1 /*	$OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 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
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