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/* $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);
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