1 // Copyright (c) 2006 Xiaogang Zhang 2 // Use, modification and distribution are subject to the 3 // Boost Software License, Version 1.0. (See accompanying file 4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) 5 6 #ifndef BOOST_MATH_BESSEL_K0_HPP 7 #define BOOST_MATH_BESSEL_K0_HPP 8 9 #ifdef _MSC_VER 10 #pragma once 11 #pragma warning(push) 12 #pragma warning(disable:4702) // Unreachable code (release mode only warning) 13 #endif 14 15 #include <boost/math/tools/rational.hpp> 16 #include <boost/math/tools/big_constant.hpp> 17 #include <boost/math/policies/error_handling.hpp> 18 #include <boost/assert.hpp> 19 20 // Modified Bessel function of the second kind of order zero 21 // minimax rational approximations on intervals, see 22 // Russon and Blair, Chalk River Report AECL-3461, 1969 23 24 namespace boost { namespace math { namespace detail{ 25 26 template <typename T, typename Policy> 27 T bessel_k0(T x, const Policy&); 28 29 template <class T, class Policy> 30 struct bessel_k0_initializer 31 { 32 struct init 33 { initboost::math::detail::bessel_k0_initializer::init34 init() 35 { 36 do_init(); 37 } do_initboost::math::detail::bessel_k0_initializer::init38 static void do_init() 39 { 40 bessel_k0(T(1), Policy()); 41 } force_instantiateboost::math::detail::bessel_k0_initializer::init42 void force_instantiate()const{} 43 }; 44 static const init initializer; force_instantiateboost::math::detail::bessel_k0_initializer45 static void force_instantiate() 46 { 47 initializer.force_instantiate(); 48 } 49 }; 50 51 template <class T, class Policy> 52 const typename bessel_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer; 53 54 template <typename T, typename Policy> 55 T bessel_k0(T x, const Policy& pol) 56 { 57 BOOST_MATH_INSTRUMENT_CODE(x); 58 59 bessel_k0_initializer<T, Policy>::force_instantiate(); 60 61 static const T P1[] = { 62 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)), 63 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)), 64 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)), 65 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)), 66 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)), 67 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04)) 68 }; 69 static const T Q1[] = { 70 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)), 71 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)), 72 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) 73 }; 74 static const T P2[] = { 75 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)), 76 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)), 77 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)), 78 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)), 79 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00)) 80 }; 81 static const T Q2[] = { 82 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)), 83 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)), 84 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+02)), 85 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) 86 }; 87 static const T P3[] = { 88 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1600249425076035558e+02)), 89 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)), 90 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)), 91 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)), 92 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)), 93 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)), 94 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)), 95 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)), 96 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)), 97 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02)) 98 }; 99 static const T Q3[] = { 100 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)), 101 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)), 102 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)), 103 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)), 104 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)), 105 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)), 106 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)), 107 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)), 108 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)), 109 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)), 110 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) 111 }; 112 T value, factor, r, r1, r2; 113 114 BOOST_MATH_STD_USING 115 using namespace boost::math::tools; 116 117 static const char* function = "boost::math::bessel_k0<%1%>(%1%,%1%)"; 118 119 if (x < 0) 120 { 121 return policies::raise_domain_error<T>(function, 122 "Got x = %1%, but argument x must be non-negative, complex number result not supported", x, pol); 123 } 124 if (x == 0) 125 { 126 return policies::raise_overflow_error<T>(function, 0, pol); 127 } 128 if (x <= 1) // x in (0, 1] 129 { 130 T y = x * x; 131 r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); 132 r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); 133 factor = log(x); 134 value = r1 - factor * r2; 135 } 136 else // x in (1, \infty) 137 { 138 T y = 1 / x; 139 r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y); 140 factor = exp(-x) / sqrt(x); 141 value = factor * r; 142 BOOST_MATH_INSTRUMENT_CODE("y = " << y); 143 BOOST_MATH_INSTRUMENT_CODE("r = " << r); 144 BOOST_MATH_INSTRUMENT_CODE("factor = " << factor); 145 BOOST_MATH_INSTRUMENT_CODE("value = " << value); 146 } 147 148 return value; 149 } 150 151 }}} // namespaces 152 153 #ifdef _MSC_VER 154 #pragma warning(pop) 155 #endif 156 157 #endif // BOOST_MATH_BESSEL_K0_HPP 158 159