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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 %


/*	$OpenBSD: s_catan.c,v 1.7 2016/09/12 19:47:02 guenther Exp $	*/
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							catan()
 *
 *	Complex circular arc tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double complex catan();
 * double complex z, w;
 *
 * w = catan (z);
 *
 *
 *
 * DESCRIPTION:
 *
 * If
 *     z = x + iy,
 *
 * then
 *          1       (    2x     )
 * Re w  =  - arctan(-----------)  +  k PI
 *          2       (     2    2)
 *                  (1 - x  - y )
 *
 *               ( 2         2)
 *          1    (x  +  (y+1) )
 * Im w  =  - log(------------)
 *          4    ( 2         2)
 *               (x  +  (y-1) )
 *
 * Where k is an arbitrary integer.
 *
 * catan(z) = -i catanh(iz).
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10,+10      5900       1.3e-16     7.8e-18
 *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
 * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
 * had peak relative error 1.5e-16, rms relative error
 * 2.9e-17.  See also clog().
 */

#include <complex.h>
#include <float.h>
#include <math.h>

#define MAXNUM 1.0e308

static const double DP1 = 3.14159265160560607910E0;
static const double DP2 = 1.98418714791870343106E-9;
static const double DP3 = 1.14423774522196636802E-17;

static double
_redupi(double x)
{
	double t;
	long i;

	t = x/M_PI;
	if(t >= 0.0)
		t += 0.5;
	else
		t -= 0.5;

	i = t;	/* the multiple */
	t = i;
	t = ((x - t * DP1) - t * DP2) - t * DP3;
	return (t);
}

double complex
catan(double complex z)
{
	double complex w;
	double a, t, x, x2, y;

	x = creal (z);
	y = cimag (z);

	if ((x == 0.0) && (y > 1.0))
		goto ovrf;

	x2 = x * x;
	a = 1.0 - x2 - (y * y);
	if (a == 0.0)
		goto ovrf;

	t = 0.5 * atan2 (2.0 * x, a);
	w = _redupi (t);

	t = y - 1.0;
	a = x2 + (t * t);
	if (a == 0.0)
	goto ovrf;

	t = y + 1.0;
	a = (x2 + (t * t))/a;
	w = w + (0.25 * log (a)) * I;
	return (w);

ovrf:
	/*mtherr ("catan", OVERFLOW);*/
	w = MAXNUM + MAXNUM * I;
	return (w);
}
DEF_STD(catan);
LDBL_MAYBE_CLONE(catan);


Generated by: GCOVR (Version 3.3)

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);