585da50d7d
This PR adds the code of Boost.Math as of version 1.89 into the third-party directory, as discussed in a recent RFC [1]. The goal is for this code to be used as a back-end for the C++17 Math Special Functions. As explained in third-paty/README.md, this code is cleared for usage inside libc++ for the Math Special functions, however the LLVM Foundation should be consulted before using this code anywhere else in the LLVM project, due to the fact that it is under the Boost Software License (as opposed to the usual LLVM license). See the RFC [1] for more details. [1]: https://discourse.llvm.org/t/rfc-libc-taking-a-dependency-on-boost-math-for-the-c-17-math-special-functions
98 lines
3.4 KiB
C++
98 lines
3.4 KiB
C++
// Copyright (c) 2015 John Maddock
|
|
// Copyright (c) 2024 Matt Borland
|
|
// 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)
|
|
|
|
#ifndef BOOST_MATH_ELLINT_HL_HPP
|
|
#define BOOST_MATH_ELLINT_HL_HPP
|
|
|
|
#ifdef _MSC_VER
|
|
#pragma once
|
|
#endif
|
|
|
|
#include <boost/math/tools/config.hpp>
|
|
#include <boost/math/tools/numeric_limits.hpp>
|
|
#include <boost/math/tools/type_traits.hpp>
|
|
#include <boost/math/special_functions/math_fwd.hpp>
|
|
#include <boost/math/special_functions/ellint_rj.hpp>
|
|
#include <boost/math/special_functions/ellint_1.hpp>
|
|
#include <boost/math/special_functions/jacobi_zeta.hpp>
|
|
#include <boost/math/constants/constants.hpp>
|
|
#include <boost/math/policies/error_handling.hpp>
|
|
#include <boost/math/tools/workaround.hpp>
|
|
|
|
// Elliptic integral the Jacobi Zeta function.
|
|
|
|
namespace boost { namespace math {
|
|
|
|
namespace detail{
|
|
|
|
// Elliptic integral - Jacobi Zeta
|
|
template <typename T, typename Policy>
|
|
BOOST_MATH_GPU_ENABLED T heuman_lambda_imp(T phi, T k, const Policy& pol)
|
|
{
|
|
BOOST_MATH_STD_USING
|
|
using namespace boost::math::tools;
|
|
using namespace boost::math::constants;
|
|
|
|
constexpr auto function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";
|
|
|
|
if(fabs(k) > 1)
|
|
return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);
|
|
|
|
T result;
|
|
T sinp = sin(phi);
|
|
T cosp = cos(phi);
|
|
T s2 = sinp * sinp;
|
|
T k2 = k * k;
|
|
T kp = 1 - k2;
|
|
T delta = sqrt(1 - (kp * s2));
|
|
if(fabs(phi) <= constants::half_pi<T>())
|
|
{
|
|
result = kp * sinp * cosp / (delta * constants::half_pi<T>());
|
|
result *= ellint_rf_imp(T(0), kp, T(1), pol) + k2 * ellint_rj(T(0), kp, T(1), T(1 - k2 / (delta * delta)), pol) / (3 * delta * delta);
|
|
}
|
|
else
|
|
{
|
|
typedef boost::math::integral_constant<int,
|
|
boost::math::is_floating_point<T>::value && boost::math::numeric_limits<T>::digits && (boost::math::numeric_limits<T>::digits <= 54) ? 0 :
|
|
boost::math::is_floating_point<T>::value && boost::math::numeric_limits<T>::digits && (boost::math::numeric_limits<T>::digits <= 64) ? 1 : 2
|
|
> precision_tag_type;
|
|
|
|
T rkp = sqrt(kp);
|
|
T ratio;
|
|
if(rkp == 1)
|
|
{
|
|
return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);
|
|
}
|
|
else
|
|
{
|
|
ratio = ellint_f_imp(phi, rkp, pol, k2) / ellint_k_imp(rkp, pol, k2);
|
|
}
|
|
result = ratio + ellint_k_imp(k, pol, precision_tag_type()) * jacobi_zeta_imp(phi, rkp, pol, k2) / constants::half_pi<T>();
|
|
}
|
|
return result;
|
|
}
|
|
|
|
} // detail
|
|
|
|
template <class T1, class T2, class Policy>
|
|
BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type heuman_lambda(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::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2>
|
|
BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi)
|
|
{
|
|
return boost::math::heuman_lambda(k, phi, policies::policy<>());
|
|
}
|
|
|
|
}} // namespaces
|
|
|
|
#endif // BOOST_MATH_ELLINT_D_HPP
|
|
|