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
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