1587 lines
67 KiB
Plaintext
1587 lines
67 KiB
Plaintext
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// math_fwd.hpp
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// TODO revise completely for new distribution classes.
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// Copyright Paul A. Bristow 2006.
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// Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// Omnibus list of forward declarations of math special functions.
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// IT = Integer type.
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// RT = Real type (built-in floating-point types, float, double, long double) & User Defined Types
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// AT = Integer or Real type
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#ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP
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#define BOOST_MATH_SPECIAL_MATH_FWD_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/special_functions/detail/round_fwd.hpp>
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#include <boost/math/tools/promotion.hpp> // for argument promotion.
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#include <boost/math/policies/policy.hpp>
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#include <boost/mpl/comparison.hpp>
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#include <boost/utility/enable_if.hpp>
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#include <boost/config/no_tr1/complex.hpp>
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#define BOOST_NO_MACRO_EXPAND /**/
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namespace boost
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{
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namespace math
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{ // Math functions (in roughly alphabetic order).
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// Beta functions.
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template <class RT1, class RT2>
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typename tools::promote_args<RT1, RT2>::type
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beta(RT1 a, RT2 b); // Beta function (2 arguments).
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template <class RT1, class RT2, class A>
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typename tools::promote_args<RT1, RT2, A>::type
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beta(RT1 a, RT2 b, A x); // Beta function (3 arguments).
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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beta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Beta function (3 arguments).
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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betac(RT1 a, RT2 b, RT3 x);
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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betac(RT1 a, RT2 b, RT3 x, const Policy& pol);
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta(RT1 a, RT2 b, RT3 x); // Incomplete beta function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac(RT1 a, RT2 b, RT3 x); // Incomplete beta complement function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac(RT1 a, RT2 b, RT3 x, const Policy& pol); // Incomplete beta complement function.
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template <class T1, class T2, class T3, class T4>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ibeta_inv(T1 a, T2 b, T3 p, T4* py);
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template <class T1, class T2, class T3, class T4, class Policy>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ibeta_inv(T1 a, T2 b, T3 p, T4* py, const Policy& pol);
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_inv(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_inv(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_inva(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_inva(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_invb(RT1 a, RT2 b, RT3 p); // Incomplete beta inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_invb(RT1 a, RT2 b, RT3 p, const Policy&); // Incomplete beta inverse function.
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template <class T1, class T2, class T3, class T4>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ibetac_inv(T1 a, T2 b, T3 q, T4* py);
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template <class T1, class T2, class T3, class T4, class Policy>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ibetac_inv(T1 a, T2 b, T3 q, T4* py, const Policy& pol);
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_inv(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_inv(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_inva(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_inva(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_invb(RT1 a, RT2 b, RT3 q); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibetac_invb(RT1 a, RT2 b, RT3 q, const Policy&); // Incomplete beta complement inverse function.
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template <class RT1, class RT2, class RT3>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_derivative(RT1 a, RT2 b, RT3 x); // derivative of incomplete beta
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template <class RT1, class RT2, class RT3, class Policy>
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typename tools::promote_args<RT1, RT2, RT3>::type
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ibeta_derivative(RT1 a, RT2 b, RT3 x, const Policy& pol); // derivative of incomplete beta
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// Binomial:
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template <class T, class Policy>
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T binomial_coefficient(unsigned n, unsigned k, const Policy& pol);
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template <class T>
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T binomial_coefficient(unsigned n, unsigned k);
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// erf & erfc error functions.
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template <class RT> // Error function.
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typename tools::promote_args<RT>::type erf(RT z);
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template <class RT, class Policy> // Error function.
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typename tools::promote_args<RT>::type erf(RT z, const Policy&);
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template <class RT>// Error function complement.
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typename tools::promote_args<RT>::type erfc(RT z);
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template <class RT, class Policy>// Error function complement.
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typename tools::promote_args<RT>::type erfc(RT z, const Policy&);
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template <class RT>// Error function inverse.
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typename tools::promote_args<RT>::type erf_inv(RT z);
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template <class RT, class Policy>// Error function inverse.
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typename tools::promote_args<RT>::type erf_inv(RT z, const Policy& pol);
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template <class RT>// Error function complement inverse.
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typename tools::promote_args<RT>::type erfc_inv(RT z);
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template <class RT, class Policy>// Error function complement inverse.
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typename tools::promote_args<RT>::type erfc_inv(RT z, const Policy& pol);
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// Polynomials:
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);
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template <class T>
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typename tools::promote_args<T>::type
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legendre_p(int l, T x);
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#if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
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template <class T, class Policy>
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typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
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legendre_p(int l, T x, const Policy& pol);
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#endif
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template <class T>
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typename tools::promote_args<T>::type
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legendre_q(unsigned l, T x);
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#if !BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
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template <class T, class Policy>
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typename boost::enable_if_c<policies::is_policy<Policy>::value, typename tools::promote_args<T>::type>::type
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legendre_q(unsigned l, T x, const Policy& pol);
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#endif
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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legendre_next(unsigned l, unsigned m, T1 x, T2 Pl, T3 Plm1);
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template <class T>
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typename tools::promote_args<T>::type
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legendre_p(int l, int m, T x);
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template <class T, class Policy>
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typename tools::promote_args<T>::type
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legendre_p(int l, int m, T x, const Policy& pol);
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1);
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1);
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template <class T>
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typename tools::promote_args<T>::type
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laguerre(unsigned n, T x);
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template <class T, class Policy>
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typename tools::promote_args<T>::type
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laguerre(unsigned n, unsigned m, T x, const Policy& pol);
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template <class T1, class T2>
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struct laguerre_result
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{
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typedef typename mpl::if_<
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policies::is_policy<T2>,
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typename tools::promote_args<T1>::type,
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typename tools::promote_args<T2>::type
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>::type type;
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};
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template <class T1, class T2>
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typename laguerre_result<T1, T2>::type
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laguerre(unsigned n, T1 m, T2 x);
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template <class T>
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typename tools::promote_args<T>::type
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hermite(unsigned n, T x);
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template <class T, class Policy>
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typename tools::promote_args<T>::type
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hermite(unsigned n, T x, const Policy& pol);
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1);
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template <class T1, class T2>
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std::complex<typename tools::promote_args<T1, T2>::type>
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spherical_harmonic(unsigned n, int m, T1 theta, T2 phi);
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template <class T1, class T2, class Policy>
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std::complex<typename tools::promote_args<T1, T2>::type>
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spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
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template <class T1, class T2>
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typename tools::promote_args<T1, T2>::type
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spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi);
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template <class T1, class T2, class Policy>
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typename tools::promote_args<T1, T2>::type
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spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
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template <class T1, class T2>
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typename tools::promote_args<T1, T2>::type
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spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi);
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template <class T1, class T2, class Policy>
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typename tools::promote_args<T1, T2>::type
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spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);
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// Elliptic integrals:
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rf(T1 x, T2 y, T3 z);
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template <class T1, class T2, class T3, class Policy>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rf(T1 x, T2 y, T3 z, const Policy& pol);
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rd(T1 x, T2 y, T3 z);
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template <class T1, class T2, class T3, class Policy>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rd(T1 x, T2 y, T3 z, const Policy& pol);
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template <class T1, class T2>
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typename tools::promote_args<T1, T2>::type
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ellint_rc(T1 x, T2 y);
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template <class T1, class T2, class Policy>
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typename tools::promote_args<T1, T2>::type
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ellint_rc(T1 x, T2 y, const Policy& pol);
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template <class T1, class T2, class T3, class T4>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ellint_rj(T1 x, T2 y, T3 z, T4 p);
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template <class T1, class T2, class T3, class T4, class Policy>
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typename tools::promote_args<T1, T2, T3, T4>::type
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ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol);
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template <class T1, class T2, class T3>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rg(T1 x, T2 y, T3 z);
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template <class T1, class T2, class T3, class Policy>
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typename tools::promote_args<T1, T2, T3>::type
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ellint_rg(T1 x, T2 y, T3 z, const Policy& pol);
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template <typename T>
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|
|
typename tools::promote_args<T>::type ellint_2(T k);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi, const Policy& pol);
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
typename tools::promote_args<T>::type ellint_1(T k);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol);
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
typename tools::promote_args<T>::type ellint_d(T k);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol);
|
||
|
|
|
||
|
|
namespace detail{
|
||
|
|
|
||
|
|
template <class T, class U, class V>
|
||
|
|
struct ellint_3_result
|
||
|
|
{
|
||
|
|
typedef typename mpl::if_<
|
||
|
|
policies::is_policy<V>,
|
||
|
|
typename tools::promote_args<T, U>::type,
|
||
|
|
typename tools::promote_args<T, U, V>::type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace detail
|
||
|
|
|
||
|
|
|
||
|
|
template <class T1, class T2, class T3>
|
||
|
|
typename detail::ellint_3_result<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi);
|
||
|
|
|
||
|
|
template <class T1, class T2, class T3, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v);
|
||
|
|
|
||
|
|
// Factorial functions.
|
||
|
|
// Note: not for integral types, at present.
|
||
|
|
template <class RT>
|
||
|
|
struct max_factorial;
|
||
|
|
template <class RT>
|
||
|
|
RT factorial(unsigned int);
|
||
|
|
template <class RT, class Policy>
|
||
|
|
RT factorial(unsigned int, const Policy& pol);
|
||
|
|
template <class RT>
|
||
|
|
RT unchecked_factorial(unsigned int BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(RT));
|
||
|
|
template <class RT>
|
||
|
|
RT double_factorial(unsigned i);
|
||
|
|
template <class RT, class Policy>
|
||
|
|
RT double_factorial(unsigned i, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type rising_factorial(RT x, int n);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol);
|
||
|
|
|
||
|
|
// Gamma functions.
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type tgamma(RT z);
|
||
|
|
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type tgamma1pm1(RT z);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT1, class RT2>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z);
|
||
|
|
|
||
|
|
template <class RT1, class RT2, class Policy>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type lgamma(RT z, int* sign);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type lgamma(RT x);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class RT1, class RT2>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z);
|
||
|
|
|
||
|
|
template <class RT1, class RT2, class Policy>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&);
|
||
|
|
|
||
|
|
template <class RT1, class RT2>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z);
|
||
|
|
|
||
|
|
template <class RT1, class RT2, class Policy>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&);
|
||
|
|
|
||
|
|
template <class RT1, class RT2>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z);
|
||
|
|
|
||
|
|
template <class RT1, class RT2, class Policy>
|
||
|
|
typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&);
|
||
|
|
|
||
|
|
// gamma inverse.
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&);
|
||
|
|
|
||
|
|
// digamma:
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type digamma(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type digamma(T x, const Policy&);
|
||
|
|
|
||
|
|
// trigamma:
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type trigamma(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type trigamma(T x, const Policy&);
|
||
|
|
|
||
|
|
// polygamma:
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type polygamma(int n, T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type polygamma(int n, T x, const Policy&);
|
||
|
|
|
||
|
|
// Hypotenuse function sqrt(x ^ 2 + y ^ 2).
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type
|
||
|
|
hypot(T1 x, T2 y);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type
|
||
|
|
hypot(T1 x, T2 y, const Policy&);
|
||
|
|
|
||
|
|
// cbrt - cube root.
|
||
|
|
template <class RT>
|
||
|
|
typename tools::promote_args<RT>::type cbrt(RT z);
|
||
|
|
|
||
|
|
template <class RT, class Policy>
|
||
|
|
typename tools::promote_args<RT>::type cbrt(RT z, const Policy&);
|
||
|
|
|
||
|
|
// log1p is log(x + 1)
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type log1p(T);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type log1p(T, const Policy&);
|
||
|
|
|
||
|
|
// log1pmx is log(x + 1) - x
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type log1pmx(T);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type log1pmx(T, const Policy&);
|
||
|
|
|
||
|
|
// Exp (x) minus 1 functions.
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type expm1(T);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type expm1(T, const Policy&);
|
||
|
|
|
||
|
|
// Power - 1
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type
|
||
|
|
powm1(const T1 a, const T2 z);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type
|
||
|
|
powm1(const T1 a, const T2 z, const Policy&);
|
||
|
|
|
||
|
|
// sqrt(1+x) - 1
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type sqrt1pm1(const T& val);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&);
|
||
|
|
|
||
|
|
// sinus cardinals:
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type sinc_pi(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type sinc_pi(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type sinhc_pi(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&);
|
||
|
|
|
||
|
|
// inverse hyperbolics:
|
||
|
|
template<typename T>
|
||
|
|
typename tools::promote_args<T>::type asinh(T x);
|
||
|
|
|
||
|
|
template<typename T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type asinh(T x, const Policy&);
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
typename tools::promote_args<T>::type acosh(T x);
|
||
|
|
|
||
|
|
template<typename T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type acosh(T x, const Policy&);
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
typename tools::promote_args<T>::type atanh(T x);
|
||
|
|
|
||
|
|
template<typename T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type atanh(T x, const Policy&);
|
||
|
|
|
||
|
|
namespace detail{
|
||
|
|
|
||
|
|
typedef mpl::int_<0> bessel_no_int_tag; // No integer optimisation possible.
|
||
|
|
typedef mpl::int_<1> bessel_maybe_int_tag; // Maybe integer optimisation.
|
||
|
|
typedef mpl::int_<2> bessel_int_tag; // Definite integer optimistaion.
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
struct bessel_traits
|
||
|
|
{
|
||
|
|
typedef typename mpl::if_<
|
||
|
|
is_integral<T1>,
|
||
|
|
typename tools::promote_args<T2>::type,
|
||
|
|
typename tools::promote_args<T1, T2>::type
|
||
|
|
>::type result_type;
|
||
|
|
|
||
|
|
typedef typename policies::precision<result_type, Policy>::type precision_type;
|
||
|
|
|
||
|
|
typedef typename mpl::if_<
|
||
|
|
mpl::or_<
|
||
|
|
mpl::less_equal<precision_type, mpl::int_<0> >,
|
||
|
|
mpl::greater<precision_type, mpl::int_<64> > >,
|
||
|
|
bessel_no_int_tag,
|
||
|
|
typename mpl::if_<
|
||
|
|
is_integral<T1>,
|
||
|
|
bessel_int_tag,
|
||
|
|
bessel_maybe_int_tag
|
||
|
|
>::type
|
||
|
|
>::type optimisation_tag;
|
||
|
|
};
|
||
|
|
} // detail
|
||
|
|
|
||
|
|
// Bessel functions:
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol);
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x);
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol);
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x);
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol);
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x);
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol);
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x);
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol);
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x);
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol);
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x);
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m);
|
||
|
|
|
||
|
|
template <class T, class OutputIterator>
|
||
|
|
OutputIterator cyl_bessel_j_zero(T v,
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it);
|
||
|
|
|
||
|
|
template <class T, class OutputIterator, class Policy>
|
||
|
|
OutputIterator cyl_bessel_j_zero(T v,
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy&);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m);
|
||
|
|
|
||
|
|
template <class T, class OutputIterator>
|
||
|
|
OutputIterator cyl_neumann_zero(T v,
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it);
|
||
|
|
|
||
|
|
template <class T, class OutputIterator, class Policy>
|
||
|
|
OutputIterator cyl_neumann_zero(T v,
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy&);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type airy_ai(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type airy_ai(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type airy_bi(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type airy_bi(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type airy_ai_prime(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type airy_ai_prime(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type airy_bi_prime(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type airy_bi_prime(T x);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
T airy_ai_zero(int m);
|
||
|
|
template <class T, class Policy>
|
||
|
|
T airy_ai_zero(int m, const Policy&);
|
||
|
|
|
||
|
|
template <class OutputIterator>
|
||
|
|
OutputIterator airy_ai_zero(
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it);
|
||
|
|
template <class OutputIterator, class Policy>
|
||
|
|
OutputIterator airy_ai_zero(
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
T airy_bi_zero(int m);
|
||
|
|
template <class T, class Policy>
|
||
|
|
T airy_bi_zero(int m, const Policy&);
|
||
|
|
|
||
|
|
template <class OutputIterator>
|
||
|
|
OutputIterator airy_bi_zero(
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it);
|
||
|
|
template <class OutputIterator, class Policy>
|
||
|
|
OutputIterator airy_bi_zero(
|
||
|
|
int start_index,
|
||
|
|
unsigned number_of_zeros,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy&);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type sin_pi(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type sin_pi(T x);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type cos_pi(T x, const Policy&);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type cos_pi(T x);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
int fpclassify BOOST_NO_MACRO_EXPAND(T t);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
bool isfinite BOOST_NO_MACRO_EXPAND(T z);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
bool isinf BOOST_NO_MACRO_EXPAND(T t);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
bool isnan BOOST_NO_MACRO_EXPAND(T t);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
bool isnormal BOOST_NO_MACRO_EXPAND(T t);
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
int signbit BOOST_NO_MACRO_EXPAND(T x);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
int sign BOOST_NO_MACRO_EXPAND(const T& z);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args_permissive<T, U>::type copysign BOOST_NO_MACRO_EXPAND(const T& x, const U& y);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args_permissive<T>::type changesign BOOST_NO_MACRO_EXPAND(const T& z);
|
||
|
|
|
||
|
|
// Exponential integrals:
|
||
|
|
namespace detail{
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
struct expint_result
|
||
|
|
{
|
||
|
|
typedef typename mpl::if_<
|
||
|
|
policies::is_policy<U>,
|
||
|
|
typename tools::promote_args<T>::type,
|
||
|
|
typename tools::promote_args<U>::type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace detail
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type expint(unsigned n, T z, const Policy&);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename detail::expint_result<T, U>::type expint(T const z, U const u);
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type expint(T z);
|
||
|
|
|
||
|
|
// Zeta:
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type zeta(T s, const Policy&);
|
||
|
|
|
||
|
|
// Owen's T function:
|
||
|
|
template <class T1, class T2, class Policy>
|
||
|
|
typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T1, class T2>
|
||
|
|
typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a);
|
||
|
|
|
||
|
|
// Jacobi Functions:
|
||
|
|
template <class T, class U, class V, class Policy>
|
||
|
|
typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn, V* pdn, const Policy&);
|
||
|
|
|
||
|
|
template <class T, class U, class V>
|
||
|
|
typename tools::promote_args<T, U, V>::type jacobi_elliptic(T k, U theta, V* pcn = 0, V* pdn = 0);
|
||
|
|
|
||
|
|
template <class U, class T, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class U, class T>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sn(U k, T theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cn(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_dn(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cd(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_dc(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_ns(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sd(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_ds(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_nc(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_nd(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_sc(T k, U theta);
|
||
|
|
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta, const Policy& pol);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type jacobi_cs(T k, U theta);
|
||
|
|
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type zeta(T s);
|
||
|
|
|
||
|
|
// pow:
|
||
|
|
template <int N, typename T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type pow(T base, const Policy& policy);
|
||
|
|
|
||
|
|
template <int N, typename T>
|
||
|
|
typename tools::promote_args<T>::type pow(T base);
|
||
|
|
|
||
|
|
// next:
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type nextafter(const T&, const U&, const Policy&);
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type nextafter(const T&, const U&);
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type float_next(const T&, const Policy&);
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type float_next(const T&);
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type float_prior(const T&, const Policy&);
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type float_prior(const T&);
|
||
|
|
template <class T, class U, class Policy>
|
||
|
|
typename tools::promote_args<T, U>::type float_distance(const T&, const U&, const Policy&);
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type float_distance(const T&, const U&);
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol);
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type float_advance(const T& val, int distance);
|
||
|
|
|
||
|
|
template <class T, class Policy>
|
||
|
|
typename tools::promote_args<T>::type ulp(const T& val, const Policy& pol);
|
||
|
|
template <class T>
|
||
|
|
typename tools::promote_args<T>::type ulp(const T& val);
|
||
|
|
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type relative_difference(const T&, const U&);
|
||
|
|
template <class T, class U>
|
||
|
|
typename tools::promote_args<T, U>::type epsilon_difference(const T&, const U&);
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
T unchecked_bernoulli_b2n(const std::size_t n);
|
||
|
|
template <class T, class Policy>
|
||
|
|
T bernoulli_b2n(const int i, const Policy &pol);
|
||
|
|
template <class T>
|
||
|
|
T bernoulli_b2n(const int i);
|
||
|
|
template <class T, class OutputIterator, class Policy>
|
||
|
|
OutputIterator bernoulli_b2n(const int start_index,
|
||
|
|
const unsigned number_of_bernoullis_b2n,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy& pol);
|
||
|
|
template <class T, class OutputIterator>
|
||
|
|
OutputIterator bernoulli_b2n(const int start_index,
|
||
|
|
const unsigned number_of_bernoullis_b2n,
|
||
|
|
OutputIterator out_it);
|
||
|
|
template <class T, class Policy>
|
||
|
|
T tangent_t2n(const int i, const Policy &pol);
|
||
|
|
template <class T>
|
||
|
|
T tangent_t2n(const int i);
|
||
|
|
template <class T, class OutputIterator, class Policy>
|
||
|
|
OutputIterator tangent_t2n(const int start_index,
|
||
|
|
const unsigned number_of_bernoullis_b2n,
|
||
|
|
OutputIterator out_it,
|
||
|
|
const Policy& pol);
|
||
|
|
template <class T, class OutputIterator>
|
||
|
|
OutputIterator tangent_t2n(const int start_index,
|
||
|
|
const unsigned number_of_bernoullis_b2n,
|
||
|
|
OutputIterator out_it);
|
||
|
|
|
||
|
|
} // namespace math
|
||
|
|
} // namespace boost
|
||
|
|
|
||
|
|
#ifdef BOOST_HAS_LONG_LONG
|
||
|
|
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T modf(const T& v, boost::long_long_type* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline boost::long_long_type lltrunc(const T& v){ using boost::math::lltrunc; return lltrunc(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline boost::long_long_type llround(const T& v){ using boost::math::llround; return llround(v, Policy()); }\
|
||
|
|
|
||
|
|
#else
|
||
|
|
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\
|
||
|
|
\
|
||
|
|
BOOST_MATH_DETAIL_LL_FUNC(Policy)\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type \
|
||
|
|
beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class A>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, A>::type \
|
||
|
|
beta(RT1 a, RT2 b, A x){ return ::boost::math::beta(a, b, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
betac(RT1 a, RT2 b, RT3 x) { return ::boost::math::betac(a, b, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibeta(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta(a, b, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibetac(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibetac(a, b, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3, class T4>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
|
||
|
|
ibeta_inv(T1 a, T2 b, T3 p, T4* py){ return ::boost::math::ibeta_inv(a, b, p, py, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibeta_inv(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inv(a, b, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3, class T4>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
|
||
|
|
ibetac_inv(T1 a, T2 b, T3 q, T4* py){ return ::boost::math::ibetac_inv(a, b, q, py, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibeta_inva(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_inva(a, b, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
|
||
|
|
ibetac_inva(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_inva(a, b, q, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibeta_invb(RT1 a, RT2 b, RT3 p){ return ::boost::math::ibeta_invb(a, b, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
|
||
|
|
ibetac_invb(T1 a, T2 b, T3 q){ return ::boost::math::ibetac_invb(a, b, q, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibetac_inv(RT1 a, RT2 b, RT3 q){ return ::boost::math::ibetac_inv(a, b, q, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2, class RT3>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2, RT3>::type \
|
||
|
|
ibeta_derivative(RT1 a, RT2 b, RT3 x){ return ::boost::math::ibeta_derivative(a, b, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T> T binomial_coefficient(unsigned n, unsigned k){ return ::boost::math::binomial_coefficient<T, Policy>(n, k, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type erf(RT z) { return ::boost::math::erf(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type erfc(RT z){ return ::boost::math::erfc(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type erf_inv(RT z) { return ::boost::math::erf_inv(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type erfc_inv(RT z){ return ::boost::math::erfc_inv(z, Policy()); }\
|
||
|
|
\
|
||
|
|
using boost::math::legendre_next;\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type \
|
||
|
|
legendre_p(int l, T x){ return ::boost::math::legendre_p(l, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type \
|
||
|
|
legendre_q(unsigned l, T x){ return ::boost::math::legendre_q(l, x, Policy()); }\
|
||
|
|
\
|
||
|
|
using ::boost::math::legendre_next;\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type \
|
||
|
|
legendre_p(int l, int m, T x){ return ::boost::math::legendre_p(l, m, x, Policy()); }\
|
||
|
|
\
|
||
|
|
using ::boost::math::laguerre_next;\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type \
|
||
|
|
laguerre(unsigned n, T x){ return ::boost::math::laguerre(n, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::laguerre_result<T1, T2>::type \
|
||
|
|
laguerre(unsigned n, T1 m, T2 x) { return ::boost::math::laguerre(n, m, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type \
|
||
|
|
hermite(unsigned n, T x){ return ::boost::math::hermite(n, x, Policy()); }\
|
||
|
|
\
|
||
|
|
using boost::math::hermite_next;\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline std::complex<typename boost::math::tools::promote_args<T1, T2>::type> \
|
||
|
|
spherical_harmonic(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic(n, m, theta, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi){ return ::boost::math::spherical_harmonic_r(n, m, theta, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi){ return boost::math::spherical_harmonic_i(n, m, theta, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class Policy>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol);\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
|
||
|
|
ellint_rf(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rf(x, y, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
|
||
|
|
ellint_rd(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rd(x, y, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
ellint_rc(T1 x, T2 y){ return ::boost::math::ellint_rc(x, y, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3, class T4>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3, T4>::type \
|
||
|
|
ellint_rj(T1 x, T2 y, T3 z, T4 p){ return boost::math::ellint_rj(x, y, z, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type \
|
||
|
|
ellint_rg(T1 x, T2 y, T3 z){ return ::boost::math::ellint_rg(x, y, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type ellint_2(T k){ return boost::math::ellint_2(k, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type ellint_2(T1 k, T2 phi){ return boost::math::ellint_2(k, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type ellint_d(T k){ return boost::math::ellint_d(k, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi){ return boost::math::ellint_d(k, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi){ return boost::math::jacobi_zeta(k, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi){ return boost::math::heuman_lambda(k, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type ellint_1(T k){ return boost::math::ellint_1(k, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi){ return boost::math::ellint_1(k, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2, class T3>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi){ return boost::math::ellint_3(k, v, phi, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v){ return boost::math::ellint_3(k, v, Policy()); }\
|
||
|
|
\
|
||
|
|
using boost::math::max_factorial;\
|
||
|
|
template <class RT>\
|
||
|
|
inline RT factorial(unsigned int i) { return boost::math::factorial<RT>(i, Policy()); }\
|
||
|
|
using boost::math::unchecked_factorial;\
|
||
|
|
template <class RT>\
|
||
|
|
inline RT double_factorial(unsigned i){ return boost::math::double_factorial<RT>(i, Policy()); }\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type falling_factorial(RT x, unsigned n){ return boost::math::falling_factorial(x, n, Policy()); }\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type rising_factorial(RT x, unsigned n){ return boost::math::rising_factorial(x, n, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type tgamma(RT z){ return boost::math::tgamma(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type tgamma1pm1(RT z){ return boost::math::tgamma1pm1(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z){ return boost::math::tgamma(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type lgamma(RT z, int* sign){ return boost::math::lgamma(z, sign, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type lgamma(RT x){ return boost::math::lgamma(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z){ return boost::math::tgamma_lower(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z){ return boost::math::gamma_q(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z){ return boost::math::gamma_p(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta){ return boost::math::tgamma_delta_ratio(z, delta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b) { return boost::math::tgamma_ratio(a, b, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x){ return boost::math::gamma_p_derivative(a, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p){ return boost::math::gamma_p_inv(a, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p){ return boost::math::gamma_p_inva(a, p, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q){ return boost::math::gamma_q_inv(a, q, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q){ return boost::math::gamma_q_inva(a, q, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type digamma(T x){ return boost::math::digamma(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type trigamma(T x){ return boost::math::trigamma(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type polygamma(int n, T x){ return boost::math::polygamma(n, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
hypot(T1 x, T2 y){ return boost::math::hypot(x, y, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT>::type cbrt(RT z){ return boost::math::cbrt(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type log1p(T x){ return boost::math::log1p(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type log1pmx(T x){ return boost::math::log1pmx(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type expm1(T x){ return boost::math::expm1(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::tools::promote_args<T1, T2>::type \
|
||
|
|
powm1(const T1 a, const T2 z){ return boost::math::powm1(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type sqrt1pm1(const T& val){ return boost::math::sqrt1pm1(val, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type sinc_pi(T x){ return boost::math::sinc_pi(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type sinhc_pi(T x){ return boost::math::sinhc_pi(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template<typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type asinh(const T x){ return boost::math::asinh(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template<typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type acosh(const T x){ return boost::math::acosh(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template<typename T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type atanh(const T x){ return boost::math::atanh(x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j(T1 v, T2 x)\
|
||
|
|
{ return boost::math::cyl_bessel_j(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type cyl_bessel_j_prime(T1 v, T2 x)\
|
||
|
|
{ return boost::math::cyl_bessel_j_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel(unsigned v, T x)\
|
||
|
|
{ return boost::math::sph_bessel(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type sph_bessel_prime(unsigned v, T x)\
|
||
|
|
{ return boost::math::sph_bessel_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_bessel_i(T1 v, T2 x) { return boost::math::cyl_bessel_i(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_bessel_i_prime(T1 v, T2 x) { return boost::math::cyl_bessel_i_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_bessel_k(T1 v, T2 x) { return boost::math::cyl_bessel_k(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_bessel_k_prime(T1 v, T2 x) { return boost::math::cyl_bessel_k_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_neumann(T1 v, T2 x){ return boost::math::cyl_neumann(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type \
|
||
|
|
cyl_neumann_prime(T1 v, T2 x){ return boost::math::cyl_neumann_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
|
||
|
|
sph_neumann(unsigned v, T x){ return boost::math::sph_neumann(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type \
|
||
|
|
sph_neumann_prime(unsigned v, T x){ return boost::math::sph_neumann_prime(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_bessel_j_zero(T v, int m)\
|
||
|
|
{ return boost::math::cyl_bessel_j_zero(v, m, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class OutputIterator, class T>\
|
||
|
|
inline void cyl_bessel_j_zero(T v,\
|
||
|
|
int start_index,\
|
||
|
|
unsigned number_of_zeros,\
|
||
|
|
OutputIterator out_it)\
|
||
|
|
{ boost::math::cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::detail::bessel_traits<T, T, Policy >::result_type cyl_neumann_zero(T v, int m)\
|
||
|
|
{ return boost::math::cyl_neumann_zero(v, m, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class OutputIterator, class T>\
|
||
|
|
inline void cyl_neumann_zero(T v,\
|
||
|
|
int start_index,\
|
||
|
|
unsigned number_of_zeros,\
|
||
|
|
OutputIterator out_it)\
|
||
|
|
{ boost::math::cyl_neumann_zero(v, start_index, number_of_zeros, out_it, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type sin_pi(T x){ return boost::math::sin_pi(x); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type cos_pi(T x){ return boost::math::cos_pi(x); }\
|
||
|
|
\
|
||
|
|
using boost::math::fpclassify;\
|
||
|
|
using boost::math::isfinite;\
|
||
|
|
using boost::math::isinf;\
|
||
|
|
using boost::math::isnan;\
|
||
|
|
using boost::math::isnormal;\
|
||
|
|
using boost::math::signbit;\
|
||
|
|
using boost::math::sign;\
|
||
|
|
using boost::math::copysign;\
|
||
|
|
using boost::math::changesign;\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T,U>::type expint(T const& z, U const& u)\
|
||
|
|
{ return boost::math::expint(z, u, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type expint(T z){ return boost::math::expint(z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type zeta(T s){ return boost::math::zeta(s, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T round(const T& v){ using boost::math::round; return round(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline int iround(const T& v){ using boost::math::iround; return iround(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline long lround(const T& v){ using boost::math::lround; return lround(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T trunc(const T& v){ using boost::math::trunc; return trunc(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline int itrunc(const T& v){ using boost::math::itrunc; return itrunc(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline long ltrunc(const T& v){ using boost::math::ltrunc; return ltrunc(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T modf(const T& v, T* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T modf(const T& v, int* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline T modf(const T& v, long* ipart){ using boost::math::modf; return modf(v, ipart, Policy()); }\
|
||
|
|
\
|
||
|
|
template <int N, class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type pow(T v){ return boost::math::pow<N>(v, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T> T nextafter(const T& a, const T& b){ return boost::math::nextafter(a, b, Policy()); }\
|
||
|
|
template <class T> T float_next(const T& a){ return boost::math::float_next(a, Policy()); }\
|
||
|
|
template <class T> T float_prior(const T& a){ return boost::math::float_prior(a, Policy()); }\
|
||
|
|
template <class T> T float_distance(const T& a, const T& b){ return boost::math::float_distance(a, b, Policy()); }\
|
||
|
|
template <class T> T ulp(const T& a){ return boost::math::ulp(a, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class RT1, class RT2>\
|
||
|
|
inline typename boost::math::tools::promote_args<RT1, RT2>::type owens_t(RT1 a, RT2 z){ return boost::math::owens_t(a, z, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_1(T1 v, T2 x)\
|
||
|
|
{ return boost::math::cyl_hankel_1(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> cyl_hankel_2(T1 v, T2 x)\
|
||
|
|
{ return boost::math::cyl_hankel_2(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_1(T1 v, T2 x)\
|
||
|
|
{ return boost::math::sph_hankel_1(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T1, class T2>\
|
||
|
|
inline std::complex<typename boost::math::detail::bessel_traits<T1, T2, Policy >::result_type> sph_hankel_2(T1 v, T2 x)\
|
||
|
|
{ return boost::math::sph_hankel_2(v, x, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T>::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\
|
||
|
|
{ return boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class U, class T>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_sn(U k, T theta)\
|
||
|
|
{ return boost::math::jacobi_sn(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_cn(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_cn(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_dn(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_dn(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_cd(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_cd(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_dc(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_dc(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_ns(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_ns(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_sd(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_sd(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_ds(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_ds(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_nc(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_nc(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_nd(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_nd(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_sc(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_sc(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T, class U>\
|
||
|
|
inline typename boost::math::tools::promote_args<T, U>::type jacobi_cs(T k, U theta)\
|
||
|
|
{ return boost::math::jacobi_cs(k, theta, Policy()); }\
|
||
|
|
\
|
||
|
|
template <class T>\
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inline typename boost::math::tools::promote_args<T>::type airy_ai(T x)\
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{ return boost::math::airy_ai(x, Policy()); }\
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\
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template <class T>\
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inline typename boost::math::tools::promote_args<T>::type airy_bi(T x)\
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{ return boost::math::airy_bi(x, Policy()); }\
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\
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template <class T>\
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inline typename boost::math::tools::promote_args<T>::type airy_ai_prime(T x)\
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{ return boost::math::airy_ai_prime(x, Policy()); }\
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\
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template <class T>\
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inline typename boost::math::tools::promote_args<T>::type airy_bi_prime(T x)\
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{ return boost::math::airy_bi_prime(x, Policy()); }\
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\
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template <class T>\
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inline T airy_ai_zero(int m)\
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{ return boost::math::airy_ai_zero<T>(m, Policy()); }\
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template <class T, class OutputIterator>\
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OutputIterator airy_ai_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
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{ return boost::math::airy_ai_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
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\
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template <class T>\
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inline T airy_bi_zero(int m)\
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{ return boost::math::airy_bi_zero<T>(m, Policy()); }\
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template <class T, class OutputIterator>\
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OutputIterator airy_bi_zero(int start_index, unsigned number_of_zeros, OutputIterator out_it)\
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{ return boost::math::airy_bi_zero<T>(start_index, number_of_zeros, out_it, Policy()); }\
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\
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template <class T>\
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T bernoulli_b2n(const int i)\
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{ return boost::math::bernoulli_b2n<T>(i, Policy()); }\
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template <class T, class OutputIterator>\
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OutputIterator bernoulli_b2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
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{ return boost::math::bernoulli_b2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
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\
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template <class T>\
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T tangent_t2n(const int i)\
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||
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{ return boost::math::tangent_t2n<T>(i, Policy()); }\
|
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template <class T, class OutputIterator>\
|
||
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OutputIterator tangent_t2n(int start_index, unsigned number_of_bernoullis_b2n, OutputIterator out_it)\
|
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{ return boost::math::tangent_t2n<T>(start_index, number_of_bernoullis_b2n, out_it, Policy()); }\
|
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\
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#endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP
|
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