1/*	$OpenBSD: s_catanl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $	*/
2
3/*
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 */
18
19/*							catanl()
20 *
21 *	Complex circular arc tangent
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex catanl();
28 * long double complex z, w;
29 *
30 * w = catanl( z );
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 * If
37 *     z = x + iy,
38 *
39 * then
40 *          1       (    2x     )
41 * Re w  =  - arctan(-----------)  +  k PI
42 *          2       (     2    2)
43 *                  (1 - x  - y )
44 *
45 *               ( 2         2)
46 *          1    (x  +  (y+1) )
47 * Im w  =  - log(------------)
48 *          4    ( 2         2)
49 *               (x  +  (y-1) )
50 *
51 * Where k is an arbitrary integer.
52 *
53 *
54 *
55 * ACCURACY:
56 *
57 *                      Relative error:
58 * arithmetic   domain     # trials      peak         rms
59 *    DEC       -10,+10      5900       1.3e-16     7.8e-18
60 *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
61 * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
62 * had peak relative error 1.5e-16, rms relative error
63 * 2.9e-17.  See also clog().
64 */
65
66#include <complex.h>
67#include <float.h>
68#include <math.h>
69
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
76redupil(long double x)
77{
78	long double t;
79	long i;
80
81	t = x / PIL;
82	if (t >= 0.0L)
83		t += 0.5L;
84	else
85		t -= 0.5L;
86
87	i = t;	/* the multiple */
88	t = i;
89	t = ((x - t * DP1) - t * DP2) - t * DP3;
90	return (t);
91}
92
93long double complex
94catanl(long double complex z)
95{
96	long double complex w;
97	long double a, t, x, x2, y;
98
99	x = creall(z);
100	y = cimagl(z);
101
102	if ((x == 0.0L) && (y > 1.0L))
103		goto ovrf;
104
105	x2 = x * x;
106	a = 1.0L - x2 - (y * y);
107	if (a == 0.0L)
108		goto ovrf;
109
110	t = atan2l(2.0L * x, a) * 0.5L;
111	w = redupil(t);
112
113	t = y - 1.0L;
114	a = x2 + (t * t);
115	if (a == 0.0L)
116		goto ovrf;
117
118	t = y + 1.0L;
119	a = (x2 + (t * t)) / a;
120	w = w + (0.25L * logl(a)) * I;
121	return (w);
122
123ovrf:
124	/*mtherr( "catanl", OVERFLOW );*/
125	w = LDBL_MAX + LDBL_MAX * I;
126	return (w);
127}
128DEF_STD(catanl);
129