1/*	$OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas 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/*							ctanl()
20 *
21 *	Complex circular tangent
22 *
23 *
24 *
25 * SYNOPSIS:
26 *
27 * long double complex ctanl();
28 * long double complex z, w;
29 *
30 * w = ctanl( z );
31 *
32 *
33 *
34 * DESCRIPTION:
35 *
36 * If
37 *     z = x + iy,
38 *
39 * then
40 *
41 *           sin 2x  +  i sinh 2y
42 *     w  =  --------------------.
43 *            cos 2x  +  cosh 2y
44 *
45 * On the real axis the denominator is zero at odd multiples
46 * of PI/2.  The denominator is evaluated by its Taylor
47 * series near these points.
48 *
49 *
50 * ACCURACY:
51 *
52 *                      Relative error:
53 * arithmetic   domain     # trials      peak         rms
54 *    DEC       -10,+10      5200       7.1e-17     1.6e-17
55 *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
56 * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
57 */
58
59#include <complex.h>
60#include <float.h>
61#include <math.h>
62
63#if	LDBL_MANT_DIG == 64
64static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
65#elif	LDBL_MANT_DIG == 113
66static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
67#endif
68
69static const long double PIL = 3.141592653589793238462643383279502884197169L;
70static const long double DP1 = 3.14159265358979323829596852490908531763125L;
71static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
72static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
73
74static long double
75redupil(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
92static long double
93ctansl(long double complex z)
94{
95	long double f, x, x2, y, y2, rn, t;
96	long double d;
97
98	x = fabsl(2.0L * creall(z));
99	y = fabsl(2.0L * cimagl(z));
100
101	x = redupil(x);
102
103	x = x * x;
104	y = y * y;
105	x2 = 1.0L;
106	y2 = 1.0L;
107	f = 1.0L;
108	rn = 0.0L;
109	d = 0.0L;
110	do {
111		rn += 1.0L;
112		f *= rn;
113		rn += 1.0L;
114		f *= rn;
115		x2 *= x;
116		y2 *= y;
117		t = y2 + x2;
118		t /= f;
119		d += t;
120
121		rn += 1.0L;
122		f *= rn;
123		rn += 1.0L;
124		f *= rn;
125		x2 *= x;
126		y2 *= y;
127		t = y2 - x2;
128		t /= f;
129		d += t;
130	}
131	while (fabsl(t/d) > MACHEPL);
132	return(d);
133}
134
135long double complex
136ctanl(long double complex z)
137{
138	long double complex w;
139	long double d, x, y;
140
141	x = creall(z);
142	y = cimagl(z);
143	d = cosl(2.0L * x) + coshl(2.0L * y);
144
145	if (fabsl(d) < 0.25L) {
146		d = fabsl(d);
147		d = ctansl(z);
148	}
149	if (d == 0.0L) {
150		/*mtherr( "ctan", OVERFLOW );*/
151		w = LDBL_MAX + LDBL_MAX * I;
152		return (w);
153	}
154
155	w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
156	return (w);
157}
158