1 /*	$OpenBSD: s_cpowf.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 /*							cpowf
19  *
20  *	Complex power function
21  *
22  *
23  *
24  * SYNOPSIS:
25  *
26  * float complex cpowf();
27  * float complex a, z, w;
28  *
29  * w = cpowf (a, z);
30  *
31  *
32  *
33  * DESCRIPTION:
34  *
35  * Raises complex A to the complex Zth power.
36  * Definition is per AMS55 # 4.2.8,
37  * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
38  *
39  * ACCURACY:
40  *
41  *                      Relative error:
42  * arithmetic   domain     # trials      peak         rms
43  *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
44  *
45  */
46 
47 #include <complex.h>
48 #include <math.h>
49 
50 float complex
51 cpowf(float complex a, float complex z)
52 {
53 	float complex w;
54 	float x, y, r, theta, absa, arga;
55 
56 	x = crealf(z);
57 	y = cimagf(z);
58 	absa = cabsf (a);
59 	if (absa == 0.0f) {
60 		return (0.0f + 0.0f * I);
61 	}
62 	arga = cargf (a);
63 	r = powf (absa, x);
64 	theta = x * arga;
65 	if (y != 0.0f) {
66 		r = r * expf (-y * arga);
67 		theta = theta + y * logf (absa);
68 	}
69 	w = r * cosf (theta) + (r * sinf (theta)) * I;
70 	return (w);
71 }
72