1 /* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
2
3 /*
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 */
18
19 /* cpowl
20 *
21 * Complex power function
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex cpowl();
28 * long double complex a, z, w;
29 *
30 * w = cpowl (a, z);
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 * Raises complex A to the complex Zth power.
37 * Definition is per AMS55 # 4.2.8,
38 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
39 *
40 * ACCURACY:
41 *
42 * Relative error:
43 * arithmetic domain # trials peak rms
44 * IEEE -10,+10 30000 9.4e-15 1.5e-15
45 *
46 */
47
48 #include <complex.h>
49 #include <math.h>
50
51 long double complex
cpowl(long double complex a,long double complex z)52 cpowl(long double complex a, long double complex z)
53 {
54 long double complex w;
55 long double x, y, r, theta, absa, arga;
56
57 x = creall(z);
58 y = cimagl(z);
59 absa = cabsl(a);
60 if (absa == 0.0L) {
61 return (0.0L + 0.0L * I);
62 }
63 arga = cargl(a);
64 r = powl(absa, x);
65 theta = x * arga;
66 if (y != 0.0L) {
67 r = r * expl(-y * arga);
68 theta = theta + y * logl(absa);
69 }
70 w = r * cosl(theta) + (r * sinl(theta)) * I;
71 return (w);
72 }
73