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Diffstat (limited to 'src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_k0.hpp')
-rw-r--r-- | src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_k0.hpp | 152 |
1 files changed, 152 insertions, 0 deletions
diff --git a/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_k0.hpp b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_k0.hpp new file mode 100644 index 00000000000..e209168e877 --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_k0.hpp @@ -0,0 +1,152 @@ +// 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) + +#ifndef BOOST_MATH_BESSEL_K0_HPP +#define BOOST_MATH_BESSEL_K0_HPP + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/tools/rational.hpp> +#include <boost/math/tools/big_constant.hpp> +#include <boost/math/policies/error_handling.hpp> +#include <boost/assert.hpp> + +// Modified Bessel function of the second kind of order zero +// minimax rational approximations on intervals, see +// Russon and Blair, Chalk River Report AECL-3461, 1969 + +namespace boost { namespace math { namespace detail{ + +template <typename T, typename Policy> +T bessel_k0(T x, const Policy&); + +template <class T, class Policy> +struct bessel_k0_initializer +{ + struct init + { + init() + { + do_init(); + } + static void do_init() + { + bessel_k0(T(1), Policy()); + } + void force_instantiate()const{} + }; + static const init initializer; + static void force_instantiate() + { + initializer.force_instantiate(); + } +}; + +template <class T, class Policy> +const typename bessel_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer; + +template <typename T, typename Policy> +T bessel_k0(T x, const Policy& pol) +{ + BOOST_MATH_INSTRUMENT_CODE(x); + + bessel_k0_initializer<T, Policy>::force_instantiate(); + + static const T P1[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04)) + }; + static const T Q1[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + static const T P2[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00)) + }; + static const T Q2[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + static const T P3[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1600249425076035558e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02)) + }; + static const T Q3[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + T value, factor, r, r1, r2; + + BOOST_MATH_STD_USING + using namespace boost::math::tools; + + static const char* function = "boost::math::bessel_k0<%1%>(%1%,%1%)"; + + if (x < 0) + { + return policies::raise_domain_error<T>(function, + "Got x = %1%, but argument x must be non-negative, complex number result not supported", x, pol); + } + if (x == 0) + { + return policies::raise_overflow_error<T>(function, 0, pol); + } + if (x <= 1) // x in (0, 1] + { + T y = x * x; + r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); + r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); + factor = log(x); + value = r1 - factor * r2; + } + else // x in (1, \infty) + { + T y = 1 / x; + r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y); + factor = exp(-x) / sqrt(x); + value = factor * r; + BOOST_MATH_INSTRUMENT_CODE("y = " << y); + BOOST_MATH_INSTRUMENT_CODE("r = " << r); + BOOST_MATH_INSTRUMENT_CODE("factor = " << factor); + BOOST_MATH_INSTRUMENT_CODE("value = " << value); + } + + return value; +} + +}}} // namespaces + +#endif // BOOST_MATH_BESSEL_K0_HPP + |