1*05a0b428SJohn Marino /* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie 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 /* clog.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 * double complex clog();
27*05a0b428SJohn Marino * double complex z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = clog (z);
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 * DEC -10,+10 7000 8.5e-17 1.9e-17
50*05a0b428SJohn Marino * IEEE -10,+10 30000 5.0e-15 1.1e-16
51*05a0b428SJohn Marino *
52*05a0b428SJohn Marino * Larger relative error can be observed for z near 1 +i0.
53*05a0b428SJohn Marino * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
54*05a0b428SJohn Marino * absolute error 1.0e-16.
55*05a0b428SJohn Marino */
56*05a0b428SJohn Marino
57*05a0b428SJohn Marino #include <complex.h>
58*05a0b428SJohn Marino #include <float.h>
59*05a0b428SJohn Marino #include <math.h>
60*05a0b428SJohn Marino
61*05a0b428SJohn Marino double complex
clog(double complex z)62*05a0b428SJohn Marino clog(double complex z)
63*05a0b428SJohn Marino {
64*05a0b428SJohn Marino double complex w;
65*05a0b428SJohn Marino double p, rr;
66*05a0b428SJohn Marino
67*05a0b428SJohn Marino /*rr = sqrt( z->r * z->r + z->i * z->i );*/
68*05a0b428SJohn Marino rr = cabs(z);
69*05a0b428SJohn Marino p = log(rr);
70*05a0b428SJohn Marino rr = atan2 (cimag (z), creal (z));
71*05a0b428SJohn Marino w = p + rr * I;
72*05a0b428SJohn Marino return (w);
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino
75*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
76*05a0b428SJohn Marino __strong_alias(clogl, clog);
77*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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