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ellint_rf.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_rf.hpp
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// 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 handle // types longer than 80-bit reals. // #ifndef BOOST_MATH_ELLINT_RF_HPP #define BOOST_MATH_ELLINT_RF_HPP #include
#include
#include
// Carlson's elliptic integral of the first kind // R_F(x, y, z) = 0.5 * \int_{0}^{\infty} [(t+x)(t+y)(t+z)]^{-1/2} dt // Carlson, Numerische Mathematik, vol 33, 1 (1979) namespace boost { namespace math { namespace detail{ template
T ellint_rf_imp(T x, T y, T z, const Policy& pol) { T value, X, Y, Z, E2, E3, u, lambda, tolerance; unsigned long k; BOOST_MATH_STD_USING using namespace boost::math::tools; static const char* function = "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)"; if (x < 0 || y < 0 || z < 0) { return policies::raise_domain_error
(function, "domain error, all arguments must be non-negative, " "only sensible result is %1%.", std::numeric_limits
::quiet_NaN(), pol); } if (x + y == 0 || y + z == 0 || z + x == 0) { return policies::raise_domain_error
(function, "domain error, at most one argument can be zero, " "only sensible result is %1%.", std::numeric_limits
::quiet_NaN(), pol); } // Carlson scales error as the 6th power of tolerance, // but this seems not to work for types larger than // 80-bit reals, this heuristic seems to work OK: if(policies::digits
() > 64) { tolerance = pow(tools::epsilon
(), T(1)/4.25f); BOOST_MATH_INSTRUMENT_VARIABLE(tolerance); } else { tolerance = pow(4*tools::epsilon
(), T(1)/6); BOOST_MATH_INSTRUMENT_VARIABLE(tolerance); } // duplication k = 1; do { u = (x + y + z) / 3; X = (u - x) / u; Y = (u - y) / u; Z = (u - z) / u; // Termination condition: if ((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance) break; T sx = sqrt(x); T sy = sqrt(y); T sz = sqrt(z); lambda = sy * (sx + sz) + sz * sx; x = (x + lambda) / 4; y = (y + lambda) / 4; z = (z + lambda) / 4; ++k; } while(k < policies::get_max_series_iterations
()); // Check to see if we gave up too soon: policies::check_series_iterations(function, k, pol); BOOST_MATH_INSTRUMENT_VARIABLE(k); // Taylor series expansion to the 5th order E2 = X * Y - Z * Z; E3 = X * Y * Z; value = (1 + E2*(E2/24 - E3*T(3)/44 - T(0.1)) + E3/14) / sqrt(u); BOOST_MATH_INSTRUMENT_VARIABLE(value); return value; } } // namespace detail template
inline typename tools::promote_args
::type ellint_rf(T1 x, T2 y, T3 z, 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_rf_imp( static_cast
(x), static_cast
(y), static_cast
(z), pol), "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)"); } template
inline typename tools::promote_args
::type ellint_rf(T1 x, T2 y, T3 z) { return ellint_rf(x, y, z, policies::policy<>()); } }} // namespaces #endif // BOOST_MATH_ELLINT_RF_HPP
ellint_rf.hpp
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