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
|
/* specfunc/bessel_Y1.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_trig.h>
#include <gsl/gsl_sf_bessel.h>
#include "error.h"
#include "bessel.h"
#include "bessel_amp_phase.h"
#include "cheb_eval.c"
/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
/* based on SLATEC besy1, 1977 version, w. fullerton */
/* chebyshev expansions
series for by1 on the interval 0. to 1.60000d+01
with weighted error 1.87e-18
log weighted error 17.73
significant figures required 17.83
decimal places required 18.30
*/
static double by1_data[14] = {
0.03208047100611908629,
1.262707897433500450,
0.00649996189992317500,
-0.08936164528860504117,
0.01325088122175709545,
-0.00089790591196483523,
0.00003647361487958306,
-0.00000100137438166600,
0.00000001994539657390,
-0.00000000030230656018,
0.00000000000360987815,
-0.00000000000003487488,
0.00000000000000027838,
-0.00000000000000000186
};
static cheb_series by1_cs = {
by1_data,
13,
-1, 1,
10
};
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result)
{
const double two_over_pi = 2.0/M_PI;
const double xmin = 1.571*GSL_DBL_MIN; /*exp ( amax1(alog(r1mach(1)), -alog(r1mach(2)))+.01) */
const double x_small = 2.0 * GSL_SQRT_DBL_EPSILON;
const double xmax = 1.0/GSL_DBL_EPSILON;
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(x < xmin) {
OVERFLOW_ERROR(result);
}
else if(x < x_small) {
const double lnterm = log(0.5*x);
gsl_sf_result J1;
gsl_sf_result c;
int status = gsl_sf_bessel_J1_e(x, &J1);
cheb_eval_e(&by1_cs, -1.0, &c);
result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
return status;
}
else if(x < 4.0) {
const double lnterm = log(0.5*x);
int status;
gsl_sf_result J1;
gsl_sf_result c;
cheb_eval_e(&by1_cs, 0.125*x*x-1.0, &c);
status = gsl_sf_bessel_J1_e(x, &J1);
result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
return status;
}
else if(x < xmax) {
const double z = 32.0/(x*x) - 1.0;
gsl_sf_result ca;
gsl_sf_result ct;
gsl_sf_result cp;
const int stat_ca = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bm1_cs, z, &ca);
const int stat_ct = cheb_eval_e(&_gsl_sf_bessel_amp_phase_bth1_cs, z, &ct);
const int stat_cp = gsl_sf_bessel_cos_pi4_e(x, ct.val/x, &cp);
const double sqrtx = sqrt(x);
const double ampl = (0.75 + ca.val) / sqrtx;
result->val = -ampl * cp.val;
result->err = fabs(cp.val) * ca.err/sqrtx + fabs(ampl) * cp.err;
result->err += GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp);
}
else {
UNDERFLOW_ERROR(result);
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_Y1(const double x)
{
EVAL_RESULT(gsl_sf_bessel_Y1_e(x, &result));
}
|
