xref: /freebsd/lib/msun/src/s_cpowl.c (revision ebacd8013fe5f7fdf9f6a5b286f6680dd2891036)
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("$FreeBSD$");
48 
49 #include <complex.h>
50 #include <math.h>
51 #include "math_private.h"
52 
53 long double complex
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