GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_catan.c Lines: 0 22 0.0 %
Date: 2017-11-13 Branches: 0 8 0.0 %

Line Branch Exec Source
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
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
DEF_STD(catan);
129
LDBL_MAYBE_CLONE(catan);