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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: head/lib/msun/src/s_csqrt.c 336488 2018-07-19 15:04:10Z bde $");
#include <complex.h>
#include <float.h>
#include <math.h>
#include "math_private.h"
/* For avoiding 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, rx, ry, scale, t;
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 + 0.0L + t, a + 0.0L + t)); /* 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)));
}
if (isnan(b)) {
t = (a - a) / (a - a); /* raise invalid */
return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
}
/* Scale to avoid overflow. */
if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
/*
* Don't scale a or b if this might give (spurious)
* underflow. Then the unscaled value is an equivalent
* infinitesmal (or 0).
*/
if (fabs(a) >= 0x1p-1020)
a *= 0.25;
if (fabs(b) >= 0x1p-1020)
b *= 0.25;
scale = 2;
} else {
scale = 1;
}
/* Scale to reduce inaccuracies when both components are denormal. */
if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
a *= 0x1p54;
b *= 0x1p54;
scale = 0x1p-27;
}
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
rx = scale * t;
ry = scale * b / (2 * t);
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
rx = scale * fabs(b) / (2 * t);
ry = copysign(scale * t, b);
}
return (CMPLX(rx, ry));
}
#if LDBL_MANT_DIG == 53
__weak_reference(csqrt, csqrtl);
#endif
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