1 /* $OpenBSD: s_clogf.c,v 1.3 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 /* clogf.c
19 *
20 * Complex natural logarithm
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * void clogf();
27 * cmplxf z, w;
28 *
29 * clogf( &z, &w );
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * Returns complex logarithm to the base e (2.718...) of
36 * the complex argument x.
37 *
38 * If z = x + iy, r = sqrt( x**2 + y**2 ),
39 * then
40 * w = log(r) + i arctan(y/x).
41 *
42 * The arctangent ranges from -PI to +PI.
43 *
44 *
45 * ACCURACY:
46 *
47 * Relative error:
48 * arithmetic domain # trials peak rms
49 * IEEE -10,+10 30000 1.9e-6 6.2e-8
50 *
51 * Larger relative error can be observed for z near 1 +i0.
52 * In IEEE arithmetic the peak absolute error is 3.1e-7.
53 *
54 */
55
56 #include <complex.h>
57 #include <math.h>
58
59 float complex
clogf(float complex z)60 clogf(float complex z)
61 {
62 float complex w;
63 float p, rr, x, y;
64
65 x = crealf(z);
66 y = cimagf(z);
67 rr = atan2f(y, x);
68 p = cabsf(z);
69 p = logf(p);
70 w = p + rr * I;
71 return (w);
72 }
73 DEF_STD(clogf);
74