1/* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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 * long double complex catanl();
24 * long double complex z, w;
25 *
26 * w = catanl( 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 *
49 * ACCURACY:
50 *
51 *                      Relative error:
52 * arithmetic   domain     # trials      peak         rms
53 *    DEC       -10,+10      5900       1.3e-16     7.8e-18
54 *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
55 * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
56 * had peak relative error 1.5e-16, rms relative error
57 * 2.9e-17.  See also clog().
58 */
59
60#include <complex.h>
61#include <float.h>
62#include "libm.h"
63
64#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
65long double complex catanl(long double complex z)
66{
67	return catan(z);
68}
69#else
70static const long double PIL = 3.141592653589793238462643383279502884197169L;
71static const long double DP1 = 3.14159265358979323829596852490908531763125L;
72static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
73static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
74
75static long double redupil(long double x)
76{
77	long double t;
78	long i;
79
80	t = x / PIL;
81	if (t >= 0.0L)
82		t += 0.5L;
83	else
84		t -= 0.5L;
85
86	i = t;  /* the multiple */
87	t = i;
88	t = ((x - t * DP1) - t * DP2) - t * DP3;
89	return t;
90}
91
92long double complex catanl(long double complex z)
93{
94	long double complex w;
95	long double a, t, x, x2, y;
96
97	x = creall(z);
98	y = cimagl(z);
99
100	if ((x == 0.0L) && (y > 1.0L))
101		goto ovrf;
102
103	x2 = x * x;
104	a = 1.0L - x2 - (y * y);
105	if (a == 0.0L)
106		goto ovrf;
107
108	t = atan2l(2.0L * x, a) * 0.5L;
109	w = redupil(t);
110
111	t = y - 1.0L;
112	a = x2 + (t * t);
113	if (a == 0.0L)
114		goto ovrf;
115
116	t = y + 1.0L;
117	a = (x2 + (t * t)) / a;
118	w = w + (0.25L * logl(a)) * I;
119	return w;
120
121ovrf:
122	// FIXME
123	w = LDBL_MAX + LDBL_MAX * I;
124	return w;
125}
126#endif
127