1*05a0b428SJohn Marino /* $OpenBSD: s_cpow.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4*05a0b428SJohn Marino *
5*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
6*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
7*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16*05a0b428SJohn Marino */
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino /* cpow
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex power function
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * double complex cpow();
27*05a0b428SJohn Marino * double complex a, z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = cpow (a, z);
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * Raises complex A to the complex Zth power.
36*05a0b428SJohn Marino * Definition is per AMS55 # 4.2.8,
37*05a0b428SJohn Marino * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
38*05a0b428SJohn Marino *
39*05a0b428SJohn Marino * ACCURACY:
40*05a0b428SJohn Marino *
41*05a0b428SJohn Marino * Relative error:
42*05a0b428SJohn Marino * arithmetic domain # trials peak rms
43*05a0b428SJohn Marino * IEEE -10,+10 30000 9.4e-15 1.5e-15
44*05a0b428SJohn Marino *
45*05a0b428SJohn Marino */
46*05a0b428SJohn Marino
47*05a0b428SJohn Marino #include <complex.h>
48*05a0b428SJohn Marino #include <float.h>
49*05a0b428SJohn Marino #include <math.h>
50*05a0b428SJohn Marino
51*05a0b428SJohn Marino double complex
cpow(double complex a,double complex z)52*05a0b428SJohn Marino cpow(double complex a, double complex z)
53*05a0b428SJohn Marino {
54*05a0b428SJohn Marino double complex w;
55*05a0b428SJohn Marino double x, y, r, theta, absa, arga;
56*05a0b428SJohn Marino
57*05a0b428SJohn Marino x = creal (z);
58*05a0b428SJohn Marino y = cimag (z);
59*05a0b428SJohn Marino absa = cabs (a);
60*05a0b428SJohn Marino if (absa == 0.0) {
61*05a0b428SJohn Marino return (0.0 + 0.0 * I);
62*05a0b428SJohn Marino }
63*05a0b428SJohn Marino arga = carg (a);
64*05a0b428SJohn Marino r = pow (absa, x);
65*05a0b428SJohn Marino theta = x * arga;
66*05a0b428SJohn Marino if (y != 0.0) {
67*05a0b428SJohn Marino r = r * exp (-y * arga);
68*05a0b428SJohn Marino theta = theta + y * log (absa);
69*05a0b428SJohn Marino }
70*05a0b428SJohn Marino w = r * cos (theta) + (r * sin (theta)) * I;
71*05a0b428SJohn Marino return (w);
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino
74*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
75*05a0b428SJohn Marino __strong_alias(cpowl, cpow);
76*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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