1*05a0b428SJohn Marino /* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
2*05a0b428SJohn Marino
3*05a0b428SJohn Marino /*
4*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
7*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
8*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
9*05a0b428SJohn Marino *
10*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17*05a0b428SJohn Marino */
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino /* cpowl
20*05a0b428SJohn Marino *
21*05a0b428SJohn Marino * Complex power function
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino *
25*05a0b428SJohn Marino * SYNOPSIS:
26*05a0b428SJohn Marino *
27*05a0b428SJohn Marino * long double complex cpowl();
28*05a0b428SJohn Marino * long double complex a, z, w;
29*05a0b428SJohn Marino *
30*05a0b428SJohn Marino * w = cpowl (a, z);
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino *
34*05a0b428SJohn Marino * DESCRIPTION:
35*05a0b428SJohn Marino *
36*05a0b428SJohn Marino * Raises complex A to the complex Zth power.
37*05a0b428SJohn Marino * Definition is per AMS55 # 4.2.8,
38*05a0b428SJohn Marino * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
39*05a0b428SJohn Marino *
40*05a0b428SJohn Marino * ACCURACY:
41*05a0b428SJohn Marino *
42*05a0b428SJohn Marino * Relative error:
43*05a0b428SJohn Marino * arithmetic domain # trials peak rms
44*05a0b428SJohn Marino * IEEE -10,+10 30000 9.4e-15 1.5e-15
45*05a0b428SJohn Marino *
46*05a0b428SJohn Marino */
47*05a0b428SJohn Marino
48*05a0b428SJohn Marino #include <complex.h>
49*05a0b428SJohn Marino #include <math.h>
50*05a0b428SJohn Marino
51*05a0b428SJohn Marino long double complex
cpowl(long double complex a,long double complex z)52*05a0b428SJohn Marino cpowl(long double complex a, long double complex z)
53*05a0b428SJohn Marino {
54*05a0b428SJohn Marino long double complex w;
55*05a0b428SJohn Marino long double x, y, r, theta, absa, arga;
56*05a0b428SJohn Marino
57*05a0b428SJohn Marino x = creall(z);
58*05a0b428SJohn Marino y = cimagl(z);
59*05a0b428SJohn Marino absa = cabsl(a);
60*05a0b428SJohn Marino if (absa == 0.0L) {
61*05a0b428SJohn Marino return (0.0L + 0.0L * I);
62*05a0b428SJohn Marino }
63*05a0b428SJohn Marino arga = cargl(a);
64*05a0b428SJohn Marino r = powl(absa, x);
65*05a0b428SJohn Marino theta = x * arga;
66*05a0b428SJohn Marino if (y != 0.0L) {
67*05a0b428SJohn Marino r = r * expl(-y * arga);
68*05a0b428SJohn Marino theta = theta + y * logl(absa);
69*05a0b428SJohn Marino }
70*05a0b428SJohn Marino w = r * cosl(theta) + (r * sinl(theta)) * I;
71*05a0b428SJohn Marino return (w);
72*05a0b428SJohn Marino }
73