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annotate DEPENDENCIES/generic/include/boost/math/special_functions/detail/bessel_k1.hpp @ 125:34e428693f5d vext

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Vext -> Repoint
author Chris Cannam
date Thu, 14 Jun 2018 11:15:39 +0100
parents 2665513ce2d3
children
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Chris@16 1 // Copyright (c) 2006 Xiaogang Zhang
Chris@16 2 // Use, modification and distribution are subject to the
Chris@16 3 // Boost Software License, Version 1.0. (See accompanying file
Chris@16 4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16 5
Chris@16 6 #ifndef BOOST_MATH_BESSEL_K1_HPP
Chris@16 7 #define BOOST_MATH_BESSEL_K1_HPP
Chris@16 8
Chris@16 9 #ifdef _MSC_VER
Chris@16 10 #pragma once
Chris@16 11 #endif
Chris@16 12
Chris@16 13 #include <boost/math/tools/rational.hpp>
Chris@16 14 #include <boost/math/tools/big_constant.hpp>
Chris@16 15 #include <boost/math/policies/error_handling.hpp>
Chris@16 16 #include <boost/assert.hpp>
Chris@16 17
Chris@16 18 // Modified Bessel function of the second kind of order one
Chris@16 19 // minimax rational approximations on intervals, see
Chris@16 20 // Russon and Blair, Chalk River Report AECL-3461, 1969
Chris@16 21
Chris@16 22 namespace boost { namespace math { namespace detail{
Chris@16 23
Chris@16 24 template <typename T, typename Policy>
Chris@16 25 T bessel_k1(T x, const Policy&);
Chris@16 26
Chris@16 27 template <class T, class Policy>
Chris@16 28 struct bessel_k1_initializer
Chris@16 29 {
Chris@16 30 struct init
Chris@16 31 {
Chris@16 32 init()
Chris@16 33 {
Chris@16 34 do_init();
Chris@16 35 }
Chris@16 36 static void do_init()
Chris@16 37 {
Chris@16 38 bessel_k1(T(1), Policy());
Chris@16 39 }
Chris@16 40 void force_instantiate()const{}
Chris@16 41 };
Chris@16 42 static const init initializer;
Chris@16 43 static void force_instantiate()
Chris@16 44 {
Chris@16 45 initializer.force_instantiate();
Chris@16 46 }
Chris@16 47 };
Chris@16 48
Chris@16 49 template <class T, class Policy>
Chris@16 50 const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
Chris@16 51
Chris@16 52 template <typename T, typename Policy>
Chris@16 53 T bessel_k1(T x, const Policy& pol)
Chris@16 54 {
Chris@16 55 bessel_k1_initializer<T, Policy>::force_instantiate();
Chris@16 56
Chris@16 57 static const T P1[] = {
Chris@16 58 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
Chris@16 59 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
Chris@16 60 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
Chris@16 61 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
Chris@16 62 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
Chris@16 63 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
Chris@16 64 };
Chris@16 65 static const T Q1[] = {
Chris@16 66 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
Chris@16 67 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
Chris@16 68 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
Chris@16 69 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16 70 };
Chris@16 71 static const T P2[] = {
Chris@16 72 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
Chris@16 73 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
Chris@16 74 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
Chris@16 75 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
Chris@16 76 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
Chris@16 77 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
Chris@16 78 };
Chris@16 79 static const T Q2[] = {
Chris@16 80 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
Chris@16 81 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
Chris@16 82 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
Chris@16 83 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16 84 };
Chris@16 85 static const T P3[] = {
Chris@16 86 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
Chris@16 87 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
Chris@16 88 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
Chris@16 89 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
Chris@16 90 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
Chris@16 91 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
Chris@16 92 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
Chris@16 93 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
Chris@16 94 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
Chris@16 95 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
Chris@16 96 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
Chris@16 97 };
Chris@16 98 static const T Q3[] = {
Chris@16 99 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
Chris@16 100 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
Chris@16 101 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
Chris@16 102 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
Chris@16 103 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
Chris@16 104 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
Chris@16 105 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
Chris@16 106 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
Chris@16 107 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
Chris@16 108 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16 109 };
Chris@16 110 T value, factor, r, r1, r2;
Chris@16 111
Chris@16 112 BOOST_MATH_STD_USING
Chris@16 113 using namespace boost::math::tools;
Chris@16 114
Chris@16 115 static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
Chris@16 116
Chris@16 117 if (x < 0)
Chris@16 118 {
Chris@16 119 return policies::raise_domain_error<T>(function,
Chris@16 120 "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
Chris@16 121 }
Chris@16 122 if (x == 0)
Chris@16 123 {
Chris@16 124 return policies::raise_overflow_error<T>(function, 0, pol);
Chris@16 125 }
Chris@16 126 if (x <= 1) // x in (0, 1]
Chris@16 127 {
Chris@16 128 T y = x * x;
Chris@16 129 r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
Chris@16 130 r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
Chris@16 131 factor = log(x);
Chris@16 132 value = (r1 + factor * r2) / x;
Chris@16 133 }
Chris@16 134 else // x in (1, \infty)
Chris@16 135 {
Chris@16 136 T y = 1 / x;
Chris@16 137 r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
Chris@16 138 factor = exp(-x) / sqrt(x);
Chris@16 139 value = factor * r;
Chris@16 140 }
Chris@16 141
Chris@16 142 return value;
Chris@16 143 }
Chris@16 144
Chris@16 145 }}} // namespaces
Chris@16 146
Chris@16 147 #endif // BOOST_MATH_BESSEL_K1_HPP
Chris@16 148