147 lines
3.8 KiB
C
147 lines
3.8 KiB
C
/* Complex square root of double value.
|
|
Copyright (C) 1997-2013 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__ double
|
|
__csqrt (__complex__ double x)
|
|
{
|
|
__complex__ double res;
|
|
int rcls = fpclassify (__real__ x);
|
|
int icls = fpclassify (__imag__ x);
|
|
|
|
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
|
|
{
|
|
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 (__builtin_expect (icls == FP_ZERO, 0))
|
|
{
|
|
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 (__builtin_expect (rcls == FP_ZERO, 0))
|
|
{
|
|
double r;
|
|
if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
|
|
r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
|
|
else
|
|
r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
|
|
|
|
__real__ res = r;
|
|
__imag__ res = __copysign (r, __imag__ x);
|
|
}
|
|
else
|
|
{
|
|
double d, r, s;
|
|
int scale = 0;
|
|
|
|
if (fabs (__real__ x) > DBL_MAX / 4.0)
|
|
{
|
|
scale = 1;
|
|
__real__ x = __scalbn (__real__ x, -2 * scale);
|
|
__imag__ x = __scalbn (__imag__ x, -2 * scale);
|
|
}
|
|
else if (fabs (__imag__ x) > DBL_MAX / 4.0)
|
|
{
|
|
scale = 1;
|
|
if (fabs (__real__ x) >= 4.0 * DBL_MIN)
|
|
__real__ x = __scalbn (__real__ x, -2 * scale);
|
|
else
|
|
__real__ x = 0.0;
|
|
__imag__ x = __scalbn (__imag__ x, -2 * scale);
|
|
}
|
|
else if (fabs (__real__ x) < DBL_MIN
|
|
&& fabs (__imag__ x) < DBL_MIN)
|
|
{
|
|
scale = -(DBL_MANT_DIG / 2);
|
|
__real__ x = __scalbn (__real__ x, -2 * scale);
|
|
__imag__ x = __scalbn (__imag__ x, -2 * scale);
|
|
}
|
|
|
|
d = __ieee754_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 = __ieee754_sqrt (0.5 * (d + __real__ x));
|
|
s = 0.5 * (__imag__ x / r);
|
|
}
|
|
else
|
|
{
|
|
s = __ieee754_sqrt (0.5 * (d - __real__ x));
|
|
r = fabs (0.5 * (__imag__ x / s));
|
|
}
|
|
|
|
if (scale)
|
|
{
|
|
r = __scalbn (r, scale);
|
|
s = __scalbn (s, scale);
|
|
}
|
|
|
|
__real__ res = r;
|
|
__imag__ res = __copysign (s, __imag__ x);
|
|
}
|
|
}
|
|
|
|
return res;
|
|
}
|
|
weak_alias (__csqrt, csqrt)
|
|
#ifdef NO_LONG_DOUBLE
|
|
strong_alias (__csqrt, __csqrtl)
|
|
weak_alias (__csqrt, csqrtl)
|
|
#endif
|