1 /* $OpenBSD: s_ccos.c,v 1.6 2013/07/03 04:46:36 espie 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 /* ccos()
19 *
20 * Complex circular cosine
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex ccos();
27 * double complex z, w;
28 *
29 * w = ccos (z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * If
36 * z = x + iy,
37 *
38 * then
39 *
40 * w = cos x cosh y - i sin x sinh y.
41 *
42 *
43 *
44 * ACCURACY:
45 *
46 * Relative error:
47 * arithmetic domain # trials peak rms
48 * DEC -10,+10 8400 4.5e-17 1.3e-17
49 * IEEE -10,+10 30000 3.8e-16 1.0e-16
50 */
51
52 #include <complex.h>
53 #include <float.h>
54 #include <math.h>
55
56 /* calculate cosh and sinh */
57
58 static void
_cchsh(double x,double * c,double * s)59 _cchsh(double x, double *c, double *s)
60 {
61 double e, ei;
62
63 if (fabs(x) <= 0.5) {
64 *c = cosh(x);
65 *s = sinh(x);
66 }
67 else {
68 e = exp(x);
69 ei = 0.5/e;
70 e = 0.5 * e;
71 *s = e - ei;
72 *c = e + ei;
73 }
74 }
75
76 double complex
ccos(double complex z)77 ccos(double complex z)
78 {
79 double complex w;
80 double ch, sh;
81
82 _cchsh( cimag(z), &ch, &sh );
83 w = cos(creal (z)) * ch - (sin (creal (z)) * sh) * I;
84 return (w);
85 }
86
87 #if LDBL_MANT_DIG == DBL_MANT_DIG
88 __strong_alias(ccosl, ccos);
89 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
90