s_cpowf.c revision 336767 
1/*-
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: stable/11/lib/msun/src/s_cpowf.c 336767 2018-07-27 17:39:36Z dim $");
48
49#include <complex.h>
50#include <math.h>
51#include "math_private.h"
52
53float complex
54cpowf(float complex a, float complex z)
55{
56	float complex w;
57	float x, y, r, theta, absa, arga;
58
59	x = crealf(z);
60	y = cimagf(z);
61	absa = cabsf (a);
62	if (absa == 0.0f) {
63		return (CMPLXF(0.0f, 0.0f));
64	}
65	arga = cargf (a);
66	r = powf (absa, x);
67	theta = x * arga;
68	if (y != 0.0f) {
69		r = r * expf (-y * arga);
70		theta = theta + y * logf (absa);
71	}
72	w = CMPLXF(r * cosf (theta), r * sinf (theta));
73	return (w);
74}
75