1 /* $OpenBSD: s_csinl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
2
3 /*
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 */
18
19 /* csinl()
20 *
21 * Complex circular sine
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex csinl();
28 * long double complex z, w;
29 *
30 * w = csinl( z );
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 * If
37 * z = x + iy,
38 *
39 * then
40 *
41 * w = sin x cosh y + i cos x sinh y.
42 *
43 *
44 *
45 * ACCURACY:
46 *
47 * Relative error:
48 * arithmetic domain # trials peak rms
49 * DEC -10,+10 8400 5.3e-17 1.3e-17
50 * IEEE -10,+10 30000 3.8e-16 1.0e-16
51 * Also tested by csin(casin(z)) = z.
52 *
53 */
54
55 #include <complex.h>
56 #include <math.h>
57
58 static void
cchshl(long double x,long double * c,long double * s)59 cchshl(long double x, long double *c, long double *s)
60 {
61 long double e, ei;
62
63 if(fabsl(x) <= 0.5L) {
64 *c = coshl(x);
65 *s = sinhl(x);
66 } else {
67 e = expl(x);
68 ei = 0.5L/e;
69 e = 0.5L * e;
70 *s = e - ei;
71 *c = e + ei;
72 }
73 }
74
75 long double complex
csinl(long double complex z)76 csinl(long double complex z)
77 {
78 long double complex w;
79 long double ch, sh;
80
81 cchshl(cimagl(z), &ch, &sh);
82 w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I;
83 return (w);
84 }
85