1 /* $OpenBSD: s_catan.c,v 1.7 2016/09/12 19:47:02 guenther Exp $ */
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 /* catan()
19 *
20 * Complex circular arc tangent
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex catan();
27 * double complex z, w;
28 *
29 * w = catan (z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * If
36 * z = x + iy,
37 *
38 * then
39 * 1 ( 2x )
40 * Re w = - arctan(-----------) + k PI
41 * 2 ( 2 2)
42 * (1 - x - y )
43 *
44 * ( 2 2)
45 * 1 (x + (y+1) )
46 * Im w = - log(------------)
47 * 4 ( 2 2)
48 * (x + (y-1) )
49 *
50 * Where k is an arbitrary integer.
51 *
52 * catan(z) = -i catanh(iz).
53 *
54 * ACCURACY:
55 *
56 * Relative error:
57 * arithmetic domain # trials peak rms
58 * DEC -10,+10 5900 1.3e-16 7.8e-18
59 * IEEE -10,+10 30000 2.3e-15 8.5e-17
60 * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
61 * had peak relative error 1.5e-16, rms relative error
62 * 2.9e-17. See also clog().
63 */
64
65 #include <complex.h>
66 #include <float.h>
67 #include <math.h>
68
69 #define MAXNUM 1.0e308
70
71 static const double DP1 = 3.14159265160560607910E0;
72 static const double DP2 = 1.98418714791870343106E-9;
73 static const double DP3 = 1.14423774522196636802E-17;
74
75 static double
_redupi(double x)76 _redupi(double x)
77 {
78 double t;
79 long i;
80
81 t = x/M_PI;
82 if(t >= 0.0)
83 t += 0.5;
84 else
85 t -= 0.5;
86
87 i = t; /* the multiple */
88 t = i;
89 t = ((x - t * DP1) - t * DP2) - t * DP3;
90 return (t);
91 }
92
93 double complex
catan(double complex z)94 catan(double complex z)
95 {
96 double complex w;
97 double a, t, x, x2, y;
98
99 x = creal (z);
100 y = cimag (z);
101
102 if ((x == 0.0) && (y > 1.0))
103 goto ovrf;
104
105 x2 = x * x;
106 a = 1.0 - x2 - (y * y);
107 if (a == 0.0)
108 goto ovrf;
109
110 t = 0.5 * atan2 (2.0 * x, a);
111 w = _redupi (t);
112
113 t = y - 1.0;
114 a = x2 + (t * t);
115 if (a == 0.0)
116 goto ovrf;
117
118 t = y + 1.0;
119 a = (x2 + (t * t))/a;
120 w = w + (0.25 * log (a)) * I;
121 return (w);
122
123 ovrf:
124 /*mtherr ("catan", OVERFLOW);*/
125 w = MAXNUM + MAXNUM * I;
126 return (w);
127 }
128 DEF_STD(catan);
129 LDBL_MAYBE_CLONE(catan);
130