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
clogl(long double complex z)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