1/*	$OpenBSD: s_ccos.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/*							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
58static void
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
76double complex
77ccos(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}
86DEF_STD(ccos);
87LDBL_MAYBE_UNUSED_CLONE(ccos);
88