1 /* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie 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 /* clog.c
19 *
20 * Complex natural logarithm
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex clog();
27 * double complex z, w;
28 *
29 * w = clog (z);
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 * DEC -10,+10 7000 8.5e-17 1.9e-17
50 * IEEE -10,+10 30000 5.0e-15 1.1e-16
51 *
52 * Larger relative error can be observed for z near 1 +i0.
53 * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
54 * absolute error 1.0e-16.
55 */
56
57 #include <complex.h>
58 #include <float.h>
59 #include <math.h>
60
61 double complex
clog(double complex z)62 clog(double complex z)
63 {
64 double complex w;
65 double p, rr;
66
67 /*rr = sqrt( z->r * z->r + z->i * z->i );*/
68 rr = cabs(z);
69 p = log(rr);
70 rr = atan2 (cimag (z), creal (z));
71 w = p + rr * I;
72 return (w);
73 }
74
75 #if LDBL_MANT_DIG == DBL_MANT_DIG
76 __strong_alias(clogl, clog);
77 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
78