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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/s_catanl.c	Lines:	0	24	0.0 %
Date:	2017-11-07	Branches:	0	8	0.0 %


/*	$OpenBSD: s_catanl.c,v 1.4 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.
 */

/*							catanl()
 *
 *	Complex circular arc tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * long double complex catanl();
 * long double complex z, w;
 *
 * w = catanl( 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.
 *
 *
 *
 * 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>

static const long double PIL = 3.141592653589793238462643383279502884197169L;
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;

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

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

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

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

	x = creall(z);
	y = cimagl(z);

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

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

	t = atan2l(2.0L * x, a) * 0.5L;
	w = redupil(t);

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

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

ovrf:
	/*mtherr( "catanl", OVERFLOW );*/
	w = LDBL_MAX + LDBL_MAX * I;
	return (w);
}
DEF_STD(catanl);


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_catanl.c,v 1.4 2016/09/12 19:47:02 guenther 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			/* catanl()
20			*
21			* Complex circular arc tangent
22			*
23			*
24			*
25			* SYNOPSIS:
26			*
27			* long double complex catanl();
28			* long double complex z, w;
29			*
30			* w = catanl( z );
31			*
32			*
33			*
34			* DESCRIPTION:
35			*
36			* If
37			* z = x + iy,
38			*
39			* then
40			* 1 ( 2x )
41			* Re w = - arctan(-----------) + k PI
42			* 2 ( 2 2)
43			* (1 - x - y )
44			*
45			* ( 2 2)
46			* 1 (x + (y+1) )
47			* Im w = - log(------------)
48			* 4 ( 2 2)
49			* (x + (y-1) )
50			*
51			* Where k is an arbitrary integer.
52			*
53			*
54			*
55			* ACCURACY:
56			*
57			* Relative error:
58			* arithmetic domain # trials peak rms
59			* DEC -10,+10 5900 1.3e-16 7.8e-18
60			* IEEE -10,+10 30000 2.3e-15 8.5e-17
61			* The check catan( ctan(z) ) = z, with \|x\| and \|y\| < PI/2,
62			* had peak relative error 1.5e-16, rms relative error
63			* 2.9e-17. See also clog().
64			*/
65
66			#include <complex.h>
67			#include <float.h>
68			#include <math.h>
69
70			static const long double PIL = 3.141592653589793238462643383279502884197169L;
71			static const long double DP1 = 3.14159265358979323829596852490908531763125L;
72			static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
73			static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
74
75			static long double
76			redupil(long double x)
77			{
78			long double t;
79			long i;
80
81			t = x / PIL;
82			if (t >= 0.0L)
83			t += 0.5L;
84			else
85			t -= 0.5L;
86
87			i = t; /* the multiple */
88			t = i;
89			t = ((x - t * DP1) - t * DP2) - t * DP3;
90			return (t);
91			}
92
93			long double complex
94			catanl(long double complex z)
95			{
96			long double complex w;
97			long double a, t, x, x2, y;
98
99			x = creall(z);
100			y = cimagl(z);
101
102			if ((x == 0.0L) && (y > 1.0L))
103			goto ovrf;
104
105			x2 = x * x;
106			a = 1.0L - x2 - (y * y);
107			if (a == 0.0L)
108			goto ovrf;
109
110			t = atan2l(2.0L * x, a) * 0.5L;
111			w = redupil(t);
112
113			t = y - 1.0L;
114			a = x2 + (t * t);
115			if (a == 0.0L)
116			goto ovrf;
117
118			t = y + 1.0L;
119			a = (x2 + (t * t)) / a;
120			w = w + (0.25L * logl(a)) * I;
121			return (w);
122
123			ovrf:
124			/mtherr( "catanl", OVERFLOW );/
125			w = LDBL_MAX + LDBL_MAX * I;
126			return (w);
127			}
128			DEF_STD(catanl);