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_K0_HPP
7 #define BOOST_MATH_BESSEL_K0_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 zero
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_k0(T x, const Policy&);
27 template <class T, class Policy>
28 struct bessel_k0_initializer
38 bessel_k0(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_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer;
52 template <typename T, typename Policy>
53 T bessel_k0(T x, const Policy& pol)
55 BOOST_MATH_INSTRUMENT_CODE(x);
57 bessel_k0_initializer<T, Policy>::force_instantiate();
59 static const T P1[] = {
60 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)),
61 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)),
62 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)),
63 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)),
64 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)),
65 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04))
67 static const T Q1[] = {
68 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)),
69 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)),
70 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
72 static const T P2[] = {
73 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
74 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)),
75 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)),
76 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)),
77 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00))
79 static const T Q2[] = {
80 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
81 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)),
82 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+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, 1.1600249425076035558e+02)),
87 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)),
88 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)),
89 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)),
90 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)),
91 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)),
92 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)),
93 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)),
94 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)),
95 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02))
97 static const T Q3[] = {
98 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)),
99 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)),
100 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)),
101 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)),
102 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)),
103 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)),
104 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)),
105 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)),
106 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)),
107 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)),
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_k0<%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;
134 else // x in (1, \infty)
137 r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
138 factor = exp(-x) / sqrt(x);
140 BOOST_MATH_INSTRUMENT_CODE("y = " << y);
141 BOOST_MATH_INSTRUMENT_CODE("r = " << r);
142 BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
143 BOOST_MATH_INSTRUMENT_CODE("value = " << value);
151 #endif // BOOST_MATH_BESSEL_K0_HPP