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/* Complex square root of long double value. */
/* Copyright (C) 1997-1999 Free Software Foundation, Inc.
This file is part of the GNU ISO C++ Library. This library is free
software; you can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option)
any later version.
This 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 General Public License for more details.
You should have received a copy of the GNU General Public License along
with this library; see the file COPYING. If not, write to the Free
Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
USA.
As a special exception, you may use this file as part of a free software
library without restriction. Specifically, if other files instantiate
templates or use macros or inline functions from this file, or you compile
this file and link it with other files to produce an executable, this
file does not by itself cause the resulting executable to be covered by
the GNU General Public License. This exception does not however
invalidate any other reasons why the executable file might be covered by
the GNU General Public License. */
#include <math.h>
#include "mathconf.h"
/* Thanks to SGI we have to trick here. At least Irix 6.2 provides hypotl,
but it has a wrong prototype. Grrr. */
extern long double local_hypotl (long double, long double) asm ("hypotl");
__complex__ long double
csqrtl (__complex__ long double x)
{
__complex__ long double res;
if (!FINITEL_P (__real__ x) || !FINITEL_P (__imag__ x))
{
if (INFINITEL_P (__imag__ x))
{
__real__ res = HUGE_VALL;
__imag__ res = __imag__ x;
}
else if (INFINITEL_P (__real__ x))
{
if (__real__ x < 0.0)
{
__real__ res = __imag__ x != __imag__ x ? NAN : 0;
__imag__ res = copysignl (HUGE_VALL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (__imag__ x != __imag__ x
? NAN : copysignl (0.0, __imag__ x));
}
}
else
{
__real__ res = NAN;
__imag__ res = NAN;
}
}
else
{
if (__imag__ x == 0.0)
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = copysignl (sqrtl (-__real__ x), __imag__ x);
}
else
{
__real__ res = fabsl (sqrtl (__real__ x));
__imag__ res = copysignl (0.0, __imag__ x);
}
}
else if (__real__ x == 0.0)
{
long double r = sqrtl (0.5 * fabsl (__imag__ x));
__real__ res = copysignl (r, __imag__ x);
__imag__ res = r;
}
else
{
__complex__ long double q;
long double t, r;
if (fabsl (__imag__ x) < 2.0e-4 * fabsl (__real__ x))
t = 0.25 * __imag__ x * (__imag__ x / __real__ x);
else
t = 0.5 * (local_hypotl (__real__ x, __imag__ x) - __real__ x);
r = sqrtl (t);
__real__ q = __imag__ x / (2.0 * r);
__imag__ q = r;
/* Heron iteration in complex arithmetic. */
res = 0.5 * (q + q / x);
}
}
return res;
}
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