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
64 static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
65 #elif	LDBL_MANT_DIG == 113
66 static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
67 #endif
68 
69 static const long double PIL = 3.141592653589793238462643383279502884197169L;
70 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
71 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
72 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
73 
74 static long double
75 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 
92 static long double
93 ctansl(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 
135 long double complex
136 ctanl(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