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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/s_ctanl.c	Lines:	0	43	0.0 %
Date:	2017-11-07	Branches:	0	8	0.0 %


/*	$OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas 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.
 */

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

#if	LDBL_MANT_DIG == 64
static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
#elif	LDBL_MANT_DIG == 113
static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
#endif

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);
}

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

	x = fabsl(2.0L * creall(z));
	y = fabsl(2.0L * cimagl(z));

	x = redupil(x);

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

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

long double complex
ctanl(long double complex z)
{
	long double complex w;
	long double d, x, y;

	x = creall(z);
	y = cimagl(z);
	d = cosl(2.0L * x) + coshl(2.0L * y);

	if (fabsl(d) < 0.25L) {
		d = fabsl(d);
		d = ctansl(z);
	}
	if (d == 0.0L) {
		/*mtherr( "ctan", OVERFLOW );*/
		w = LDBL_MAX + LDBL_MAX * I;
		return (w);
	}

	w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
	return (w);
}


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas 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			/* ctanl()
20			*
21			* Complex circular tangent
22			*
23			*
24			*
25			* SYNOPSIS:
26			*
27			* long double complex ctanl();
28			* long double complex z, w;
29			*
30			* w = ctanl( z );
31			*
32			*
33			*
34			* DESCRIPTION:
35			*
36			* If
37			* z = x + iy,
38			*
39			* then
40			*
41			* sin 2x + i sinh 2y
42			* w = --------------------.
43			* cos 2x + cosh 2y
44			*
45			* On the real axis the denominator is zero at odd multiples
46			* of PI/2. The denominator is evaluated by its Taylor
47			* series near these points.
48			*
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			#if LDBL_MANT_DIG == 64
64			static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
65			#elif LDBL_MANT_DIG == 113
66			static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
67			#endif
68
69			static const long double PIL = 3.141592653589793238462643383279502884197169L;
70			static const long double DP1 = 3.14159265358979323829596852490908531763125L;
71			static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
72			static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
73
74			static long double
75			redupil(long double x)
76			{
77			long double t;
78			long i;
79
80			t = x / PIL;
81			if (t >= 0.0L)
82			t += 0.5L;
83			else
84			t -= 0.5L;
85
86			i = t; /* the multiple */
87			t = i;
88			t = ((x - t * DP1) - t * DP2) - t * DP3;
89			return (t);
90			}
91
92			static long double
93			ctansl(long double complex z)
94			{
95			long double f, x, x2, y, y2, rn, t;
96			long double d;
97
98			x = fabsl(2.0L * creall(z));
99			y = fabsl(2.0L * cimagl(z));
100
101			x = redupil(x);
102
103			x = x * x;
104			y = y * y;
105			x2 = 1.0L;
106			y2 = 1.0L;
107			f = 1.0L;
108			rn = 0.0L;
109			d = 0.0L;
110			do {
111			rn += 1.0L;
112			f *= rn;
113			rn += 1.0L;
114			f *= rn;
115			x2 *= x;
116			y2 *= y;
117			t = y2 + x2;
118			t /= f;
119			d += t;
120
121			rn += 1.0L;
122			f *= rn;
123			rn += 1.0L;
124			f *= rn;
125			x2 *= x;
126			y2 *= y;
127			t = y2 - x2;
128			t /= f;
129			d += t;
130			}
131			while (fabsl(t/d) > MACHEPL);
132			return(d);
133			}
134
135			long double complex
136			ctanl(long double complex z)
137			{
138			long double complex w;
139			long double d, x, y;
140
141			x = creall(z);
142			y = cimagl(z);
143			d = cosl(2.0L * x) + coshl(2.0L * y);
144
145			if (fabsl(d) < 0.25L) {
146			d = fabsl(d);
147			d = ctansl(z);
148			}
149			if (d == 0.0L) {
150			/mtherr( "ctan", OVERFLOW );/
151			w = LDBL_MAX + LDBL_MAX * I;
152			return (w);
153			}
154
155			w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
156			return (w);
157			}