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/* $OpenBSD: n_csqrt.c,v 1.1 2008/10/07 22:25:53 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.
*/
/* csqrt()
*
* Complex square root
*
*
*
* SYNOPSIS:
*
* double complex csqrt();
* double complex z, w;
*
* w = csqrt (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
* DEC -10,+10 25000 3.2e-17 9.6e-18
* IEEE -10,+10 1,000,000 2.9e-16 6.1e-17
*
*/
#include <complex.h>
#include <math.h>
double complex
csqrt(double complex z)
{
double complex w;
double x, y, r, t, scale;
x = creal (z);
y = cimag (z);
if (y == 0.0) {
if (x == 0.0) {
w = 0.0 + y * I;
}
else {
r = fabs (x);
r = sqrt (r);
if (x < 0.0) {
w = 0.0 + r * I;
}
else {
w = r + y * I;
}
}
return (w);
}
if (x == 0.0) {
r = fabs (y);
r = sqrt (0.5*r);
if (y > 0)
w = r + r * I;
else
w = r - r * I;
return (w);
}
/* Rescale to avoid internal overflow or underflow. */
if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
x *= 0.25;
y *= 0.25;
scale = 2.0;
}
else {
x *= 1.8014398509481984e16; /* 2^54 */
y *= 1.8014398509481984e16;
scale = 7.450580596923828125e-9; /* 2^-27 */
#if 0
x *= 4.0;
y *= 4.0;
scale = 0.5;
#endif
}
w = x + y * I;
r = cabs(w);
if (x > 0) {
t = sqrt(0.5 * r + 0.5 * x);
r = scale * fabs((0.5 * y) / t);
t *= scale;
}
else {
r = sqrt( 0.5 * r - 0.5 * x );
t = scale * fabs( (0.5 * y) / r );
r *= scale;
}
if (y < 0)
w = t - r * I;
else
w = t + r * I;
return (w);
}
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