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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 | { | |
34 | init() | |
35 | { | |
36 | do_init(); | |
37 | } | |
38 | static void do_init() | |
39 | { | |
40 | bessel_k0(T(1), Policy()); | |
41 | } | |
42 | void force_instantiate()const{} | |
43 | }; | |
44 | static const init initializer; | |
45 | 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 |