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 /* cpowl
18 *
19 * Complex power function
20 *
21 *
22 *
23 * SYNOPSIS:
24 *
25 * long double complex cpowl();
26 * long double complex a, z, w;
27 *
28 * w = cpowl (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_cpowl.c 336563 2018-07-20 18:27:30Z dim $");
48
49 #include <complex.h>
50 #include <math.h>
51 #include "math_private.h"
52
53 long double complex
cpowl(long double complex a,long double complex z)54 cpowl(long double complex a, long double complex z)
55 {
56 long double complex w;
57 long double x, y, r, theta, absa, arga;
58
59 x = creall(z);
60 y = cimagl(z);
61 absa = cabsl(a);
62 if (absa == 0.0L) {
63 return (CMPLXL(0.0L, 0.0L));
64 }
65 arga = cargl(a);
66 r = powl(absa, x);
67 theta = x * arga;
68 if (y != 0.0L) {
69 r = r * expl(-y * arga);
70 theta = theta + y * logl(absa);
71 }
72 w = CMPLXL(r * cosl(theta), r * sinl(theta));
73 return (w);
74 }
75