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
redupil(long double x)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
ctansl(long double complex z)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
ctanl(long double complex z)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