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
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
|
/* specfunc/bessel_K0.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman */
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_exp.h>
#include <gsl/gsl_sf_bessel.h>
#include "error.h"
#include "chebyshev.h"
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC bk0(), bk0e() */
/* chebyshev expansions
series for bk0 on the interval 0. to 4.00000d+00
with weighted error 3.57e-19
log weighted error 18.45
significant figures required 17.99
decimal places required 18.97
series for ak0 on the interval 1.25000d-01 to 5.00000d-01
with weighted error 5.34e-17
log weighted error 16.27
significant figures required 14.92
decimal places required 16.89
series for ak02 on the interval 0. to 1.25000d-01
with weighted error 2.34e-17
log weighted error 16.63
significant figures required 14.67
decimal places required 17.20
*/
static double bk0_data[11] = {
-0.03532739323390276872,
0.3442898999246284869,
0.03597993651536150163,
0.00126461541144692592,
0.00002286212103119451,
0.00000025347910790261,
0.00000000190451637722,
0.00000000001034969525,
0.00000000000004259816,
0.00000000000000013744,
0.00000000000000000035
};
static cheb_series bk0_cs = {
bk0_data,
10,
-1, 1,
10
};
static double ak0_data[17] = {
-0.07643947903327941,
-0.02235652605699819,
0.00077341811546938,
-0.00004281006688886,
0.00000308170017386,
-0.00000026393672220,
0.00000002563713036,
-0.00000000274270554,
0.00000000031694296,
-0.00000000003902353,
0.00000000000506804,
-0.00000000000068895,
0.00000000000009744,
-0.00000000000001427,
0.00000000000000215,
-0.00000000000000033,
0.00000000000000005
};
static cheb_series ak0_cs = {
ak0_data,
16,
-1, 1,
10
};
static double ak02_data[14] = {
-0.01201869826307592,
-0.00917485269102569,
0.00014445509317750,
-0.00000401361417543,
0.00000015678318108,
-0.00000000777011043,
0.00000000046111825,
-0.00000000003158592,
0.00000000000243501,
-0.00000000000020743,
0.00000000000001925,
-0.00000000000000192,
0.00000000000000020,
-0.00000000000000002
};
static cheb_series ak02_cs = {
ak02_data,
13,
-1, 1,
8
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_K0_scaled_e(const double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(x <= 2.0) {
const double lx = log(x);
const double ex = exp(x);
int stat_I0;
gsl_sf_result I0;
gsl_sf_result c;
cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
result->val = ex * ((-lx+M_LN2)*I0.val - 0.25 + c.val);
result->err = ex * ((M_LN2+fabs(lx))*I0.err + c.err);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_I0;
}
else if(x <= 8.0) {
const double sx = sqrt(x);
gsl_sf_result c;
cheb_eval_e(&ak0_cs, (16.0/x-5.0)/3.0, &c);
result->val = (1.25 + c.val) / sx;
result->err = c.err / sx;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double sx = sqrt(x);
gsl_sf_result c;
cheb_eval_e(&ak02_cs, 16.0/x-1.0, &c);
result->val = (1.25 + c.val) / sx;
result->err = (c.err + GSL_DBL_EPSILON) / sx;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int gsl_sf_bessel_K0_e(const double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(x <= 2.0) {
const double lx = log(x);
int stat_I0;
gsl_sf_result I0;
gsl_sf_result c;
cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
result->val = (-lx+M_LN2)*I0.val - 0.25 + c.val;
result->err = (fabs(lx) + M_LN2) * I0.err + c.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_I0;
}
else {
gsl_sf_result K0_scaled;
int stat_K0 = gsl_sf_bessel_K0_scaled_e(x, &K0_scaled);
int stat_e = gsl_sf_exp_mult_err_e(-x, GSL_DBL_EPSILON*fabs(x),
K0_scaled.val, K0_scaled.err,
result);
return GSL_ERROR_SELECT_2(stat_e, stat_K0);
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_K0_scaled(const double x)
{
EVAL_RESULT(gsl_sf_bessel_K0_scaled_e(x, &result));
}
double gsl_sf_bessel_K0(const double x)
{
EVAL_RESULT(gsl_sf_bessel_K0_e(x, &result));
}
|
