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/* Complex square root of a float type.
Copyright (C) 1997-2018 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 "quadmath-imp.h"
__complex128
csqrtq (__complex128 x)
{
__complex128 res;
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
{
if (icls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
__imag__ res = __imag__ x;
}
else if (rcls == QUADFP_INFINITE)
{
if (__real__ x < 0)
{
__real__ res = icls == QUADFP_NAN ? nanq ("") : 0;
__imag__ res = copysignq (HUGE_VALQ, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == QUADFP_NAN
? nanq ("") : copysignq (0, __imag__ x));
}
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
}
}
else
{
if (__glibc_unlikely (icls == QUADFP_ZERO))
{
if (__real__ x < 0)
{
__real__ res = 0;
__imag__ res = copysignq (sqrtq (-__real__ x), __imag__ x);
}
else
{
__real__ res = fabsq (sqrtq (__real__ x));
__imag__ res = copysignq (0, __imag__ x);
}
}
else if (__glibc_unlikely (rcls == QUADFP_ZERO))
{
__float128 r;
if (fabsq (__imag__ x) >= 2 * FLT128_MIN)
r = sqrtq (0.5Q * fabsq (__imag__ x));
else
r = 0.5Q * sqrtq (2 * fabsq (__imag__ x));
__real__ res = r;
__imag__ res = copysignq (r, __imag__ x);
}
else
{
__float128 d, r, s;
int scale = 0;
if (fabsq (__real__ x) > FLT128_MAX / 4)
{
scale = 1;
__real__ x = scalbnq (__real__ x, -2 * scale);
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
else if (fabsq (__imag__ x) > FLT128_MAX / 4)
{
scale = 1;
if (fabsq (__real__ x) >= 4 * FLT128_MIN)
__real__ x = scalbnq (__real__ x, -2 * scale);
else
__real__ x = 0;
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
else if (fabsq (__real__ x) < 2 * FLT128_MIN
&& fabsq (__imag__ x) < 2 * FLT128_MIN)
{
scale = -((FLT128_MANT_DIG + 1) / 2);
__real__ x = scalbnq (__real__ x, -2 * scale);
__imag__ x = scalbnq (__imag__ x, -2 * scale);
}
d = hypotq (__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 = sqrtq (0.5Q * (d + __real__ x));
if (scale == 1 && fabsq (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = scalbnq (r, scale);
scale = 0;
}
else
s = 0.5Q * (__imag__ x / r);
}
else
{
s = sqrtq (0.5Q * (d - __real__ x));
if (scale == 1 && fabsq (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
r = fabsq (__imag__ x / s);
s = scalbnq (s, scale);
scale = 0;
}
else
r = fabsq (0.5Q * (__imag__ x / s));
}
if (scale)
{
r = scalbnq (r, scale);
s = scalbnq (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = copysignq (s, __imag__ x);
}
}
return res;
}
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