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/* Complex square root of long double value.
Copyright (C) 1997-2015 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <complex.h>
#include <math.h>
#include <math_private.h>
#include <float.h>
__complex__ long double
__csqrtl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanl ("") : 0;
__imag__ res = __copysignl (HUGE_VALL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanl ("") : __copysignl (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else
{
if (__glibc_unlikely (icls == FP_ZERO))
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignl (__ieee754_sqrtl (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsl (__ieee754_sqrtl (__real__ x));
__imag__ res = __copysignl (0.0, __imag__ x);
}
}
else if (__glibc_unlikely (rcls == FP_ZERO))
{
long double r;
if (fabsl (__imag__ x) >= 2.0L * LDBL_MIN)
r = __ieee754_sqrtl (0.5L * fabsl (__imag__ x));
else
r = 0.5L * __ieee754_sqrtl (2.0L * fabsl (__imag__ x));
__real__ res = r;
__imag__ res = __copysignl (r, __imag__ x);
}
else
{
long double d, r, s;
int scale = 0;
if (fabsl (__real__ x) > LDBL_MAX / 4.0L)
{
scale = 1;
__real__ x = __scalbnl (__real__ x, -2 * scale);
__imag__ x = __scalbnl (__imag__ x, -2 * scale);
}
else if (fabsl (__imag__ x) > LDBL_MAX / 4.0L)
{
scale = 1;
if (fabsl (__real__ x) >= 4.0L * LDBL_MIN)
__real__ x = __scalbnl (__real__ x, -2 * scale);
else
__real__ x = 0.0L;
__imag__ x = __scalbnl (__imag__ x, -2 * scale);
}
else if (fabsl (__real__ x) < 2.0L * LDBL_MIN
&& fabsl (__imag__ x) < 2.0L * LDBL_MIN)
{
scale = -((LDBL_MANT_DIG + 1) / 2);
__real__ x = __scalbnl (__real__ x, -2 * scale);
__imag__ x = __scalbnl (__imag__ x, -2 * scale);
}
d = __ieee754_hypotl (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = __ieee754_sqrtl (0.5L * (d + __real__ x));
if (scale == 1 && fabsl (__imag__ x) < 1.0L)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = __scalbnl (r, scale);
scale = 0;
}
else
s = 0.5L * (__imag__ x / r);
}
else
{
s = __ieee754_sqrtl (0.5L * (d - __real__ x));
if (scale == 1 && fabsl (__imag__ x) < 1.0L)
{
/* Avoid possible intermediate underflow. */
r = fabsl (__imag__ x / s);
s = __scalbnl (s, scale);
scale = 0;
}
else
r = fabsl (0.5L * (__imag__ x / s));
}
if (scale)
{
r = __scalbnl (r, scale);
s = __scalbnl (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = __copysignl (s, __imag__ x);
}
}
return res;
}
weak_alias (__csqrtl, csqrtl)
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