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/*-
* 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"
/*
* gcc doesn't implement complex multiplication or division correctly,
* so we need to handle infinities specially. We turn on this pragma to
* notify conforming c99 compilers that the fast-but-incorrect code that
* gcc generates is acceptable, since the special cases have already been
* handled.
*/
#pragma STDC CX_LIMITED_RANGE ON
float complex
csqrtf(float complex z)
{
float a = crealf(z), b = cimagf(z);
double t;
/* Handle special cases. */
if (z == 0)
return (cpackf(0, b));
if (isinf(b))
return (cpackf(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpackf(a, t)); /* return 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 (cpackf(fabsf(b - b), copysignf(a, b)));
else
return (cpackf(a, copysignf(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
* the normal code path below.
*/
/*
* 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 (cpackf(t, b / (2.0 * t)));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
}
}
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