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1// Copyright (c) 2015 John Maddock2// Copyright (c) 2024 Matt Borland3// Use, modification and distribution are subject to the4// Boost Software License, Version 1.0. (See accompanying file5// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)6 7#ifndef BOOST_MATH_ELLINT_HL_HPP8#define BOOST_MATH_ELLINT_HL_HPP9 10#ifdef _MSC_VER11#pragma once12#endif13 14#include <boost/math/tools/config.hpp>15#include <boost/math/tools/numeric_limits.hpp>16#include <boost/math/tools/type_traits.hpp>17#include <boost/math/special_functions/math_fwd.hpp>18#include <boost/math/special_functions/ellint_rj.hpp>19#include <boost/math/special_functions/ellint_1.hpp>20#include <boost/math/special_functions/jacobi_zeta.hpp>21#include <boost/math/constants/constants.hpp>22#include <boost/math/policies/error_handling.hpp>23#include <boost/math/tools/workaround.hpp>24 25// Elliptic integral the Jacobi Zeta function.26 27namespace boost { namespace math { 28 29namespace detail{30 31// Elliptic integral - Jacobi Zeta32template <typename T, typename Policy>33BOOST_MATH_GPU_ENABLED T heuman_lambda_imp(T phi, T k, const Policy& pol)34{35 BOOST_MATH_STD_USING36 using namespace boost::math::tools;37 using namespace boost::math::constants;38 39 constexpr auto function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";40 41 if(fabs(k) > 1)42 return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);43 44 T result;45 T sinp = sin(phi);46 T cosp = cos(phi);47 T s2 = sinp * sinp;48 T k2 = k * k;49 T kp = 1 - k2;50 T delta = sqrt(1 - (kp * s2));51 if(fabs(phi) <= constants::half_pi<T>())52 {53 result = kp * sinp * cosp / (delta * constants::half_pi<T>());54 result *= ellint_rf_imp(T(0), kp, T(1), pol) + k2 * ellint_rj(T(0), kp, T(1), T(1 - k2 / (delta * delta)), pol) / (3 * delta * delta);55 }56 else57 {58 typedef boost::math::integral_constant<int,59 boost::math::is_floating_point<T>::value && boost::math::numeric_limits<T>::digits && (boost::math::numeric_limits<T>::digits <= 54) ? 0 :60 boost::math::is_floating_point<T>::value && boost::math::numeric_limits<T>::digits && (boost::math::numeric_limits<T>::digits <= 64) ? 1 : 261 > precision_tag_type;62 63 T rkp = sqrt(kp);64 T ratio;65 if(rkp == 1)66 {67 return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);68 }69 else70 {71 ratio = ellint_f_imp(phi, rkp, pol, k2) / ellint_k_imp(rkp, pol, k2);72 }73 result = ratio + ellint_k_imp(k, pol, precision_tag_type()) * jacobi_zeta_imp(phi, rkp, pol, k2) / constants::half_pi<T>();74 }75 return result;76}77 78} // detail79 80template <class T1, class T2, class Policy>81BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol)82{83 typedef typename tools::promote_args<T1, T2>::type result_type;84 typedef typename policies::evaluation<result_type, Policy>::type value_type;85 return policies::checked_narrowing_cast<result_type, Policy>(detail::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%1%>(%1%,%1%)");86}87 88template <class T1, class T2>89BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi)90{91 return boost::math::heuman_lambda(k, phi, policies::policy<>());92}93 94}} // namespaces95 96#endif // BOOST_MATH_ELLINT_D_HPP97 98