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/* Complex square root of double value.
Copyright (C) 1997 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 Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include <complex.h>
#include <math.h>
#include "math_private.h"
__complex__ double
__csqrt (__complex__ double x)
{
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VAL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nan ("") : 0;
__imag__ res = __copysign (HUGE_VAL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nan ("") : __copysign (0.0, __imag__ x));
}
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else
{
if (icls == FP_ZERO)
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabs (__ieee754_sqrt (__real__ x));
__imag__ res = __copysign (0.0, __imag__ x);
}
}
else if (rcls == FP_ZERO)
{
double r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
__real__ res = __copysign (r, __imag__ x);
__imag__ res = r;
}
else
{
#if 0 /* FIXME: this is broken. */
__complex__ double q;
double t, r;
if (fabs (__imag__ x) < 2.0e-4 * fabs (__real__ x))
t = 0.25 * __imag__ x * (__imag__ x / __real__ x);
else
t = 0.5 * (__ieee754_hypot (__real__ x, __imag__ x) - __real__ x);
r = __ieee754_sqrt (t);
__real__ q = __imag__ x / (2.0 * r);
__imag__ q = r;
/* Heron iteration in complex arithmetic. */
res = 0.5 * (q + q / x);
#else
double d, imag;
d = __ieee754_hypot (__real__ x, __imag__ x);
imag = __ieee754_sqrt (0.5 * (d - __real__ x));
__real__ res = __ieee754_sqrt (0.5 * (d + __real__ x));
__imag__ res = __copysign (imag, __imag__ x);
#endif
}
}
return res;
}
weak_alias (__csqrt, csqrt)
#ifdef NO_LONG_DOUBLE
strong_alias (__csqrt, __csqrtl)
weak_alias (__csqrt, csqrtl)
#endif
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