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1// Copyright (c) 2015 John Maddock2// Use, modification and distribution are subject to the3// Boost Software License, Version 1.0. (See accompanying file4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)5//6 7#ifndef BOOST_MATH_ELLINT_JZ_HPP8#define BOOST_MATH_ELLINT_JZ_HPP9 10#ifdef _MSC_VER11#pragma once12#endif13 14#include <boost/math/tools/config.hpp>15#include <boost/math/tools/promotion.hpp>16#include <boost/math/special_functions/math_fwd.hpp>17#include <boost/math/special_functions/ellint_1.hpp>18#include <boost/math/special_functions/ellint_rj.hpp>19#include <boost/math/special_functions/sign.hpp>20#include <boost/math/constants/constants.hpp>21#include <boost/math/policies/error_handling.hpp>22#include <boost/math/tools/workaround.hpp>23 24// Elliptic integral the Jacobi Zeta function.25 26namespace boost { namespace math { 27 28namespace detail{29 30// Elliptic integral - Jacobi Zeta31template <typename T, typename Policy>32BOOST_MATH_GPU_ENABLED T jacobi_zeta_imp(T phi, T k, const Policy& pol, T kp)33{34 BOOST_MATH_STD_USING35 using namespace boost::math::tools;36 using namespace boost::math::constants;37 38 bool invert = false;39 if(phi < 0)40 {41 phi = fabs(phi);42 invert = true;43 }44 45 T result;46 T sinp = sin(phi);47 T cosp = cos(phi);48 T c2 = cosp * cosp;49 T one_minus_ks2 = kp + c2 - kp * c2;50 T k2 = k * k;51 if(k == 1)52 result = sinp * (boost::math::sign)(cosp); // We get here by simplifying JacobiZeta[w, 1] in Mathematica, and the fact that 0 <= phi.53 else54 {55 result = k2 * sinp * cosp * sqrt(one_minus_ks2) * ellint_rj_imp(T(0), kp, T(1), one_minus_ks2, pol) / (3 * ellint_k_imp(k, pol, kp));56 }57 return invert ? T(-result) : result;58}59template <typename T, typename Policy>60BOOST_MATH_GPU_ENABLED inline T jacobi_zeta_imp(T phi, T k, const Policy& pol)61{62 return jacobi_zeta_imp(phi, k, pol, T(1 - k * k));63}64} // detail65 66template <class T1, class T2, class Policy>67BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol)68{69 typedef typename tools::promote_args<T1, T2>::type result_type;70 typedef typename policies::evaluation<result_type, Policy>::type value_type;71 return policies::checked_narrowing_cast<result_type, Policy>(detail::jacobi_zeta_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::jacobi_zeta<%1%>(%1%,%1%)");72}73 74template <class T1, class T2>75BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi)76{77 return boost::math::jacobi_zeta(k, phi, policies::policy<>());78}79 80}} // namespaces81 82#endif // BOOST_MATH_ELLINT_D_HPP83 84