| // Copyright (c) 2006 Xiaogang Zhang |
| // 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 correctly |
| // handle the y < 0 case. |
| // |
| |
| #ifndef BOOST_MATH_ELLINT_RC_HPP |
| #define BOOST_MATH_ELLINT_RC_HPP |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/policies/error_handling.hpp> |
| #include <boost/math/tools/config.hpp> |
| #include <boost/math/special_functions/math_fwd.hpp> |
| |
| // Carlson's degenerate elliptic integral |
| // R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt |
| // Carlson, Numerische Mathematik, vol 33, 1 (1979) |
| |
| namespace boost { namespace math { namespace detail{ |
| |
| template <typename T, typename Policy> |
| T ellint_rc_imp(T x, T y, const Policy& pol) |
| { |
| T value, S, u, lambda, tolerance, prefix; |
| unsigned long k; |
| |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| |
| static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)"; |
| |
| if(x < 0) |
| { |
| return policies::raise_domain_error<T>(function, |
| "Argument x must be non-negative but got %1%", x, pol); |
| } |
| if(y == 0) |
| { |
| return policies::raise_domain_error<T>(function, |
| "Argument y must not be zero but got %1%", y, pol); |
| } |
| |
| // error scales as the 6th power of tolerance |
| tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6); |
| |
| // for y < 0, the integral is singular, return Cauchy principal value |
| if (y < 0) |
| { |
| prefix = sqrt(x / (x - y)); |
| x = x - y; |
| y = -y; |
| } |
| else |
| prefix = 1; |
| |
| // duplication: |
| k = 1; |
| do |
| { |
| u = (x + y + y) / 3; |
| S = y / u - 1; // 1 - x / u = 2 * S |
| |
| if (2 * abs(S) < tolerance) |
| break; |
| |
| T sx = sqrt(x); |
| T sy = sqrt(y); |
| lambda = 2 * sx * sy + y; |
| x = (x + lambda) / 4; |
| y = (y + lambda) / 4; |
| ++k; |
| }while(k < policies::get_max_series_iterations<Policy>()); |
| // Check to see if we gave up too soon: |
| policies::check_series_iterations(function, k, pol); |
| |
| // Taylor series expansion to the 5th order |
| value = (1 + S * S * (T(3) / 10 + S * (T(1) / 7 + S * (T(3) / 8 + S * T(9) / 22)))) / sqrt(u); |
| |
| return value * prefix; |
| } |
| |
| } // namespace detail |
| |
| template <class T1, class T2, class Policy> |
| inline typename tools::promote_args<T1, T2>::type |
| ellint_rc(T1 x, T2 y, 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_rc_imp( |
| static_cast<value_type>(x), |
| static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)"); |
| } |
| |
| template <class T1, class T2> |
| inline typename tools::promote_args<T1, T2>::type |
| ellint_rc(T1 x, T2 y) |
| { |
| return ellint_rc(x, y, policies::policy<>()); |
| } |
| |
| }} // namespaces |
| |
| #endif // BOOST_MATH_ELLINT_RC_HPP |
| |