(unsigned n, unsigned k, const Policy& pol); template <class T> BOOST_MATH_GPU_ENABLED T binomial_coefficient(unsigned n, unsigned k); // erf & erfc error functions. template <class RT> // Error function. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erf(RT z); template <class RT, class Policy> // Error function. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erf(RT z, const Policy&); template <class RT>// Error function complement. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erfc(RT z); template <class RT, class Policy>// Error function complement. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erfc(RT z, const Policy&); template <class RT>// Error function inverse. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erf_inv(RT z); template <class RT, class Policy>// Error function inverse. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erf_inv(RT z, const Policy& pol); template <class RT>// Error function complement inverse. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erfc_inv(RT z); template <class RT, class Policy>// Error function complement inverse. BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> erfc_inv(RT z, const Policy& pol); // Polynomials: template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1); template <class T> tools::promote_args_t<T> legendre_p(int l, T x); template <class T> tools::promote_args_t<T> legendre_p_prime(int l, T x); template <class T, class Policy> inline std::vector<T> legendre_p_zeros(int l, const Policy& pol); template <class T> inline std::vector<T> legendre_p_zeros(int l); template <class T, class Policy> typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type legendre_p(int l, T x, const Policy& pol); template <class T, class Policy> inline typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type legendre_p_prime(int l, T x, const Policy& pol); template <class T> tools::promote_args_t<T> legendre_q(unsigned l, T x); template <class T, class Policy> typename std::enable_if<policies::is_policy<Policy>::value, tools::promote_args_t<T>>::type legendre_q(unsigned l, T x, const Policy& pol); template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1); template <class T> tools::promote_args_t<T> legendre_p(int l, int m, T x); template <class T, class Policy> tools::promote_args_t<T> legendre_p(int l, int m, T x, const Policy& pol); template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1); template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1); template <class T> tools::promote_args_t<T> laguerre(unsigned n, T x); template <class T, class Policy> tools::promote_args_t<T> laguerre(unsigned n, unsigned m, T x, const Policy& pol); template <class T1, class T2> struct laguerre_result { using type = typename std::conditional< policies::is_policy<T2>::value, typename tools::promote_args<T1>::type, typename tools::promote_args<T2>::type >::type; }; template <class T1, class T2> typename laguerre_result<T1, T2>::type laguerre(unsigned n, T1 m, T2 x); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> hermite(unsigned n, T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> hermite(unsigned n, T x, const Policy& pol); template <class T1, class T2, class T3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1); template<class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> chebyshev_next(T1 const & x, T2 const & Tn, T3 const & Tn_1); template <class Real, class Policy> tools::promote_args_t<Real> chebyshev_t(unsigned n, Real const & x, const Policy&); template<class Real> tools::promote_args_t<Real> chebyshev_t(unsigned n, Real const & x); template <class Real, class Policy> tools::promote_args_t<Real> chebyshev_u(unsigned n, Real const & x, const Policy&); template<class Real> tools::promote_args_t<Real> chebyshev_u(unsigned n, Real const & x); template <class Real, class Policy> tools::promote_args_t<Real> chebyshev_t_prime(unsigned n, Real const & x, const Policy&); template<class Real> tools::promote_args_t<Real> chebyshev_t_prime(unsigned n, Real const & x); template<class Real, class T2> Real chebyshev_clenshaw_recurrence(const Real* const c, size_t length, const T2& x); template <class T1, class T2> std::complex<tools::promote_args_t<T1, T2>> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> std::complex<tools::promote_args_t<T1, T2>> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); template <class T1, class T2> tools::promote_args_t<T1, T2> spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); template <class T1, class T2> tools::promote_args_t<T1, T2> spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi); template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol); // Elliptic integrals: template <class T1, class T2, class T3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rf(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rf(T1 x, T2 y, T3 z, const Policy& pol); template <class T1, class T2, class T3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rd(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rd(T1 x, T2 y, T3 z, const Policy& pol); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_rc(T1 x, T2 y); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_rc(T1 x, T2 y, const Policy& pol); template <class T1, class T2, class T3, class T4> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ellint_rj(T1 x, T2 y, T3 z, T4 p); template <class T1, class T2, class T3, class T4, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3, T4> ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol); template <class T1, class T2, class T3> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rg(T1 x, T2 y, T3 z); template <class T1, class T2, class T3, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_rg(T1 x, T2 y, T3 z, const Policy& pol); template <typename T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> ellint_2(T k); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi, const Policy& pol); template <typename T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> ellint_1(T k); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi, const Policy& pol); template <typename T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> ellint_d(T k); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi, const Policy& pol); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi, const Policy& pol); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi, const Policy& pol); namespace detail{ template <class T, class U, class V> struct ellint_3_result { using type = typename boost::math::conditional< policies::is_policy<V>::value, tools::promote_args_t<T, U>, tools::promote_args_t<T, U, V> >::type; }; } // namespace detail template <class T1, class T2, class T3> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3> ellint_3(T1 k, T2 v, T3 phi, const Policy& pol); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> ellint_3(T1 k, T2 v); // Factorial functions. // Note: not for integral types, at present. template <class RT> struct max_factorial; template <class RT> BOOST_MATH_GPU_ENABLED RT factorial(unsigned int); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED RT factorial(unsigned int, const Policy& pol); template <class RT> BOOST_MATH_GPU_ENABLED RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT)); template <class RT> BOOST_MATH_GPU_ENABLED RT double_factorial(unsigned i); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED RT double_factorial(unsigned i, const Policy& pol); template <class RT> tools::promote_args_t<RT> falling_factorial(RT x, unsigned n); template <class RT, class Policy> tools::promote_args_t<RT> falling_factorial(RT x, unsigned n, const Policy& pol); template <class RT> tools::promote_args_t<RT> rising_factorial(RT x, int n); template <class RT, class Policy> tools::promote_args_t<RT> rising_factorial(RT x, int n, const Policy& pol); // Gamma functions. template <class RT> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> tgamma(RT z); template <class RT> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> tgamma1pm1(RT z); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> tgamma1pm1(RT z, const Policy& pol); template <class RT1, class RT2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z, const Policy& pol); template <class RT> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> lgamma(RT z, int* sign); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> lgamma(RT z, int* sign, const Policy& pol); template <class RT> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> lgamma(RT x); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> lgamma(RT x, const Policy& pol); template <class RT1, class RT2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z, const Policy&); template <class RT1, class RT2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z, const Policy&); template <class RT1, class RT2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z); template <class RT1, class RT2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x, const Policy&); // gamma inverse. template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q, const Policy&); // digamma: template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> digamma(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> digamma(T x, const Policy&); // trigamma: template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> trigamma(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> trigamma(T x, const Policy&); // polygamma: template <class T> tools::promote_args_t<T> polygamma(int n, T x); template <class T, class Policy> tools::promote_args_t<T> polygamma(int n, T x, const Policy&); // Hypotenuse function sqrt(x ^ 2 + y ^ 2). template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> hypot(T1 x, T2 y); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> hypot(T1 x, T2 y, const Policy&); // cbrt - cube root. template <class RT> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> cbrt(RT z); template <class RT, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<RT> cbrt(RT z, const Policy&); // log1p is log(x + 1) template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> log1p(T); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> log1p(T, const Policy&); // log1pmx is log(x + 1) - x template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> log1pmx(T); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> log1pmx(T, const Policy&); // Exp (x) minus 1 functions. template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> expm1(T); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> expm1(T, const Policy&); // Power - 1 template <class T1, class T2> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> powm1(const T1 a, const T2 z); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2> powm1(const T1 a, const T2 z, const Policy&); // sqrt(1+x) - 1 template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sqrt1pm1(const T& val); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sqrt1pm1(const T& val, const Policy&); // sinus cardinals: template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sinc_pi(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sinc_pi(T x, const Policy&); template <class T> tools::promote_args_t<T> sinhc_pi(T x); template <class T, class Policy> tools::promote_args_t<T> sinhc_pi(T x, const Policy&); // inverse hyperbolics: template<typename T> tools::promote_args_t<T> asinh(T x); template<typename T, class Policy> tools::promote_args_t<T> asinh(T x, const Policy&); template<typename T> tools::promote_args_t<T> acosh(T x); template<typename T, class Policy> tools::promote_args_t<T> acosh(T x, const Policy&); template<typename T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> atanh(T x); template<typename T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> atanh(T x, const Policy&); namespace detail{ typedef boost::math::integral_constant<int, 0> bessel_no_int_tag; // No integer optimisation possible. typedef boost::math::integral_constant<int, 1> bessel_maybe_int_tag; // Maybe integer optimisation. typedef boost::math::integral_constant<int, 2> bessel_int_tag; // Definite integer optimisation. template <class T1, class T2, class Policy> struct bessel_traits { using result_type = typename boost::math::conditional< boost::math::is_integral<T1>::value, typename tools::promote_args<T2>::type, tools::promote_args_t<T1, T2> >::type; typedef typename policies::precision<result_type, Policy>::type precision_type; using optimisation_tag = typename boost::math::conditional< (precision_type::value <= 0 || precision_type::value > 64), bessel_no_int_tag, typename boost::math::conditional< boost::math::is_integral<T1>::value, bessel_int_tag, bessel_maybe_int_tag >::type >::type; using optimisation_tag128 = typename boost::math::conditional< (precision_type::value <= 0 || precision_type::value > 113), bessel_no_int_tag, typename boost::math::conditional< boost::math::is_integral<T1>::value, bessel_int_tag, bessel_maybe_int_tag >::type >::type; }; } // detail // Bessel functions: template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x); template <class T1, class T2> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x); template <class T1, class T2, class Policy> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x); template <class T1, class T2> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x); template <class T1, class T2> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED 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> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol); template <class T1, class T2> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x); template <class T1, class T2> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m); template <class T, class OutputIterator> BOOST_MATH_GPU_ENABLED OutputIterator cyl_bessel_j_zero(T v, int start_index, unsigned number_of_zeros, OutputIterator out_it); template <class T, class OutputIterator, class Policy> BOOST_MATH_GPU_ENABLED OutputIterator cyl_bessel_j_zero(T v, int start_index, unsigned number_of_zeros, OutputIterator out_it, const Policy&); template <class T, class Policy> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol); template <class T> BOOST_MATH_GPU_ENABLED typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m); template <class T, class OutputIterator> BOOST_MATH_GPU_ENABLED OutputIterator cyl_neumann_zero(T v, int start_index, unsigned number_of_zeros, OutputIterator out_it); template <class T, class OutputIterator, class Policy> BOOST_MATH_GPU_ENABLED OutputIterator cyl_neumann_zero(T v, int start_index, unsigned number_of_zeros, OutputIterator out_it, const Policy&); template <class T1, class T2> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::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> BOOST_MATH_GPU_ENABLED boost::math::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_ai(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_ai(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_bi(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_bi(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_ai_prime(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_ai_prime(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_bi_prime(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> airy_bi_prime(T x); template <class T> BOOST_MATH_GPU_ENABLED T airy_ai_zero(int m); template <class T, class Policy> BOOST_MATH_GPU_ENABLED T airy_ai_zero(int m, const Policy&); template <class OutputIterator> BOOST_MATH_GPU_ENABLED OutputIterator airy_ai_zero( int start_index, unsigned number_of_zeros, OutputIterator out_it); template <class OutputIterator, class Policy> BOOST_MATH_GPU_ENABLED OutputIterator airy_ai_zero( int start_index, unsigned number_of_zeros, OutputIterator out_it, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED T airy_bi_zero(int m); template <class T, class Policy> BOOST_MATH_GPU_ENABLED T airy_bi_zero(int m, const Policy&); template <class OutputIterator> BOOST_MATH_GPU_ENABLED OutputIterator airy_bi_zero( int start_index, unsigned number_of_zeros, OutputIterator out_it); template <class OutputIterator, class Policy> BOOST_MATH_GPU_ENABLED OutputIterator airy_bi_zero( int start_index, unsigned number_of_zeros, OutputIterator out_it, const Policy&); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sin_pi(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> sin_pi(T x); template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> cos_pi(T x, const Policy&); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> cos_pi(T x); template <class T> BOOST_MATH_GPU_ENABLED int fpclassify BOOST_NO_MACRO_EXPAND(T t); template <class T> BOOST_MATH_GPU_ENABLED bool isfinite BOOST_NO_MACRO_EXPAND(T z); template <class T> BOOST_MATH_GPU_ENABLED bool isinf BOOST_NO_MACRO_EXPAND(T t); template <class T> BOOST_MATH_GPU_ENABLED bool isnan BOOST_NO_MACRO_EXPAND(T t); template <class T> BOOST_MATH_GPU_ENABLED bool isnormal BOOST_NO_MACRO_EXPAND(T t); template<class T> BOOST_MATH_GPU_ENABLED int signbit BOOST_NO_MACRO_EXPAND(T x); template <class T> BOOST_MATH_GPU_ENABLED int sign BOOST_NO_MACRO_EXPAND(const T& z); template <class T, class U> BOOST_MATH_GPU_ENABLED typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y); template <class T> BOOST_MATH_GPU_ENABLED 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 boost::math::conditional< policies::is_policy<U>::value, tools::promote_args_t<T>, typename tools::promote_args<U>::type >::type type; }; } // namespace detail template <class T, class Policy> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> expint(unsigned n, T z, const Policy&); template <class T, class U> BOOST_MATH_GPU_ENABLED typename detail::expint_result<T, U>::type expint(T const z, U const u); template <class T> BOOST_MATH_GPU_ENABLED tools::promote_args_t<T> expint(T z); // Zeta: template <class T, class Policy> tools::promote_args_t<T> zeta(T s, const Policy&); // Owen's T function: template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> owens_t(T1 h, T2 a, const Policy& pol); template <class T1, class T2> tools::promote_args_t<T1, T2> owens_t(T1 h, T2 a); // Jacobi Functions: template <class T, class U, class V, class Policy> tools::promote_args_t<T, U, V> jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&); template <class T, class U, class V> tools::promote_args_t<T, U, V> jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0); template <class U, class T, class Policy> tools::promote_args_t<T, U> jacobi_sn(U k, T theta, const Policy& pol); template <class U, class T> tools::promote_args_t<T, U> jacobi_sn(U k, T theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_cn(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_cn(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_dn(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_dn(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_cd(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_cd(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_dc(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_dc(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_ns(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_ns(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_sd(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_sd(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_ds(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_ds(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_nc(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_nc(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_nd(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_nd(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_sc(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_sc(T k, U theta); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_cs(T k, U theta, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_cs(T k, U theta); // Jacobi Theta Functions: template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta1(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta1(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta2(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta2(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta3(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta3(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta4(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta4(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta1tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta1tau(T z, U tau); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta2tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta2tau(T z, U tau); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta3tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta3tau(T z, U tau); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta4tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta4tau(T z, U tau); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U tau); template <class T, class U, class Policy> tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U tau, const Policy& pol); template <class T, class U> tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U tau); template <class T> tools::promote_args_t<T> zeta(T s); // pow: template <int N, typename T, class Policy> BOOST_MATH_GPU_ENABLED BOOST_MATH_CXX14_CONSTEXPR tools::promote_args_t<T> pow(T base, const Policy& policy); template <int N, typename T> BOOST_MATH_GPU_ENABLED BOOST_MATH_CXX14_CONSTEXPR tools::promote_args_t<T> pow(T base); // next: template <class T, class U, class Policy> tools::promote_args_t<T, U> nextafter(const T&, const U&, const Policy&); template <class T, class U> tools::promote_args_t<T, U> nextafter(const T&, const U&); template <class T, class Policy> tools::promote_args_t<T> float_next(const T&, const Policy&); template <class T> tools::promote_args_t<T> float_next(const T&); template <class T, class Policy> tools::promote_args_t<T> float_prior(const T&, const Policy&); template <class T> tools::promote_args_t<T> float_prior(const T&); template <class T, class U, class Policy> tools::promote_args_t<T, U> float_distance(const T&, const U&, const Policy&); template <class T, class U> tools::promote_args_t<T, U> float_distance(const T&, const U&); template <class T, class Policy> tools::promote_args_t<T> float_advance(T val, int distance, const Policy& pol); template <class T> tools::promote_args_t<T> float_advance(const T& val, int distance); template <class T, class Policy> tools::promote_args_t<T> ulp(const T& val, const Policy& pol); template <class T> tools::promote_args_t<T> ulp(const T& val); template <class T, class U> tools::promote_args_t<T, U> relative_difference(const T&, const U&); template <class T, class U> tools::promote_args_t<T, U> epsilon_difference(const T&, const U&); template<class T> BOOST_MATH_CONSTEXPR_TABLE_FUNCTION T unchecked_bernoulli_b2n(const std::size_t n); template <class T, class Policy> T bernoulli_b2n(const int i, const Policy &pol); template <class T> T bernoulli_b2n(const int i); template <class T, class OutputIterator, class Policy> OutputIterator bernoulli_b2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it, const Policy& pol); template <class T, class OutputIterator> OutputIterator bernoulli_b2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it); template <class T, class Policy> T tangent_t2n(const int i, const Policy &pol); template <class T> T tangent_t2n(const int i); template <class T, class OutputIterator, class Policy> OutputIterator tangent_t2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it, const Policy& pol); template <class T, class OutputIterator> OutputIterator tangent_t2n(const int start_index, const unsigned number_of_bernoullis_b2n, OutputIterator out_it); // Lambert W: template <class T, class Policy> boost::math::tools::promote_args_t<T> lambert_w0(T z, const Policy& pol); template <class T> boost::math::tools::promote_args_t<T> lambert_w0(T z); template <class T, class Policy> boost::math::tools::promote_args_t<T> lambert_wm1(T z, const Policy& pol); template <class T> boost::math::tools::promote_args_t<T> lambert_wm1(T z); template <class T, class Policy> boost::math::tools::promote_args_t<T> lambert_w0_prime(T z, const Policy& pol); template <class T> boost::math::tools::promote_args_t<T> lambert_w0_prime(T z); template <class T, class Policy> boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z, const Policy& pol); template <class T> boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z); // Hypergeometrics: template <class T1, class T2> tools::promote_args_t<T1, T2> hypergeometric_1F0(T1 a, T2 z); template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> hypergeometric_1F0(T1 a, T2 z, const Policy&); template <class T1, class T2> tools::promote_args_t<T1, T2> hypergeometric_0F1(T1 b, T2 z); template <class T1, class T2, class Policy> tools::promote_args_t<T1, T2> hypergeometric_0F1(T1 b, T2 z, const Policy&); template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> hypergeometric_2F0(T1 a1, T2 a2, T3 z); template <class T1, class T2, class T3, class Policy> tools::promote_args_t<T1, T2, T3> hypergeometric_2F0(T1 a1, T2 a2, T3 z, const Policy&); template <class T1, class T2, class T3> tools::promote_args_t<T1, T2, T3> hypergeometric_1F1(T1 a, T2 b, T3 z); template <class T1, class T2, class T3, class Policy> tools::promote_args_t<T1, T2, T3> hypergeometric_1F1(T1 a, T2 b, T3 z, const Policy&); } // namespace math } // namespace boost #define BOOST_MATH_DETAIL_LL_FUNC(Policy)\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T modf(const T& v, long long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline long long lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline long long llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\ # define BOOST_MATH_DETAIL_11_FUNC(Policy)\ template <class T, class U, class V>\ inline boost::math::tools::promote_args_t<T, U> hypergeometric_1F1(const T& a, const U& b, const V& z)\ { return boost::math::hypergeometric_1F1(a, b, z, Policy()); }\ #define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\ \ BOOST_MATH_DETAIL_LL_FUNC(Policy)\ BOOST_MATH_DETAIL_11_FUNC(Policy)\ \ template <class RT1, class RT2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2> \ beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\ \ template <class RT1, class RT2, class A>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, A> \ beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\ \ template <class T1, class T2, class T3, class T4>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \ 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \ 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\ \ template <class T1, class T2, class T3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> \ ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\ \ template <class T1, class T2, class T3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> \ ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\ \ template <class RT1, class RT2, class RT3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2, RT3> \ ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\ \ template <class T> BOOST_MATH_GPU_ENABLED T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> erf(RT z) { return ::boost::math::erf(z, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\ \ using boost::math::legendre_next;\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> \ legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> \ legendre_p_prime(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> \ legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\ \ using ::boost::math::legendre_next;\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> \ 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 boost::math::tools::promote_args_t<T> \ 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> \ hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\ \ using boost::math::hermite_next;\ \ using boost::math::chebyshev_next;\ \ template<class Real>\ Real chebyshev_t(unsigned n, Real const & x){ return ::boost::math::chebyshev_t(n, x, Policy()); }\ \ template<class Real>\ Real chebyshev_u(unsigned n, Real const & x){ return ::boost::math::chebyshev_u(n, x, Policy()); }\ \ template<class Real>\ Real chebyshev_t_prime(unsigned n, Real const & x){ return ::boost::math::chebyshev_t_prime(n, x, Policy()); }\ \ using ::boost::math::chebyshev_clenshaw_recurrence;\ \ template <class T1, class T2>\ inline std::complex<boost::math::tools::promote_args_t<T1, T2>> \ 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 boost::math::tools::promote_args_t<T1, T2> \ 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 boost::math::tools::promote_args_t<T1, T2> \ 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 boost::math::tools::promote_args_t<T1, T2> \ spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\ \ template <class T1, class T2, class T3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> \ ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\ \ template <class T1, class T2, class T3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> \ ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> \ ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\ \ template <class T1, class T2, class T3, class T4>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3, T4> \ 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> \ ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\ \ template <typename T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\ \ template <typename T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\ \ template <typename T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\ \ template <class T1, class T2, class T3>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2, T3> ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\ \ using boost::math::max_factorial;\ template <class RT>\ BOOST_MATH_GPU_ENABLED inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\ using boost::math::unchecked_factorial;\ template <class RT>\ BOOST_MATH_GPU_ENABLED inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\ template <class RT>\ inline boost::math::tools::promote_args_t<RT> falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\ template <class RT>\ inline boost::math::tools::promote_args_t<RT> rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\ \ template <class RT1, class RT2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2> tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\ \ template <class RT>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT> lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\ \ template <class RT1, class RT2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2> tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\ \ template <class RT1, class RT2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2> gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\ \ template <class RT1, class RT2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<RT1, RT2> gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\ \ template <class T1, class T2>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T1, T2> gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> digamma(T x){ return boost::math::digamma(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> trigamma(T x){ return boost::math::trigamma(x, Policy()); }\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\ \ template <class T1, class T2>\ inline boost::math::tools::promote_args_t<T1, T2> \ BOOST_MATH_GPU_ENABLED hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\ \ template <class RT>\ inline boost::math::tools::promote_args_t<RT> cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> log1p(T x){ return boost::math::log1p(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> expm1(T x){ return boost::math::expm1(x, Policy()); }\ \ template <class T1, class T2>\ inline boost::math::tools::promote_args_t<T1, T2> \ BOOST_MATH_GPU_ENABLED powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\ \ template<typename T>\ inline boost::math::tools::promote_args_t<T> asinh(const T x){ return boost::math::asinh(x, Policy()); }\ \ template<typename T>\ inline boost::math::tools::promote_args_t<T> acosh(const T x){ return boost::math::acosh(x, Policy()); }\ \ template<typename T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> 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>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> sin_pi(T x){ return boost::math::sin_pi(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> cos_pi(T x){ return boost::math::cos_pi(x, Policy()); }\ \ 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>\ BOOST_MATH_GPU_ENABLED inline typename boost::math::tools::promote_args_t<T,U> expint(T const& z, U const& u)\ { return boost::math::expint(z, u, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> expint(T z){ return boost::math::expint(z, Policy()); }\ \ template <class T>\ inline boost::math::tools::promote_args_t<T> zeta(T s){ return boost::math::zeta(s, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\ \ template <int N, class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> pow(T v){ return boost::math::pow<N>(v, Policy()); }\ \ template <class T> T nextafter(const T& a, const T& b){ return static_cast<T>(boost::math::nextafter(a, b, Policy())); }\ template <class T> T float_next(const T& a){ return static_cast<T>(boost::math::float_next(a, Policy())); }\ template <class T> T float_prior(const T& a){ return static_cast<T>(boost::math::float_prior(a, Policy())); }\ template <class T> T float_distance(const T& a, const T& b){ return static_cast<T>(boost::math::float_distance(a, b, Policy())); }\ template <class T> T ulp(const T& a){ return static_cast<T>(boost::math::ulp(a, Policy())); }\ \ template <class RT1, class RT2>\ inline boost::math::tools::promote_args_t<RT1, RT2> owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\ \ template <class T1, class T2>\ inline BOOST_MATH_GPU_ENABLED boost::math::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 BOOST_MATH_GPU_ENABLED boost::math::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 BOOST_MATH_GPU_ENABLED boost::math::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 BOOST_MATH_GPU_ENABLED boost::math::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 boost::math::tools::promote_args_t<T> jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\ { return static_cast<boost::math::tools::promote_args_t<T>>(boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy())); }\ \ template <class U, class T>\ inline boost::math::tools::promote_args_t<T, U> jacobi_sn(U k, T theta)\ { return boost::math::jacobi_sn(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_cn(T k, U theta)\ { return boost::math::jacobi_cn(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_dn(T k, U theta)\ { return boost::math::jacobi_dn(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_cd(T k, U theta)\ { return boost::math::jacobi_cd(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_dc(T k, U theta)\ { return boost::math::jacobi_dc(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_ns(T k, U theta)\ { return boost::math::jacobi_ns(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_sd(T k, U theta)\ { return boost::math::jacobi_sd(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_ds(T k, U theta)\ { return boost::math::jacobi_ds(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_nc(T k, U theta)\ { return boost::math::jacobi_nc(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_nd(T k, U theta)\ { return boost::math::jacobi_nd(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_sc(T k, U theta)\ { return boost::math::jacobi_sc(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_cs(T k, U theta)\ { return boost::math::jacobi_cs(k, theta, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta1(T z, U q)\ { return boost::math::jacobi_theta1(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta2(T z, U q)\ { return boost::math::jacobi_theta2(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta3(T z, U q)\ { return boost::math::jacobi_theta3(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta4(T z, U q)\ { return boost::math::jacobi_theta4(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta1tau(T z, U q)\ { return boost::math::jacobi_theta1tau(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta2tau(T z, U q)\ { return boost::math::jacobi_theta2tau(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta3tau(T z, U q)\ { return boost::math::jacobi_theta3tau(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta4tau(T z, U q)\ { return boost::math::jacobi_theta4tau(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta3m1(T z, U q)\ { return boost::math::jacobi_theta3m1(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta4m1(T z, U q)\ { return boost::math::jacobi_theta4m1(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta3m1tau(T z, U q)\ { return boost::math::jacobi_theta3m1tau(z, q, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> jacobi_theta4m1tau(T z, U q)\ { return boost::math::jacobi_theta4m1tau(z, q, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> airy_ai(T x)\ { return boost::math::airy_ai(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> airy_bi(T x)\ { return boost::math::airy_bi(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> airy_ai_prime(T x)\ { return boost::math::airy_ai_prime(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline boost::math::tools::promote_args_t<T> airy_bi_prime(T x)\ { return boost::math::airy_bi_prime(x, Policy()); }\ \ template <class T>\ BOOST_MATH_GPU_ENABLED inline T airy_ai_zero(int m)\ { return boost::math::airy_ai_zero<T>(m, Policy()); }\ template <class T, class OutputIterator>\ BOOST_MATH_GPU_ENABLED 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>\ BOOST_MATH_GPU_ENABLED inline T airy_bi_zero(int m)\ { return boost::math::airy_bi_zero<T>(m, Policy()); }\ template <class T, class OutputIterator>\ BOOST_MATH_GPU_ENABLED 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()); }\ \ template <class T> inline boost::math::tools::promote_args_t<T> lambert_w0(T z) { return boost::math::lambert_w0(z, Policy()); }\ template <class T> inline boost::math::tools::promote_args_t<T> lambert_wm1(T z) { return boost::math::lambert_w0(z, Policy()); }\ template <class T> inline boost::math::tools::promote_args_t<T> lambert_w0_prime(T z) { return boost::math::lambert_w0(z, Policy()); }\ template <class T> inline boost::math::tools::promote_args_t<T> lambert_wm1_prime(T z) { return boost::math::lambert_w0(z, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> hypergeometric_1F0(const T& a, const U& z)\ { return boost::math::hypergeometric_1F0(a, z, Policy()); }\ \ template <class T, class U>\ inline boost::math::tools::promote_args_t<T, U> hypergeometric_0F1(const T& a, const U& z)\ { return boost::math::hypergeometric_0F1(a, z, Policy()); }\ \ template <class T, class U, class V>\ inline boost::math::tools::promote_args_t<T, U> hypergeometric_2F0(const T& a1, const U& a2, const V& z)\ { return boost::math::hypergeometric_2F0(a1, a2, z, Policy()); }\ \ #endif // BOOST_MATH_HAS_NVRTC #endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP