1 /* specfunc/clausen.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 /* Author: G. Jungman */
21
22 #include "gsl__config.h"
23 #include "gsl_math.h"
24 #include "gsl_errno.h"
25 #include "gsl_sf_trig.h"
26 #include "gsl_sf_clausen.h"
27
28 #include "gsl_specfunc__chebyshev.h"
29 #include "gsl_specfunc__cheb_eval.c"
30
31 static double aclaus_data[15] = {
32 2.142694363766688447e+00,
33 0.723324281221257925e-01,
34 0.101642475021151164e-02,
35 0.3245250328531645e-04,
36 0.133315187571472e-05,
37 0.6213240591653e-07,
38 0.313004135337e-08,
39 0.16635723056e-09,
40 0.919659293e-11,
41 0.52400462e-12,
42 0.3058040e-13,
43 0.18197e-14,
44 0.1100e-15,
45 0.68e-17,
46 0.4e-18
47 };
48 static cheb_series aclaus_cs = {
49 aclaus_data,
50 14,
51 -1, 1,
52 8 /* FIXME: this is a guess, correct value needed here BJG */
53 };
54
55
56 /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
57
gsl_sf_clausen_e(double x,gsl_sf_result * result)58 int gsl_sf_clausen_e(double x, gsl_sf_result *result)
59 {
60 const double x_cut = M_PI * GSL_SQRT_DBL_EPSILON;
61
62 double sgn = 1.0;
63 int status_red;
64
65 if(x < 0.0) {
66 x = -x;
67 sgn = -1.0;
68 }
69
70 /* Argument reduction to [0, 2pi) */
71 status_red = gsl_sf_angle_restrict_pos_e(&x);
72
73 /* Further reduction to [0,pi) */
74 if(x > M_PI) {
75 /* simulated extra precision: 2PI = p0 + p1 */
76 const double p0 = 6.28125;
77 const double p1 = 0.19353071795864769253e-02;
78 x = (p0 - x) + p1;
79 sgn = -sgn;
80 }
81
82 if(x == 0.0) {
83 result->val = 0.0;
84 result->err = 0.0;
85 }
86 else if(x < x_cut) {
87 result->val = x * (1.0 - log(x));
88 result->err = x * GSL_DBL_EPSILON;
89 }
90 else {
91 const double t = 2.0*(x*x / (M_PI*M_PI) - 0.5);
92 gsl_sf_result result_c;
93 cheb_eval_e(&aclaus_cs, t, &result_c);
94 result->val = x * (result_c.val - log(x));
95 result->err = x * (result_c.err + GSL_DBL_EPSILON);
96 }
97
98 result->val *= sgn;
99
100 return status_red;
101 }
102
103
104 /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
105
106 #include "gsl_specfunc__eval.h"
107
gsl_sf_clausen(const double x)108 double gsl_sf_clausen(const double x)
109 {
110 EVAL_RESULT(gsl_sf_clausen_e(x, &result));
111 }
112