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