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Diffstat (limited to 'boost/math/special_functions/ellint_d.hpp')
| -rw-r--r-- | boost/math/special_functions/ellint_d.hpp | 180 |
1 files changed, 180 insertions, 0 deletions
diff --git a/boost/math/special_functions/ellint_d.hpp b/boost/math/special_functions/ellint_d.hpp new file mode 100644 index 0000000000..5bd065d6e3 --- /dev/null +++ b/boost/math/special_functions/ellint_d.hpp @@ -0,0 +1,180 @@ +// 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_D_HPP +#define BOOST_MATH_ELLINT_D_HPP + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/special_functions/math_fwd.hpp> +#include <boost/math/special_functions/ellint_rf.hpp> +#include <boost/math/special_functions/ellint_rd.hpp> +#include <boost/math/special_functions/ellint_rg.hpp> +#include <boost/math/constants/constants.hpp> +#include <boost/math/policies/error_handling.hpp> +#include <boost/math/tools/workaround.hpp> +#include <boost/math/special_functions/round.hpp> + +// Elliptic integrals (complete and incomplete) of the second 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_d(T1 k, T2 phi, const Policy& pol); + +namespace detail{ + +template <typename T, typename Policy> +T ellint_d_imp(T k, const Policy& pol); + +// Elliptic integral (Legendre form) of the second kind +template <typename T, typename Policy> +T ellint_d_imp(T phi, T k, const Policy& pol) +{ + BOOST_MATH_STD_USING + using namespace boost::math::tools; + using namespace boost::math::constants; + + bool invert = false; + if(phi < 0) + { + 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>("boost::math::ellint_e<%1%>(%1%,%1%)", 0, pol); + } + 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_d_imp(k, pol) / constants::pi<T>(); + } + else + { + // Carlson's algorithm works only for |phi| <= pi/2, + // use the integrand's periodicity to normalize phi + // + T rphi = boost::math::tools::fmod_workaround(phi, T(constants::half_pi<T>())); + T m = boost::math::round((phi - rphi) / constants::half_pi<T>()); + int s = 1; + if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5) + { + m += 1; + s = -1; + rphi = constants::half_pi<T>() - rphi; + } + T sinp = sin(rphi); + T cosp = cos(rphi); + T c = 1 / (sinp * sinp); + T cm1 = cosp * cosp / (sinp * sinp); // c - 1 + T k2 = k * k; + if(k2 > 1) + { + return policies::raise_domain_error<T>("boost::math::ellint_d<%1%>(%1%, %1%)", "The parameter k is out of range, got k = %1%", k, pol); + } + else if(rphi == 0) + { + result = 0; + } + else + { + // http://dlmf.nist.gov/19.25#E10 + result = s * ellint_rd_imp(cm1, T(c - k2), c, pol) / 3; + } + if(m != 0) + result += m * ellint_d_imp(k, pol); + } + return invert ? T(-result) : result; +} + +// Complete elliptic integral (Legendre form) of the second kind +template <typename T, typename Policy> +T ellint_d_imp(T k, const Policy& pol) +{ + BOOST_MATH_STD_USING + using namespace boost::math::tools; + + if (abs(k) > 1) + { + return policies::raise_domain_error<T>("boost::math::ellint_e<%1%>(%1%)", + "Got k = %1%, function requires |k| <= 1", k, pol); + } + if (abs(k) == 1) + { + return static_cast<T>(1); + } + if(fabs(k) <= tools::root_epsilon<T>()) + return constants::pi<T>() / 4; + + T x = 0; + T t = k * k; + T y = 1 - t; + T z = 1; + T value = ellint_rd_imp(x, y, z, pol) / 3; + + return value; +} + +template <typename T, typename Policy> +inline typename tools::promote_args<T>::type ellint_d(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_d_imp(static_cast<value_type>(k), pol), "boost::math::ellint_d<%1%>(%1%)"); +} + +// Elliptic integral (Legendre form) of the second kind +template <class T1, class T2> +inline typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const mpl::false_&) +{ + return boost::math::ellint_d(k, phi, policies::policy<>()); +} + +} // detail + +// Complete elliptic integral (Legendre form) of the second kind +template <typename T> +inline typename tools::promote_args<T>::type ellint_d(T k) +{ + return ellint_d(k, policies::policy<>()); +} + +// Elliptic integral (Legendre form) of the second kind +template <class T1, class T2> +inline typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi) +{ + typedef typename policies::is_policy<T2>::type tag_type; + return detail::ellint_d(k, phi, tag_type()); +} + +template <class T1, class T2, class Policy> +inline typename tools::promote_args<T1, T2>::type ellint_d(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_d_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::ellint_2<%1%>(%1%,%1%)"); +} + +}} // namespaces + +#endif // BOOST_MATH_ELLINT_D_HPP + |