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/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
/*-
* 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 "libm.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
/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
#define THRESH 0x1.a827999fcef32p+1022
double complex csqrt(double complex z)
{
double complex result;
double a, b;
double t;
int scale;
a = creal(z);
b = cimag(z);
/* Handle special cases. */
if (z == 0)
return CMPLX(0, b);
if (isinf(b))
return CMPLX(INFINITY, b);
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return CMPLX(a, t); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrt(inf + NaN i) = inf + NaN i
* csqrt(inf + y i) = inf + 0 i
* csqrt(-inf + NaN i) = NaN +- inf i
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return CMPLX(fabs(b - b), copysign(a, b));
else
return CMPLX(a, copysign(b - b, b));
}
/*
* The remaining special case (b is NaN) is handled just fine by
* the normal code path below.
*/
/* Scale to avoid overflow. */
if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
a *= 0.25;
b *= 0.25;
scale = 1;
} else {
scale = 0;
}
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
result = CMPLX(t, b / (2 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
}
/* Rescale. */
if (scale)
result *= 2;
return result;
}
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