1/*	$OpenBSD: s_ccosl.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/*							ccosl()
20 *
21 *	Complex circular cosine
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex ccosl();
28 * long double complex z, w;
29 *
30 * w = ccosl( z );
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 * If
37 *     z = x + iy,
38 *
39 * then
40 *
41 *     w = cos x  cosh y  -  i sin x sinh y.
42 *
43 *
44 *
45 * ACCURACY:
46 *
47 *                      Relative error:
48 * arithmetic   domain     # trials      peak         rms
49 *    DEC       -10,+10      8400       4.5e-17     1.3e-17
50 *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
51 */
52
53#include <complex.h>
54#include <math.h>
55
56static void
57cchshl(long double x, long double *c, long double *s)
58{
59	long double e, ei;
60
61	if(fabsl(x) <= 0.5L) {
62		*c = coshl(x);
63		*s = sinhl(x);
64	} else {
65		e = expl(x);
66		ei = 0.5L/e;
67		e = 0.5L * e;
68		*s = e - ei;
69		*c = e + ei;
70	}
71}
72
73long double complex
74ccosl(long double complex z)
75{
76	long double complex w;
77	long double ch, sh;
78
79	cchshl(cimagl(z), &ch, &sh);
80	w = cosl(creall(z)) * ch + (-sinl(creall(z)) * sh) * I;
81	return (w);
82}
83