1 /*	$OpenBSD: s_cexpl.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 /*							cexpl()
20  *
21  *	Complex exponential function
22  *
23  *
24  *
25  * SYNOPSIS:
26  *
27  * long double complex cexpl();
28  * long double complex z, w;
29  *
30  * w = cexpl( z );
31  *
32  *
33  *
34  * DESCRIPTION:
35  *
36  * Returns the exponential of the complex argument z
37  * into the complex result w.
38  *
39  * If
40  *     z = x + iy,
41  *     r = exp(x),
42  *
43  * then
44  *
45  *     w = r cos y + i r sin y.
46  *
47  *
48  * ACCURACY:
49  *
50  *                      Relative error:
51  * arithmetic   domain     # trials      peak         rms
52  *    DEC       -10,+10      8700       3.7e-17     1.1e-17
53  *    IEEE      -10,+10     30000       3.0e-16     8.7e-17
54  *
55  */
56 
57 #include <complex.h>
58 #include <math.h>
59 
60 long double complex
61 cexpl(long double complex z)
62 {
63 	long double complex w;
64 	long double r;
65 
66 	r = expl(creall(z));
67 	w = r * cosl(cimagl(z)) + (r * sinl(cimagl(z))) * I;
68 	return (w);
69 }
70