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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/s_csqrtl.c	Lines:	0	33	0.0 %
Date:	2017-11-07	Branches:	0	12	0.0 %


/*	$OpenBSD: s_csqrtl.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.
 */

/*							csqrtl()
 *
 *	Complex square root
 *
 *
 *
 * SYNOPSIS:
 *
 * long double complex csqrtl();
 * long double complex z, w;
 *
 * w = csqrtl( z );
 *
 *
 *
 * DESCRIPTION:
 *
 *
 * If z = x + iy,  r = |z|, then
 *
 *                       1/2
 * Re w  =  [ (r + x)/2 ]   ,
 *
 *                       1/2
 * Im w  =  [ (r - x)/2 ]   .
 *
 * Cancellation error in r-x or r+x is avoided by using the
 * identity  2 Re w Im w  =  y.
 *
 * Note that -w is also a square root of z.  The root chosen
 * is always in the right half plane and Im w has the same sign as y.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10,+10     500000      1.1e-19     3.0e-20
 *
 */

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

long double complex
csqrtl(long double complex z)
{
	long double complex w;
	long double x, y, r, t, scale;

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

	if (y == 0.0L) {
		if (x < 0.0L) {
			w = 0.0L + copysign(sqrtl(-x), y) * I;
			return (w);
		}
		else {
			w = sqrtl(x) + 0.0L * I;
			return (w);
		}
	}

	if (x == 0.0L) {
		r = fabsl(y);
		r = sqrtl(0.5L * r);
		if (y > 0.0L)
			w = r + r * I;
		else
			w = r - r * I;
		return (w);
	}

	/* Rescale to avoid internal overflow or underflow.  */
	if ((fabsl(x) > 4.0L) || (fabsl(y) > 4.0L)) {
		x *= 0.25L;
		y *= 0.25L;
		scale = 2.0L;
	}
	else {
#if 1
		x *= 7.3786976294838206464e19;  /* 2^66 */
		y *= 7.3786976294838206464e19;
		scale = 1.16415321826934814453125e-10;  /* 2^-33 */
#else
		x *= 4.0L;
		y *= 4.0L;
		scale = 0.5L;
#endif
	}
	w = x + y * I;
	r = cabsl(w);
	if (x > 0) {
		t = sqrtl(0.5L * r + 0.5L * x);
		r = scale * fabsl((0.5L * y) / t);
		t *= scale;
	}
	else {
		r = sqrtl(0.5L * r - 0.5L * x);
		t = scale * fabsl((0.5L * y) / r);
		r *= scale;
	}
	if (y < 0)
		w = t - r * I;
	else
		w = t + r * I;
	return (w);
}
DEF_STD(csqrtl);


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: s_csqrtl.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			/* csqrtl()
20			*
21			* Complex square root
22			*
23			*
24			*
25			* SYNOPSIS:
26			*
27			* long double complex csqrtl();
28			* long double complex z, w;
29			*
30			* w = csqrtl( z );
31			*
32			*
33			*
34			* DESCRIPTION:
35			*
36			*
37			* If z = x + iy, r = \|z\|, then
38			*
39			* 1/2
40			* Re w = [ (r + x)/2 ] ,
41			*
42			* 1/2
43			* Im w = [ (r - x)/2 ] .
44			*
45			* Cancellation error in r-x or r+x is avoided by using the
46			* identity 2 Re w Im w = y.
47			*
48			* Note that -w is also a square root of z. The root chosen
49			* is always in the right half plane and Im w has the same sign as y.
50			*
51			*
52			*
53			* ACCURACY:
54			*
55			* Relative error:
56			* arithmetic domain # trials peak rms
57			* IEEE -10,+10 500000 1.1e-19 3.0e-20
58			*
59			*/
60
61			#include <complex.h>
62			#include <math.h>
63
64			long double complex
65			csqrtl(long double complex z)
66			{
67			long double complex w;
68			long double x, y, r, t, scale;
69
70			x = creall(z);
71			y = cimagl(z);
72
73			if (y == 0.0L) {
74			if (x < 0.0L) {
75			w = 0.0L + copysign(sqrtl(-x), y) * I;
76			return (w);
77			}
78			else {
79			w = sqrtl(x) + 0.0L * I;
80			return (w);
81			}
82			}
83
84			if (x == 0.0L) {
85			r = fabsl(y);
86			r = sqrtl(0.5L * r);
87			if (y > 0.0L)
88			w = r + r * I;
89			else
90			w = r - r * I;
91			return (w);
92			}
93
94			/* Rescale to avoid internal overflow or underflow. */
95			if ((fabsl(x) > 4.0L) \|\| (fabsl(y) > 4.0L)) {
96			x *= 0.25L;
97			y *= 0.25L;
98			scale = 2.0L;
99			}
100			else {
101			#if 1
102			x = 7.3786976294838206464e19; / 2^66 */
103			y *= 7.3786976294838206464e19;
104			scale = 1.16415321826934814453125e-10; /* 2^-33 */
105			#else
106			x *= 4.0L;
107			y *= 4.0L;
108			scale = 0.5L;
109			#endif
110			}
111			w = x + y * I;
112			r = cabsl(w);
113			if (x > 0) {
114			t = sqrtl(0.5L * r + 0.5L * x);
115			r = scale * fabsl((0.5L * y) / t);
116			t *= scale;
117			}
118			else {
119			r = sqrtl(0.5L * r - 0.5L * x);
120			t = scale * fabsl((0.5L * y) / r);
121			r *= scale;
122			}
123			if (y < 0)
124			w = t - r * I;
125			else
126			w = t + r * I;
127			return (w);
128			}
129			DEF_STD(csqrtl);