| // 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 |
| |