1 /*	$OpenBSD: s_clogl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $	*/
2 
3 /*
4  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5  *
6  * Permission to use, copy, modify, and distribute this software for any
7  * purpose with or without fee is hereby granted, provided that the above
8  * copyright notice and this permission notice appear in all copies.
9  *
10  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17  */
18 
19 /*							clogl.c
20  *
21  *	Complex natural logarithm
22  *
23  *
24  *
25  * SYNOPSIS:
26  *
27  * long double complex clogl();
28  * long double complex z, w;
29  *
30  * w = clogl( z );
31  *
32  *
33  *
34  * DESCRIPTION:
35  *
36  * Returns complex logarithm to the base e (2.718...) of
37  * the complex argument x.
38  *
39  * If z = x + iy, r = sqrt( x**2 + y**2 ),
40  * then
41  *       w = log(r) + i arctan(y/x).
42  *
43  * The arctangent ranges from -PI to +PI.
44  *
45  *
46  * ACCURACY:
47  *
48  *                      Relative error:
49  * arithmetic   domain     # trials      peak         rms
50  *    DEC       -10,+10      7000       8.5e-17     1.9e-17
51  *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
52  *
53  * Larger relative error can be observed for z near 1 +i0.
54  * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
55  * absolute error 1.0e-16.
56  */
57 
58 #include <complex.h>
59 #include <math.h>
60 
61 long double complex
62 clogl(long double complex z)
63 {
64 	long double complex w;
65 	long double p, rr;
66 
67 	/*rr = sqrt(z->r * z->r  +  z->i * z->i);*/
68 	p = cabsl(z);
69 	p = logl(p);
70 	rr = atan2l(cimagl(z), creall(z));
71 	w = p + rr * I;
72 	return (w);
73 }
74