1 /* $OpenBSD: s_csinf.c,v 1.2 2010/07/18 18:42:26 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 /* csinf()
19 *
20 * Complex circular sine
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * void csinf();
27 * cmplxf z, w;
28 *
29 * csinf( &z, &w );
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 *
43 *
44 * ACCURACY:
45 *
46 * Relative error:
47 * arithmetic domain # trials peak rms
48 * IEEE -10,+10 30000 1.9e-7 5.5e-8
49 *
50 */
51
52 #include <complex.h>
53 #include <math.h>
54
55 /* calculate cosh and sinh */
56
57 static void
cchshf(float xx,float * c,float * s)58 cchshf(float xx, float *c, float *s)
59 {
60 float x, e, ei;
61
62 x = xx;
63 if(fabsf(x) <= 0.5f) {
64 *c = coshf(x);
65 *s = sinhf(x);
66 }
67 else {
68 e = expf(x);
69 ei = 0.5f/e;
70 e = 0.5f * e;
71 *s = e - ei;
72 *c = e + ei;
73 }
74 }
75
76 float complex
csinf(float complex z)77 csinf(float complex z)
78 {
79 float complex w;
80 float ch, sh;
81
82 cchshf(cimagf(z), &ch, &sh);
83 w = sinf(crealf(z)) * ch + (cosf(crealf(z)) * sh) * I;
84 return (w);
85 }
86