1*05a0b428SJohn Marino /* $OpenBSD: s_clogl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
2*05a0b428SJohn Marino
3*05a0b428SJohn Marino /*
4*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
7*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
8*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
9*05a0b428SJohn Marino *
10*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17*05a0b428SJohn Marino */
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino /* clogl.c
20*05a0b428SJohn Marino *
21*05a0b428SJohn Marino * Complex natural logarithm
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino *
25*05a0b428SJohn Marino * SYNOPSIS:
26*05a0b428SJohn Marino *
27*05a0b428SJohn Marino * long double complex clogl();
28*05a0b428SJohn Marino * long double complex z, w;
29*05a0b428SJohn Marino *
30*05a0b428SJohn Marino * w = clogl( z );
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino *
34*05a0b428SJohn Marino * DESCRIPTION:
35*05a0b428SJohn Marino *
36*05a0b428SJohn Marino * Returns complex logarithm to the base e (2.718...) of
37*05a0b428SJohn Marino * the complex argument x.
38*05a0b428SJohn Marino *
39*05a0b428SJohn Marino * If z = x + iy, r = sqrt( x**2 + y**2 ),
40*05a0b428SJohn Marino * then
41*05a0b428SJohn Marino * w = log(r) + i arctan(y/x).
42*05a0b428SJohn Marino *
43*05a0b428SJohn Marino * The arctangent ranges from -PI to +PI.
44*05a0b428SJohn Marino *
45*05a0b428SJohn Marino *
46*05a0b428SJohn Marino * ACCURACY:
47*05a0b428SJohn Marino *
48*05a0b428SJohn Marino * Relative error:
49*05a0b428SJohn Marino * arithmetic domain # trials peak rms
50*05a0b428SJohn Marino * DEC -10,+10 7000 8.5e-17 1.9e-17
51*05a0b428SJohn Marino * IEEE -10,+10 30000 5.0e-15 1.1e-16
52*05a0b428SJohn Marino *
53*05a0b428SJohn Marino * Larger relative error can be observed for z near 1 +i0.
54*05a0b428SJohn Marino * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
55*05a0b428SJohn Marino * absolute error 1.0e-16.
56*05a0b428SJohn Marino */
57*05a0b428SJohn Marino
58*05a0b428SJohn Marino #include <complex.h>
59*05a0b428SJohn Marino #include <math.h>
60*05a0b428SJohn Marino
61*05a0b428SJohn Marino long double complex
clogl(long double complex z)62*05a0b428SJohn Marino clogl(long double complex z)
63*05a0b428SJohn Marino {
64*05a0b428SJohn Marino long double complex w;
65*05a0b428SJohn Marino long double p, rr;
66*05a0b428SJohn Marino
67*05a0b428SJohn Marino /*rr = sqrt(z->r * z->r + z->i * z->i);*/
68*05a0b428SJohn Marino p = cabsl(z);
69*05a0b428SJohn Marino p = logl(p);
70*05a0b428SJohn Marino rr = atan2l(cimagl(z), creall(z));
71*05a0b428SJohn Marino w = p + rr * I;
72*05a0b428SJohn Marino return (w);
73*05a0b428SJohn Marino }
74