# GL Profile Suite / boost_1_51_0 / boost / math / special_functions / detail / bessel_k1.hpp

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 // 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_K1_HPP #define BOOST_MATH_BESSEL_K1_HPP #ifdef _MSC_VER #pragma once #endif #include #include #include #include // Modified Bessel function of the second kind of order one // minimax rational approximations on intervals, see // Russon and Blair, Chalk River Report AECL-3461, 1969 namespace boost { namespace math { namespace detail{ template T bessel_k1(T x, const Policy&); template struct bessel_k1_initializer { struct init { init() { do_init(); } static void do_init() { bessel_k1(T(1), Policy()); } void force_instantiate()const{} }; static const init initializer; static void force_instantiate() { initializer.force_instantiate(); } }; template const typename bessel_k1_initializer::init bessel_k1_initializer::initializer; template T bessel_k1(T x, const Policy& pol) { bessel_k1_initializer::force_instantiate(); static const T P1[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01)) }; static const T Q1[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) }; static const T P2[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01)) }; static const T Q2[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) }; static const T P3[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02)) }; static const T Q3[] = { static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)), static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)), static_cast(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_k1<%1%>(%1%,%1%)"; if (x < 0) { return policies::raise_domain_error(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(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) / x; } 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; } return value; } }}} // namespaces #endif // BOOST_MATH_BESSEL_K1_HPP