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)
6 #ifndef BOOST_MATH_BESSEL_K1_HPP
7 #define BOOST_MATH_BESSEL_K1_HPP
13 #include <boost/math/tools/rational.hpp>
14 #include <boost/math/tools/big_constant.hpp>
15 #include <boost/math/policies/error_handling.hpp>
16 #include <boost/assert.hpp>
18 // Modified Bessel function of the second kind of order one
19 // minimax rational approximations on intervals, see
20 // Russon and Blair, Chalk River Report AECL-3461, 1969
22 namespace boost { namespace math { namespace detail{
24 template <typename T, typename Policy>
25 T bessel_k1(T x, const Policy&);
27 template <class T, class Policy>
28 struct bessel_k1_initializer
38 bessel_k1(T(1), Policy());
40 void force_instantiate()const{}
42 static const init initializer;
43 static void force_instantiate()
45 initializer.force_instantiate();
49 template <class T, class Policy>
50 const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
52 template <typename T, typename Policy>
53 T bessel_k1(T x, const Policy& pol)
55 bessel_k1_initializer<T, Policy>::force_instantiate();
57 static const T P1[] = {
58 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
59 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
60 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
61 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
62 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
63 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
65 static const T Q1[] = {
66 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
67 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
68 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
69 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
71 static const T P2[] = {
72 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
73 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
74 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
75 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
76 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
77 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
79 static const T Q2[] = {
80 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
81 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
82 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
83 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
85 static const T P3[] = {
86 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
87 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
88 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
89 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
90 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
91 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
92 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
93 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
94 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
95 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
96 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
98 static const T Q3[] = {
99 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
100 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
101 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
102 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
103 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
104 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
105 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
106 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
107 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
108 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
110 T value, factor, r, r1, r2;
113 using namespace boost::math::tools;
115 static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
119 return policies::raise_domain_error<T>(function,
120 "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
124 return policies::raise_overflow_error<T>(function, 0, pol);
126 if (x <= 1) // x in (0, 1]
129 r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
130 r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
132 value = (r1 + factor * r2) / x;
134 else // x in (1, \infty)
137 r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
138 factor = exp(-x) / sqrt(x);
147 #endif // BOOST_MATH_BESSEL_K1_HPP