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ellint_1.hpp - Hosted on DriveHQ Cloud IT Platform
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路径: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\special_functions\ellint_1.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_1_HPP #define BOOST_MATH_ELLINT_1_HPP #include
#include
#include
#include
// Elliptic integrals (complete and incomplete) of the first kind // Carlson, Numerische Mathematik, vol 33, 1 (1979) namespace boost { namespace math { template
typename tools::promote_args
::type ellint_1(T1 k, T2 phi, const Policy& pol); namespace detail{ template
T ellint_k_imp(T k, const Policy& pol); // Elliptic integral (Legendre form) of the first kind template
T ellint_f_imp(T phi, T k, const Policy& pol) { BOOST_MATH_STD_USING using namespace boost::math::tools; using namespace boost::math::constants; static const char* function = "boost::math::ellint_f<%1%>(%1%,%1%)"; BOOST_MATH_INSTRUMENT_VARIABLE(phi); BOOST_MATH_INSTRUMENT_VARIABLE(k); BOOST_MATH_INSTRUMENT_VARIABLE(function); if (abs(k) > 1) { return policies::raise_domain_error
(function, "Got k = %1%, function requires |k| <= 1", k, pol); } bool invert = false; if(phi < 0) { BOOST_MATH_INSTRUMENT_VARIABLE(phi); 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
(function, 0, pol); BOOST_MATH_INSTRUMENT_VARIABLE(result); } 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_k_imp(k, pol) / constants::pi
(); BOOST_MATH_INSTRUMENT_VARIABLE(result); } 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: // BOOST_MATH_INSTRUMENT_CODE("pi/2 = " << constants::pi
() / 2); T rphi = boost::math::tools::fmod_workaround(phi, constants::pi
() / 2); BOOST_MATH_INSTRUMENT_VARIABLE(rphi); T m = 2 * (phi - rphi) / constants::pi
(); BOOST_MATH_INSTRUMENT_VARIABLE(m); int s = 1; if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5) { m += 1; s = -1; rphi = constants::pi
() / 2 - rphi; BOOST_MATH_INSTRUMENT_VARIABLE(rphi); } T sinp = sin(rphi); T cosp = cos(rphi); BOOST_MATH_INSTRUMENT_VARIABLE(sinp); BOOST_MATH_INSTRUMENT_VARIABLE(cosp); result = s * sinp * ellint_rf_imp(cosp * cosp, 1 - k * k * sinp * sinp, T(1), pol); BOOST_MATH_INSTRUMENT_VARIABLE(result); if(m != 0) { result += m * ellint_k_imp(k, pol); BOOST_MATH_INSTRUMENT_VARIABLE(result); } } return invert ? -result : result; } // Complete elliptic integral (Legendre form) of the first kind template
T ellint_k_imp(T k, const Policy& pol) { BOOST_MATH_STD_USING using namespace boost::math::tools; static const char* function = "boost::math::ellint_k<%1%>(%1%)"; if (abs(k) > 1) { return policies::raise_domain_error
(function, "Got k = %1%, function requires |k| <= 1", k, pol); } if (abs(k) == 1) { return policies::raise_overflow_error
(function, 0, pol); } T x = 0; T y = 1 - k * k; T z = 1; T value = ellint_rf_imp(x, y, z, pol); return value; } template
inline typename tools::promote_args
::type ellint_1(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_k_imp(static_cast
(k), pol), "boost::math::ellint_1<%1%>(%1%)"); } template
inline typename tools::promote_args
::type ellint_1(T1 k, T2 phi, const mpl::false_&) { return boost::math::ellint_1(k, phi, policies::policy<>()); } } // Complete elliptic integral (Legendre form) of the first kind template
inline typename tools::promote_args
::type ellint_1(T k) { return ellint_1(k, policies::policy<>()); } // Elliptic integral (Legendre form) of the first kind template
inline typename tools::promote_args
::type ellint_1(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_f_imp(static_cast
(phi), static_cast
(k), pol), "boost::math::ellint_1<%1%>(%1%,%1%)"); } template
inline typename tools::promote_args
::type ellint_1(T1 k, T2 phi) { typedef typename policies::is_policy
::type tag_type; return detail::ellint_1(k, phi, tag_type()); } }} // namespaces #endif // BOOST_MATH_ELLINT_1_HPP
ellint_1.hpp
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