xref: /openbsd-src/lib/libm/src/s_cpow.c (revision d13be5d47e4149db2549a9828e244d59dbc43f15)
1 /*	$OpenBSD: s_cpow.c,v 1.2 2011/07/08 19:25:31 martynas Exp $	*/
2 /*
3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4  *
5  * Permission to use, copy, modify, and distribute this software for any
6  * purpose with or without fee is hereby granted, provided that the above
7  * copyright notice and this permission notice appear in all copies.
8  *
9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16  */
17 
18 /* LINTLIBRARY */
19 
20 /*							cpow
21  *
22  *	Complex power function
23  *
24  *
25  *
26  * SYNOPSIS:
27  *
28  * double complex cpow();
29  * double complex a, z, w;
30  *
31  * w = cpow (a, z);
32  *
33  *
34  *
35  * DESCRIPTION:
36  *
37  * Raises complex A to the complex Zth power.
38  * Definition is per AMS55 # 4.2.8,
39  * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
40  *
41  * ACCURACY:
42  *
43  *                      Relative error:
44  * arithmetic   domain     # trials      peak         rms
45  *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
46  *
47  */
48 
49 #include <sys/cdefs.h>
50 #include <complex.h>
51 #include <float.h>
52 #include <math.h>
53 
54 double complex
55 cpow(double complex a, double complex z)
56 {
57 	double complex w;
58 	double x, y, r, theta, absa, arga;
59 
60 	x = creal (z);
61 	y = cimag (z);
62 	absa = cabs (a);
63 	if (absa == 0.0) {
64 		return (0.0 + 0.0 * I);
65 	}
66 	arga = carg (a);
67 	r = pow (absa, x);
68 	theta = x * arga;
69 	if (y != 0.0) {
70 		r = r * exp (-y * arga);
71 		theta = theta + y * log (absa);
72 	}
73 	w = r * cos (theta) + (r * sin (theta)) * I;
74 	return (w);
75 }
76 
77 #if	LDBL_MANT_DIG == 53
78 #ifdef	lint
79 /* PROTOLIB1 */
80 long double complex cpowl(long double complex, long double complex);
81 #else	/* lint */
82 __weak_alias(cpowl, cpow);
83 #endif	/* lint */
84 #endif	/* LDBL_MANT_DIG == 53 */
85