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/* $NetBSD: csqrt.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */
/*-
* Copyright (c) 2007 The NetBSD Foundation, Inc.
* All rights reserved.
*
* This code is derived from software written by Stephen L. Moshier.
* It is redistributed by the NetBSD Foundation by permission of the author.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
* imported and modified include for newlib 2010/10/03
* Marco Atzeri <marco_atzeri@yahoo.it>
*/
/*
FUNCTION
<<csqrt>>, <<csqrtf>>---complex square root
INDEX
csqrt
INDEX
csqrtf
SYNOPSIS
#include <complex.h>
double complex csqrt(double complex <[z]>);
float complex csqrtf(float complex <[z]>);
DESCRIPTION
These functions compute the complex square root of <[z]>, with
a branch cut along the negative real axis.
<<csqrtf>> is identical to <<csqrt>>, except that it performs
its calculations on <<floats complex>>.
RETURNS
The csqrt functions return the complex square root value, in
the range of the right halfplane (including the imaginary axis).
PORTABILITY
<<csqrt>> and <<csqrtf>> are ISO C99
QUICKREF
<<csqrt>> and <<csqrtf>> are ISO C99
*/
#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 * (double complex) I;
} else {
r = fabs(x);
r = sqrt(r);
if (x < 0.0) {
w = 0.0 + r * (double complex) I;
} else {
w = r + y * (double complex) I;
}
}
return w;
}
if (x == 0.0) {
r = fabs(y);
r = sqrt(0.5 * r);
if (y > 0)
w = r + r * (double complex) I;
else
w = r - r * (double complex) 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 {
#if 1
x *= 1.8014398509481984e16; /* 2^54 */
y *= 1.8014398509481984e16;
scale = 7.450580596923828125e-9; /* 2^-27 */
#else
x *= 4.0;
y *= 4.0;
scale = 0.5;
#endif
}
w = x + y * (double complex) 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 * (double complex) I;
else
w = t + r * (double complex) I;
return w;
}
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