1 /* $OpenBSD: s_csin.c,v 1.7 2016/09/12 19:47:02 guenther Exp $ */
2 /*
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4 *
5 * Permission to use, copy, modify, and distribute this software for any
6 * purpose with or without fee is hereby granted, provided that the above
7 * copyright notice and this permission notice appear in all copies.
8 *
9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16 */
17
18 /* csin()
19 *
20 * Complex circular sine
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex csin();
27 * double complex z, w;
28 *
29 * w = csin (z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * If
36 * z = x + iy,
37 *
38 * then
39 *
40 * w = sin x cosh y + i cos x sinh y.
41 *
42 * csin(z) = -i csinh(iz).
43 *
44 * ACCURACY:
45 *
46 * Relative error:
47 * arithmetic domain # trials peak rms
48 * DEC -10,+10 8400 5.3e-17 1.3e-17
49 * IEEE -10,+10 30000 3.8e-16 1.0e-16
50 * Also tested by csin(casin(z)) = z.
51 *
52 */
53
54 #include <complex.h>
55 #include <float.h>
56 #include <math.h>
57
58 /* calculate cosh and sinh */
59
60 static void
cchsh(double x,double * c,double * s)61 cchsh(double x, double *c, double *s)
62 {
63 double e, ei;
64
65 if (fabs(x) <= 0.5) {
66 *c = cosh(x);
67 *s = sinh(x);
68 }
69 else {
70 e = exp(x);
71 ei = 0.5/e;
72 e = 0.5 * e;
73 *s = e - ei;
74 *c = e + ei;
75 }
76 }
77
78 double complex
csin(double complex z)79 csin(double complex z)
80 {
81 double complex w;
82 double ch, sh;
83
84 cchsh( cimag (z), &ch, &sh );
85 w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
86 return (w);
87 }
88 DEF_STD(csin);
89 LDBL_MAYBE_UNUSED_CLONE(csin);
90