177 lines
5.8 KiB
Plaintext
177 lines
5.8 KiB
Plaintext
// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 John Maddock
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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//
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// History:
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// XZ wrote the original of this file as part of the Google
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// Summer of Code 2006. JM modified it to fit into the
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// Boost.Math conceptual framework better, and to ensure
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// that the code continues to work no matter how many digits
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// type T has.
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#ifndef BOOST_MATH_ELLINT_D_HPP
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#define BOOST_MATH_ELLINT_D_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/ellint_rf.hpp>
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#include <boost/math/special_functions/ellint_rd.hpp>
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#include <boost/math/special_functions/ellint_rg.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/tools/workaround.hpp>
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#include <boost/math/special_functions/round.hpp>
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// Elliptic integrals (complete and incomplete) of the second kind
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// Carlson, Numerische Mathematik, vol 33, 1 (1979)
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namespace boost { namespace math {
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template <class T1, class T2, class Policy>
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typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol);
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namespace detail{
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template <typename T, typename Policy>
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T ellint_d_imp(T k, const Policy& pol);
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// Elliptic integral (Legendre form) of the second kind
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template <typename T, typename Policy>
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T ellint_d_imp(T phi, T k, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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using namespace boost::math::constants;
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bool invert = false;
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if(phi < 0)
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{
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phi = fabs(phi);
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invert = true;
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}
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T result;
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if(phi >= tools::max_value<T>())
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{
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// Need to handle infinity as a special case:
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result = policies::raise_overflow_error<T>("boost::math::ellint_d<%1%>(%1%,%1%)", 0, pol);
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}
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else if(phi > 1 / tools::epsilon<T>())
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{
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// Phi is so large that phi%pi is necessarily zero (or garbage),
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// just return the second part of the duplication formula:
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result = 2 * phi * ellint_d_imp(k, pol) / constants::pi<T>();
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}
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else
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{
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// Carlson's algorithm works only for |phi| <= pi/2,
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// use the integrand's periodicity to normalize phi
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//
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T rphi = boost::math::tools::fmod_workaround(phi, T(constants::half_pi<T>()));
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T m = boost::math::round((phi - rphi) / constants::half_pi<T>());
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int s = 1;
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if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5)
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{
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m += 1;
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s = -1;
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rphi = constants::half_pi<T>() - rphi;
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}
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T sinp = sin(rphi);
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T cosp = cos(rphi);
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T c = 1 / (sinp * sinp);
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T cm1 = cosp * cosp / (sinp * sinp); // c - 1
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T k2 = k * k;
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if(k2 > 1)
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{
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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);
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}
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else if(rphi == 0)
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{
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result = 0;
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}
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else
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{
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// http://dlmf.nist.gov/19.25#E10
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result = s * ellint_rd_imp(cm1, T(c - k2), c, pol) / 3;
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}
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if(m != 0)
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result += m * ellint_d_imp(k, pol);
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}
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return invert ? T(-result) : result;
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}
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// Complete elliptic integral (Legendre form) of the second kind
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template <typename T, typename Policy>
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T ellint_d_imp(T k, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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if (abs(k) >= 1)
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{
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return policies::raise_domain_error<T>("boost::math::ellint_d<%1%>(%1%)",
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"Got k = %1%, function requires |k| <= 1", k, pol);
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}
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if(fabs(k) <= tools::root_epsilon<T>())
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return constants::pi<T>() / 4;
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T x = 0;
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T t = k * k;
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T y = 1 - t;
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T z = 1;
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T value = ellint_rd_imp(x, y, z, pol) / 3;
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return value;
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}
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template <typename T, typename Policy>
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inline typename tools::promote_args<T>::type ellint_d(T k, const Policy& pol, const mpl::true_&)
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{
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typedef typename tools::promote_args<T>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return policies::checked_narrowing_cast<result_type, Policy>(detail::ellint_d_imp(static_cast<value_type>(k), pol), "boost::math::ellint_d<%1%>(%1%)");
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}
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// Elliptic integral (Legendre form) of the second kind
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template <class T1, class T2>
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inline typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const mpl::false_&)
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{
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return boost::math::ellint_d(k, phi, policies::policy<>());
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}
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} // detail
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// Complete elliptic integral (Legendre form) of the second kind
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template <typename T>
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inline typename tools::promote_args<T>::type ellint_d(T k)
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{
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return ellint_d(k, policies::policy<>());
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}
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// Elliptic integral (Legendre form) of the second kind
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template <class T1, class T2>
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inline typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi)
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{
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typedef typename policies::is_policy<T2>::type tag_type;
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return detail::ellint_d(k, phi, tag_type());
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}
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template <class T1, class T2, class Policy>
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inline typename tools::promote_args<T1, T2>::type ellint_d(T1 k, T2 phi, const Policy& pol)
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{
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typedef typename tools::promote_args<T1, T2>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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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%)");
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}
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}} // namespaces
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#endif // BOOST_MATH_ELLINT_D_HPP
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