GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_csqrt.c Lines: 0 32 0.0 %
Date: 2017-11-13 Branches: 0 14 0.0 %

Line Branch Exec Source
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/*	$OpenBSD: s_csqrt.c,v 1.8 2016/09/12 19:47:02 guenther Exp $	*/
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/*
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 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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 *
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 * Permission to use, copy, modify, and distribute this software for any
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 * purpose with or without fee is hereby granted, provided that the above
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 * copyright notice and this permission notice appear in all copies.
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 *
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 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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 */
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/*							csqrt()
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 *
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 *	Complex square root
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 *
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 *
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 *
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 * SYNOPSIS:
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 *
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 * double complex csqrt();
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 * double complex z, w;
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 *
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 * w = csqrt (z);
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 *
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 *
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 *
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 * DESCRIPTION:
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 *
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 *
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 * If z = x + iy,  r = |z|, then
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 *
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 *                       1/2
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 * Re w  =  [ (r + x)/2 ]   ,
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 *
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 *                       1/2
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 * Im w  =  [ (r - x)/2 ]   .
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 *
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 * Cancellation error in r-x or r+x is avoided by using the
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 * identity  2 Re w Im w  =  y.
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 *
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 * Note that -w is also a square root of z.  The root chosen
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 * is always in the right half plane and Im w has the same sign as y.
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 *
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 *
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 *
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 * ACCURACY:
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 *
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 *                      Relative error:
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 * arithmetic   domain     # trials      peak         rms
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 *    DEC       -10,+10     25000       3.2e-17     9.6e-18
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 *    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
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 *
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 */
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#include <complex.h>
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#include <float.h>
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#include <math.h>
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double complex
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csqrt(double complex z)
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{
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	double complex w;
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	double x, y, r, t, scale;
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	x = creal (z);
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	y = cimag (z);
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	if (y == 0.0) {
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		if (x == 0.0) {
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			w = 0.0 + y * I;
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		}
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		else {
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			r = fabs (x);
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			r = sqrt (r);
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			if (x < 0.0) {
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				w = 0.0 + copysign(r, y) * I;
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			}
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			else {
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				w = r + y * I;
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			}
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		}
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		return (w);
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	}
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	if (x == 0.0) {
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		r = fabs (y);
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		r = sqrt (0.5*r);
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		if (y > 0)
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			w = r + r * I;
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		else
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			w = r - r * I;
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		return (w);
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	}
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	/* Rescale to avoid internal overflow or underflow.  */
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	if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
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		x *= 0.25;
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		y *= 0.25;
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		scale = 2.0;
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	}
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	else {
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		x *= 1.8014398509481984e16;  /* 2^54 */
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		y *= 1.8014398509481984e16;
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		scale = 7.450580596923828125e-9; /* 2^-27 */
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#if 0
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		x *= 4.0;
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		y *= 4.0;
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		scale = 0.5;
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#endif
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	}
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	w = x + y * I;
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	r = cabs(w);
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	if (x > 0) {
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		t = sqrt(0.5 * r + 0.5 * x);
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		r = scale * fabs((0.5 * y) / t);
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		t *= scale;
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	}
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	else {
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		r = sqrt( 0.5 * r - 0.5 * x );
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		t = scale * fabs( (0.5 * y) / r );
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		r *= scale;
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	}
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	if (y < 0)
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		w = t - r * I;
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	else
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		w = t + r * I;
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	return (w);
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}
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DEF_STD(csqrt);
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LDBL_MAYBE_CLONE(csqrt);