| // Copyright (c) 2006 Xiaogang Zhang |
| // Copyright (c) 2006 John Maddock |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| // |
| // History: |
| // XZ wrote the original of this file as part of the Google |
| // Summer of Code 2006. JM modified it to fit into the |
| // Boost.Math conceptual framework better, and to ensure |
| // that the code continues to work no matter how many digits |
| // type T has. |
| |
| #ifndef BOOST_MATH_ELLINT_1_HPP |
| #define BOOST_MATH_ELLINT_1_HPP |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/special_functions/ellint_rf.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/math/policies/error_handling.hpp> |
| #include <boost/math/tools/workaround.hpp> |
| |
| // Elliptic integrals (complete and incomplete) of the first kind |
| // Carlson, Numerische Mathematik, vol 33, 1 (1979) |
| |
| namespace boost { namespace math { |
| |
| template <class T1, class T2, class Policy> |
| typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol); |
| |
| namespace detail{ |
| |
| template <typename T, typename Policy> |
| T ellint_k_imp(T k, const Policy& pol); |
| |
| // Elliptic integral (Legendre form) of the first kind |
| template <typename T, typename Policy> |
| T ellint_f_imp(T phi, T k, const Policy& pol) |
| { |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| using namespace boost::math::constants; |
| |
| static const char* function = "boost::math::ellint_f<%1%>(%1%,%1%)"; |
| BOOST_MATH_INSTRUMENT_VARIABLE(phi); |
| BOOST_MATH_INSTRUMENT_VARIABLE(k); |
| BOOST_MATH_INSTRUMENT_VARIABLE(function); |
| |
| if (abs(k) > 1) |
| { |
| return policies::raise_domain_error<T>(function, |
| "Got k = %1%, function requires |k| <= 1", k, pol); |
| } |
| |
| bool invert = false; |
| if(phi < 0) |
| { |
| BOOST_MATH_INSTRUMENT_VARIABLE(phi); |
| phi = fabs(phi); |
| invert = true; |
| } |
| |
| T result; |
| |
| if(phi >= tools::max_value<T>()) |
| { |
| // Need to handle infinity as a special case: |
| result = policies::raise_overflow_error<T>(function, 0, pol); |
| BOOST_MATH_INSTRUMENT_VARIABLE(result); |
| } |
| else if(phi > 1 / tools::epsilon<T>()) |
| { |
| // Phi is so large that phi%pi is necessarily zero (or garbage), |
| // just return the second part of the duplication formula: |
| result = 2 * phi * ellint_k_imp(k, pol) / constants::pi<T>(); |
| BOOST_MATH_INSTRUMENT_VARIABLE(result); |
| } |
| else |
| { |
| // Carlson's algorithm works only for |phi| <= pi/2, |
| // use the integrand's periodicity to normalize phi |
| // |
| // Xiaogang's original code used a cast to long long here |
| // but that fails if T has more digits than a long long, |
| // so rewritten to use fmod instead: |
| // |
| BOOST_MATH_INSTRUMENT_CODE("pi/2 = " << constants::pi<T>() / 2); |
| T rphi = boost::math::tools::fmod_workaround(phi, T(constants::pi<T>() / 2)); |
| BOOST_MATH_INSTRUMENT_VARIABLE(rphi); |
| T m = floor((2 * phi) / constants::pi<T>()); |
| BOOST_MATH_INSTRUMENT_VARIABLE(m); |
| int s = 1; |
| if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5) |
| { |
| m += 1; |
| s = -1; |
| rphi = constants::pi<T>() / 2 - rphi; |
| BOOST_MATH_INSTRUMENT_VARIABLE(rphi); |
| } |
| T sinp = sin(rphi); |
| T cosp = cos(rphi); |
| BOOST_MATH_INSTRUMENT_VARIABLE(sinp); |
| BOOST_MATH_INSTRUMENT_VARIABLE(cosp); |
| result = s * sinp * ellint_rf_imp(T(cosp * cosp), T(1 - k * k * sinp * sinp), T(1), pol); |
| BOOST_MATH_INSTRUMENT_VARIABLE(result); |
| if(m != 0) |
| { |
| result += m * ellint_k_imp(k, pol); |
| BOOST_MATH_INSTRUMENT_VARIABLE(result); |
| } |
| } |
| return invert ? T(-result) : result; |
| } |
| |
| // Complete elliptic integral (Legendre form) of the first kind |
| template <typename T, typename Policy> |
| T ellint_k_imp(T k, const Policy& pol) |
| { |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| |
| static const char* function = "boost::math::ellint_k<%1%>(%1%)"; |
| |
| if (abs(k) > 1) |
| { |
| return policies::raise_domain_error<T>(function, |
| "Got k = %1%, function requires |k| <= 1", k, pol); |
| } |
| if (abs(k) == 1) |
| { |
| return policies::raise_overflow_error<T>(function, 0, pol); |
| } |
| |
| T x = 0; |
| T y = 1 - k * k; |
| T z = 1; |
| T value = ellint_rf_imp(x, y, z, pol); |
| |
| return value; |
| } |
| |
| template <typename T, typename Policy> |
| inline typename tools::promote_args<T>::type ellint_1(T k, const Policy& pol, const mpl::true_&) |
| { |
| typedef typename tools::promote_args<T>::type result_type; |
| typedef typename policies::evaluation<result_type, Policy>::type value_type; |
| return policies::checked_narrowing_cast<result_type, Policy>(detail::ellint_k_imp(static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%)"); |
| } |
| |
| template <class T1, class T2> |
| inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const mpl::false_&) |
| { |
| return boost::math::ellint_1(k, phi, policies::policy<>()); |
| } |
| |
| } |
| |
| // Complete elliptic integral (Legendre form) of the first kind |
| template <typename T> |
| inline typename tools::promote_args<T>::type ellint_1(T k) |
| { |
| return ellint_1(k, policies::policy<>()); |
| } |
| |
| // Elliptic integral (Legendre form) of the first kind |
| template <class T1, class T2, class Policy> |
| inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol) |
| { |
| typedef typename tools::promote_args<T1, T2>::type result_type; |
| typedef typename policies::evaluation<result_type, Policy>::type value_type; |
| return policies::checked_narrowing_cast<result_type, Policy>(detail::ellint_f_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%,%1%)"); |
| } |
| |
| template <class T1, class T2> |
| inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi) |
| { |
| typedef typename policies::is_policy<T2>::type tag_type; |
| return detail::ellint_1(k, phi, tag_type()); |
| } |
| |
| }} // namespaces |
| |
| #endif // BOOST_MATH_ELLINT_1_HPP |
| |