1*05a0b428SJohn Marino /* $OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4*05a0b428SJohn Marino *
5*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
6*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
7*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16*05a0b428SJohn Marino */
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino /* clogf.c
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex natural logarithm
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * void clogf();
27*05a0b428SJohn Marino * cmplxf z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * clogf( &z, &w );
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * Returns complex logarithm to the base e (2.718...) of
36*05a0b428SJohn Marino * the complex argument x.
37*05a0b428SJohn Marino *
38*05a0b428SJohn Marino * If z = x + iy, r = sqrt( x**2 + y**2 ),
39*05a0b428SJohn Marino * then
40*05a0b428SJohn Marino * w = log(r) + i arctan(y/x).
41*05a0b428SJohn Marino *
42*05a0b428SJohn Marino * The arctangent ranges from -PI to +PI.
43*05a0b428SJohn Marino *
44*05a0b428SJohn Marino *
45*05a0b428SJohn Marino * ACCURACY:
46*05a0b428SJohn Marino *
47*05a0b428SJohn Marino * Relative error:
48*05a0b428SJohn Marino * arithmetic domain # trials peak rms
49*05a0b428SJohn Marino * IEEE -10,+10 30000 1.9e-6 6.2e-8
50*05a0b428SJohn Marino *
51*05a0b428SJohn Marino * Larger relative error can be observed for z near 1 +i0.
52*05a0b428SJohn Marino * In IEEE arithmetic the peak absolute error is 3.1e-7.
53*05a0b428SJohn Marino *
54*05a0b428SJohn Marino */
55*05a0b428SJohn Marino
56*05a0b428SJohn Marino #include <complex.h>
57*05a0b428SJohn Marino #include <math.h>
58*05a0b428SJohn Marino
59*05a0b428SJohn Marino float complex
clogf(float complex z)60*05a0b428SJohn Marino clogf(float complex z)
61*05a0b428SJohn Marino {
62*05a0b428SJohn Marino float complex w;
63*05a0b428SJohn Marino float p, rr, x, y;
64*05a0b428SJohn Marino
65*05a0b428SJohn Marino x = crealf(z);
66*05a0b428SJohn Marino y = cimagf(z);
67*05a0b428SJohn Marino rr = atan2f(y, x);
68*05a0b428SJohn Marino p = cabsf(z);
69*05a0b428SJohn Marino p = logf(p);
70*05a0b428SJohn Marino w = p + rr * I;
71*05a0b428SJohn Marino return (w);
72*05a0b428SJohn Marino }
73