// 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 | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/math/special_functions/ellint_rf.hpp> | |
#include <boost/math/constants/constants.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
#include <boost/math/tools/workaround.hpp> | |
// Elliptic integrals (complete and incomplete) of the first 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_1(T1 k, T2 phi, const Policy& pol); | |
namespace detail{ | |
template <typename T, typename Policy> | |
T ellint_k_imp(T k, const Policy& pol); | |
// Elliptic integral (Legendre form) of the first kind | |
template <typename T, typename Policy> | |
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<T>(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<T>()) | |
{ | |
// Need to handle infinity as a special case: | |
result = policies::raise_overflow_error<T>(function, 0, pol); | |
BOOST_MATH_INSTRUMENT_VARIABLE(result); | |
} | |
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_k_imp(k, pol) / constants::pi<T>(); | |
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<T>() / 2); | |
T rphi = boost::math::tools::fmod_workaround(phi, T(constants::pi<T>() / 2)); | |
BOOST_MATH_INSTRUMENT_VARIABLE(rphi); | |
T m = floor((2 * phi) / constants::pi<T>()); | |
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<T>() / 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(T(cosp * cosp), T(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 ? T(-result) : result; | |
} | |
// Complete elliptic integral (Legendre form) of the first kind | |
template <typename T, typename Policy> | |
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<T>(function, | |
"Got k = %1%, function requires |k| <= 1", k, pol); | |
} | |
if (abs(k) == 1) | |
{ | |
return policies::raise_overflow_error<T>(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 <typename T, typename Policy> | |
inline typename tools::promote_args<T>::type ellint_1(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_k_imp(static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%)"); | |
} | |
template <class T1, class T2> | |
inline typename tools::promote_args<T1, T2>::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 <typename T> | |
inline typename tools::promote_args<T>::type ellint_1(T k) | |
{ | |
return ellint_1(k, policies::policy<>()); | |
} | |
// Elliptic integral (Legendre form) of the first kind | |
template <class T1, class T2, class Policy> | |
inline typename tools::promote_args<T1, T2>::type ellint_1(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_f_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%,%1%)"); | |
} | |
template <class T1, class T2> | |
inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi) | |
{ | |
typedef typename policies::is_policy<T2>::type tag_type; | |
return detail::ellint_1(k, phi, tag_type()); | |
} | |
}} // namespaces | |
#endif // BOOST_MATH_ELLINT_1_HPP | |