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
149
150
151
152
|
// 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_K0_HPP
#define BOOST_MATH_BESSEL_K0_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/tools/rational.hpp>
#include <boost/math/tools/big_constant.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/assert.hpp>
// Modified Bessel function of the second kind of order zero
// minimax rational approximations on intervals, see
// Russon and Blair, Chalk River Report AECL-3461, 1969
namespace boost { namespace math { namespace detail{
template <typename T, typename Policy>
T bessel_k0(T x, const Policy&);
template <class T, class Policy>
struct bessel_k0_initializer
{
struct init
{
init()
{
do_init();
}
static void do_init()
{
bessel_k0(T(1), Policy());
}
void force_instantiate()const{}
};
static const init initializer;
static void force_instantiate()
{
initializer.force_instantiate();
}
};
template <class T, class Policy>
const typename bessel_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer;
template <typename T, typename Policy>
T bessel_k0(T x, const Policy& pol)
{
BOOST_MATH_INSTRUMENT_CODE(x);
bessel_k0_initializer<T, Policy>::force_instantiate();
static const T P1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04))
};
static const T Q1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
};
static const T P2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00))
};
static const T Q2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
};
static const T P3[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1600249425076035558e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02))
};
static const T Q3[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)),
static_cast<T>(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_k0<%1%>(%1%,%1%)";
if (x < 0)
{
return policies::raise_domain_error<T>(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<T>(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;
}
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;
BOOST_MATH_INSTRUMENT_CODE("y = " << y);
BOOST_MATH_INSTRUMENT_CODE("r = " << r);
BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
BOOST_MATH_INSTRUMENT_CODE("value = " << value);
}
return value;
}
}}} // namespaces
#endif // BOOST_MATH_BESSEL_K0_HPP
|
