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/*-
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
*
* Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* 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 AUTHOR 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 AUTHOR 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.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
float complex
csqrtf(float complex z)
{
double t;
float a, b;
a = creal(z);
b = cimag(z);
/* Handle special cases. */
if (z == 0)
return (CMPLXF(0, b));
if (isinf(b))
return (CMPLXF(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (CMPLXF(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrtf(inf + NaN i) = inf + NaN i
* csqrtf(inf + y i) = inf + 0 i
* csqrtf(-inf + NaN i) = NaN +- inf i
* csqrtf(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (CMPLXF(fabsf(b - b), copysignf(a, b)));
else
return (CMPLXF(a, copysignf(b - b, b)));
}
if (isnan(b)) {
t = (a - a) / (a - a); /* raise invalid */
return (CMPLXF(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
}
/*
* We compute t in double precision to avoid overflow and to
* provide correct rounding in nearly all cases.
* This is Algorithm 312, CACM vol 10, Oct 1967.
*/
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
return (CMPLXF(t, b / (2 * t)));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
return (CMPLXF(fabsf(b) / (2 * t), copysignf(t, b)));
}
}
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