1/* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */
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 *      Complex circular arc tangent
19 *
20 *
21 * SYNOPSIS:
22 *
23 * double complex catan();
24 * double complex z, w;
25 *
26 * w = catan (z);
27 *
28 *
29 * DESCRIPTION:
30 *
31 * If
32 *     z = x + iy,
33 *
34 * then
35 *          1       (    2x     )
36 * Re w  =  - arctan(-----------)  +  k PI
37 *          2       (     2    2)
38 *                  (1 - x  - y )
39 *
40 *               ( 2         2)
41 *          1    (x  +  (y+1) )
42 * Im w  =  - log(------------)
43 *          4    ( 2         2)
44 *               (x  +  (y-1) )
45 *
46 * Where k is an arbitrary integer.
47 *
48 * catan(z) = -i catanh(iz).
49 *
50 * ACCURACY:
51 *
52 *                      Relative error:
53 * arithmetic   domain     # trials      peak         rms
54 *    DEC       -10,+10      5900       1.3e-16     7.8e-18
55 *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
56 * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
57 * had peak relative error 1.5e-16, rms relative error
58 * 2.9e-17.  See also clog().
59 */
60
61#include "libm.h"
62
63#define MAXNUM 1.0e308
64
65static const double DP1 = 3.14159265160560607910E0;
66static const double DP2 = 1.98418714791870343106E-9;
67static const double DP3 = 1.14423774522196636802E-17;
68
69static double _redupi(double x)
70{
71	double t;
72	long i;
73
74	t = x/M_PI;
75	if (t >= 0.0)
76		t += 0.5;
77	else
78		t -= 0.5;
79
80	i = t;  /* the multiple */
81	t = i;
82	t = ((x - t * DP1) - t * DP2) - t * DP3;
83	return t;
84}
85
86double complex catan(double complex z)
87{
88	double complex w;
89	double a, t, x, x2, y;
90
91	x = creal(z);
92	y = cimag(z);
93
94	if (x == 0.0 && y > 1.0)
95		goto ovrf;
96
97	x2 = x * x;
98	a = 1.0 - x2 - (y * y);
99	if (a == 0.0)
100		goto ovrf;
101
102	t = 0.5 * atan2(2.0 * x, a);
103	w = _redupi(t);
104
105	t = y - 1.0;
106	a = x2 + (t * t);
107	if (a == 0.0)
108		goto ovrf;
109
110	t = y + 1.0;
111	a = (x2 + t * t)/a;
112	w = w + (0.25 * log(a)) * I;
113	return w;
114
115ovrf:
116	// FIXME
117	w = MAXNUM + MAXNUM * I;
118	return w;
119}
120