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
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
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