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ellint_2.hpp - Hosted on DriveHQ Cloud IT Platform
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Ruta de la carpeta: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\special_functions\ellint_2.hpp
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// 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_2_HPP #define BOOST_MATH_ELLINT_2_HPP #include
#include
#include
#include
#include
// Elliptic integrals (complete and incomplete) of the second kind // Carlson, Numerische Mathematik, vol 33, 1 (1979) namespace boost { namespace math { template
typename tools::promote_args
::type ellint_2(T1 k, T2 phi, const Policy& pol); namespace detail{ template
T ellint_e_imp(T k, const Policy& pol); // Elliptic integral (Legendre form) of the second kind template
T ellint_e_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
()) { // Need to handle infinity as a special case: result = policies::raise_overflow_error
("boost::math::ellint_e<%1%>(%1%,%1%)", 0, pol); } else if(phi > 1 / tools::epsilon
()) { // 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_e_imp(k, pol) / constants::pi
(); } 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: // T rphi = boost::math::tools::fmod_workaround(phi, constants::pi
() / 2); T m = 2 * (phi - rphi) / constants::pi
(); int s = 1; if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5) { m += 1; s = -1; rphi = constants::pi
() / 2 - rphi; } T sinp = sin(rphi); T cosp = cos(rphi); T x = cosp * cosp; T t = k * k * sinp * sinp; T y = 1 - t; T z = 1; result = s * sinp * (ellint_rf_imp(x, y, z, pol) - t * ellint_rd_imp(x, y, z, pol) / 3); if(m != 0) result += m * ellint_e_imp(k, pol); } return invert ? -result : result; } // Complete elliptic integral (Legendre form) of the second kind template
T ellint_e_imp(T k, const Policy& pol) { BOOST_MATH_STD_USING using namespace boost::math::tools; if (abs(k) > 1) { return policies::raise_domain_error
("boost::math::ellint_e<%1%>(%1%)", "Got k = %1%, function requires |k| <= 1", k, pol); } if (abs(k) == 1) { return static_cast
(1); } T x = 0; T t = k * k; T y = 1 - t; T z = 1; T value = ellint_rf_imp(x, y, z, pol) - t * ellint_rd_imp(x, y, z, pol) / 3; return value; } template
inline typename tools::promote_args
::type ellint_2(T k, const Policy& pol, const mpl::true_&) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; return policies::checked_narrowing_cast
(detail::ellint_e_imp(static_cast
(k), pol), "boost::math::ellint_2<%1%>(%1%)"); } // Elliptic integral (Legendre form) of the second kind template
inline typename tools::promote_args
::type ellint_2(T1 k, T2 phi, const mpl::false_&) { return boost::math::ellint_2(k, phi, policies::policy<>()); } } // detail // Complete elliptic integral (Legendre form) of the second kind template
inline typename tools::promote_args
::type ellint_2(T k) { return ellint_2(k, policies::policy<>()); } // Elliptic integral (Legendre form) of the second kind template
inline typename tools::promote_args
::type ellint_2(T1 k, T2 phi) { typedef typename policies::is_policy
::type tag_type; return detail::ellint_2(k, phi, tag_type()); } template
inline typename tools::promote_args
::type ellint_2(T1 k, T2 phi, const Policy& pol) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; return policies::checked_narrowing_cast
(detail::ellint_e_imp(static_cast
(phi), static_cast
(k), pol), "boost::math::ellint_2<%1%>(%1%,%1%)"); } }} // namespaces #endif // BOOST_MATH_ELLINT_2_HPP
ellint_2.hpp
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