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/* Complex square root of a float type.
Copyright (C) 1997-2020 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
<https://www.gnu.org/licenses/>. */
#include <complex.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <float.h>
CFLOAT
M_DECL_FUNC (__csqrt) (CFLOAT x)
{
CFLOAT 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 = M_HUGE_VAL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0)
{
__real__ res = icls == FP_NAN ? M_NAN : 0;
__imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? M_NAN : M_COPYSIGN (0, __imag__ x));
}
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
}
}
else
{
if (__glibc_unlikely (icls == FP_ZERO))
{
if (__real__ x < 0)
{
__real__ res = 0;
__imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
}
else
{
__real__ res = M_FABS (M_SQRT (__real__ x));
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
}
else if (__glibc_unlikely (rcls == FP_ZERO))
{
FLOAT r;
if (M_FABS (__imag__ x) >= 2 * M_MIN)
r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
else
r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));
__real__ res = r;
__imag__ res = M_COPYSIGN (r, __imag__ x);
}
else
{
FLOAT d, r, s;
int scale = 0;
if (M_FABS (__real__ x) > M_MAX / 4)
{
scale = 1;
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__imag__ x) > M_MAX / 4)
{
scale = 1;
if (M_FABS (__real__ x) >= 4 * M_MIN)
__real__ x = M_SCALBN (__real__ x, -2 * scale);
else
__real__ x = 0;
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__real__ x) < 2 * M_MIN
&& M_FABS (__imag__ x) < 2 * M_MIN)
{
scale = -((M_MANT_DIG + 1) / 2);
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
d = M_HYPOT (__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 = M_SQRT (M_LIT (0.5) * (d + __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = M_SCALBN (r, scale);
scale = 0;
}
else
s = M_LIT (0.5) * (__imag__ x / r);
}
else
{
s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
r = M_FABS (__imag__ x / s);
s = M_SCALBN (s, scale);
scale = 0;
}
else
r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
}
if (scale)
{
r = M_SCALBN (r, scale);
s = M_SCALBN (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = M_COPYSIGN (s, __imag__ x);
}
}
return res;
}
declare_mgen_alias (__csqrt, csqrt)
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