blob: 6e27f57790aa9f8795d8b14403afe18dfd7d7ffa [file] [log] [blame]
Elliott Hughesab528072018-07-24 00:01:52 +00001/*-
2 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
3 *
4 * Permission to use, copy, modify, and distribute this software for any
5 * purpose with or without fee is hereby granted, provided that the above
6 * copyright notice and this permission notice appear in all copies.
7 *
8 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
9 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
10 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
11 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
12 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
13 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
14 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
15 */
16
17/* cpowf
18 *
19 * Complex power function
20 *
21 *
22 *
23 * SYNOPSIS:
24 *
25 * float complex cpowf();
26 * float complex a, z, w;
27 *
28 * w = cpowf (a, z);
29 *
30 *
31 *
32 * DESCRIPTION:
33 *
34 * Raises complex A to the complex Zth power.
35 * Definition is per AMS55 # 4.2.8,
36 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
37 *
38 * ACCURACY:
39 *
40 * Relative error:
41 * arithmetic domain # trials peak rms
42 * IEEE -10,+10 30000 9.4e-15 1.5e-15
43 *
44 */
45
46#include <sys/cdefs.h>
47__FBSDID("$FreeBSD: head/lib/msun/src/s_cpowf.c 336299 2018-07-15 00:23:10Z mmacy $");
48
49#include <complex.h>
50#include <math.h>
51
52float complex
53cpowf(float complex a, float complex z)
54{
55 float complex w;
56 float x, y, r, theta, absa, arga;
57
58 x = crealf(z);
59 y = cimagf(z);
60 absa = cabsf (a);
61 if (absa == 0.0f) {
62 return (0.0f + 0.0f * I);
63 }
64 arga = cargf (a);
65 r = powf (absa, x);
66 theta = x * arga;
67 if (y != 0.0f) {
68 r = r * expf (-y * arga);
69 theta = theta + y * logf (absa);
70 }
71 w = r * cosf (theta) + (r * sinf (theta)) * I;
72 return (w);
73}