1 /*	$OpenBSD: s_catan.c,v 1.6 2013/07/03 04:46:36 espie 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
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
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 
129 #if	LDBL_MANT_DIG == DBL_MANT_DIG
130 __strong_alias(catanl, catan);
131 #endif	/* LDBL_MANT_DIG == DBL_MANT_DIG */
132