1 /* $OpenBSD: s_cpow.c,v 1.7 2016/09/12 19:47:02 guenther 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 /* cpow
19 *
20 * Complex power function
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex cpow();
27 * double complex a, z, w;
28 *
29 * w = cpow (a, z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * Raises complex A to the complex Zth power.
36 * Definition is per AMS55 # 4.2.8,
37 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
38 *
39 * ACCURACY:
40 *
41 * Relative error:
42 * arithmetic domain # trials peak rms
43 * IEEE -10,+10 30000 9.4e-15 1.5e-15
44 *
45 */
46
47 #include <complex.h>
48 #include <float.h>
49 #include <math.h>
50
51 double complex
cpow(double complex a,double complex z)52 cpow(double complex a, double complex z)
53 {
54 double complex w;
55 double x, y, r, theta, absa, arga;
56
57 x = creal (z);
58 y = cimag (z);
59 absa = cabs (a);
60 if (absa == 0.0) {
61 return (0.0 + 0.0 * I);
62 }
63 arga = carg (a);
64 r = pow (absa, x);
65 theta = x * arga;
66 if (y != 0.0) {
67 r = r * exp (-y * arga);
68 theta = theta + y * log (absa);
69 }
70 w = r * cos (theta) + (r * sin (theta)) * I;
71 return (w);
72 }
73 DEF_STD(cpow);
74 LDBL_MAYBE_UNUSED_CLONE(cpow);
75