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
cpowf(float complex a,float complex z)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