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/*-
* Copyright (c) 2007-2008 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: head/lib/msun/src/s_csqrtl.c 275819 2014-12-16 09:21:56Z ed $");
#include <complex.h>
#include <float.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
/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L)
long double complex
csqrtl(long double complex z)
{
long double complex result;
long double a, b;
long double t;
int scale;
a = creall(z);
b = cimagl(z);
/* Handle special cases. */
if (z == 0)
return (CMPLXL(0, b));
if (isinf(b))
return (CMPLXL(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (CMPLXL(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 (CMPLXL(fabsl(b - b), copysignl(a, b)));
else
return (CMPLXL(a, copysignl(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 (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
a *= 0.25;
b *= 0.25;
scale = 1;
} else {
scale = 0;
}
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrtl((a + hypotl(a, b)) * 0.5);
result = CMPLXL(t, b / (2 * t));
} else {
t = sqrtl((-a + hypotl(a, b)) * 0.5);
result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
}
/* Rescale. */
if (scale)
return (result * 2);
else
return (result);
}
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