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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/s_ctan.c	Lines:	0	41	0.0 %
Date:	2017-11-13	Branches:	0	8	0.0 %


/*	$OpenBSD: s_ctan.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.
 */

/*							ctan()
 *
 *	Complex circular tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double complex ctan();
 * double complex z, w;
 *
 * w = ctan (z);
 *
 *
 *
 * DESCRIPTION:
 *
 * If
 *     z = x + iy,
 *
 * then
 *
 *           sin 2x  +  i sinh 2y
 *     w  =  --------------------.
 *            cos 2x  +  cosh 2y
 *
 * On the real axis the denominator is zero at odd multiples
 * of PI/2.  The denominator is evaluated by its Taylor
 * series near these points.
 *
 * ctan(z) = -i ctanh(iz).
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10,+10      5200       7.1e-17     1.6e-17
 *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
 * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
 */

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

#define MACHEP 1.1e-16
#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);
}

/*  Taylor series expansion for cosh(2y) - cos(2x)	*/

static double
_ctans(double complex z)
{
	double f, x, x2, y, y2, rn, t;
	double d;

	x = fabs (2.0 * creal (z));
	y = fabs (2.0 * cimag(z));

	x = _redupi(x);

	x = x * x;
	y = y * y;
	x2 = 1.0;
	y2 = 1.0;
	f = 1.0;
	rn = 0.0;
	d = 0.0;
	do {
		rn += 1.0;
		f *= rn;
		rn += 1.0;
		f *= rn;
		x2 *= x;
		y2 *= y;
		t = y2 + x2;
		t /= f;
		d += t;

		rn += 1.0;
		f *= rn;
		rn += 1.0;
		f *= rn;
		x2 *= x;
		y2 *= y;
		t = y2 - x2;
		t /= f;
		d += t;
	}
	while (fabs(t/d) > MACHEP)
		;
	return (d);
}

double complex
ctan(double complex z)
{
	double complex w;
	double d;

	d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));

	if (fabs(d) < 0.25)
		d = _ctans (z);

	if (d == 0.0) {
		/*mtherr ("ctan", OVERFLOW);*/
		w = MAXNUM + MAXNUM * I;
		return (w);
	}

	w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I;
	return (w);
}
DEF_STD(ctan);
LDBL_MAYBE_UNUSED_CLONE(ctan);


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_ctan.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			/* ctan()
19			*
20			* Complex circular tangent
21			*
22			*
23			*
24			* SYNOPSIS:
25			*
26			* double complex ctan();
27			* double complex z, w;
28			*
29			* w = ctan (z);
30			*
31			*
32			*
33			* DESCRIPTION:
34			*
35			* If
36			* z = x + iy,
37			*
38			* then
39			*
40			* sin 2x + i sinh 2y
41			* w = --------------------.
42			* cos 2x + cosh 2y
43			*
44			* On the real axis the denominator is zero at odd multiples
45			* of PI/2. The denominator is evaluated by its Taylor
46			* series near these points.
47			*
48			* ctan(z) = -i ctanh(iz).
49			*
50			* ACCURACY:
51			*
52			* Relative error:
53			* arithmetic domain # trials peak rms
54			* DEC -10,+10 5200 7.1e-17 1.6e-17
55			* IEEE -10,+10 30000 7.2e-16 1.2e-16
56			* Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
57			*/
58
59			#include <complex.h>
60			#include <float.h>
61			#include <math.h>
62
63			#define MACHEP 1.1e-16
64			#define MAXNUM 1.0e308
65
66			static const double DP1 = 3.14159265160560607910E0;
67			static const double DP2 = 1.98418714791870343106E-9;
68			static const double DP3 = 1.14423774522196636802E-17;
69
70			static double
71			_redupi(double x)
72			{
73			double t;
74			long i;
75
76			t = x/M_PI;
77			if (t >= 0.0)
78			t += 0.5;
79			else
80			t -= 0.5;
81
82			i = t; /* the multiple */
83			t = i;
84			t = ((x - t * DP1) - t * DP2) - t * DP3;
85			return (t);
86			}
87
88			/* Taylor series expansion for cosh(2y) - cos(2x) */
89
90			static double
91			_ctans(double complex z)
92			{
93			double f, x, x2, y, y2, rn, t;
94			double d;
95
96			x = fabs (2.0 * creal (z));
97			y = fabs (2.0 * cimag(z));
98
99			x = _redupi(x);
100
101			x = x * x;
102			y = y * y;
103			x2 = 1.0;
104			y2 = 1.0;
105			f = 1.0;
106			rn = 0.0;
107			d = 0.0;
108			do {
109			rn += 1.0;
110			f *= rn;
111			rn += 1.0;
112			f *= rn;
113			x2 *= x;
114			y2 *= y;
115			t = y2 + x2;
116			t /= f;
117			d += t;
118
119			rn += 1.0;
120			f *= rn;
121			rn += 1.0;
122			f *= rn;
123			x2 *= x;
124			y2 *= y;
125			t = y2 - x2;
126			t /= f;
127			d += t;
128			}
129			while (fabs(t/d) > MACHEP)
130			;
131			return (d);
132			}
133
134			double complex
135			ctan(double complex z)
136			{
137			double complex w;
138			double d;
139
140			d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));
141
142			if (fabs(d) < 0.25)
143			d = _ctans (z);
144
145			if (d == 0.0) {
146			/mtherr ("ctan", OVERFLOW);/
147			w = MAXNUM + MAXNUM * I;
148			return (w);
149			}
150
151			w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I;
152			return (w);
153			}
154			DEF_STD(ctan);
155			LDBL_MAYBE_UNUSED_CLONE(ctan);