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/* Return arc tangent of complex double value.
Copyright (C) 1997-2014 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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
__catan (__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 (rcls == FP_INFINITE)
{
__real__ res = __copysign (M_PI_2, __real__ x);
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = __copysign (M_PI_2, __real__ x);
else
__real__ res = __nan ("");
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = __nan ("");
__imag__ res = __copysign (0.0, __imag__ x);
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__real__ res = __copysign (M_PI_2, __real__ x);
if (fabs (__real__ x) <= 1.0)
__imag__ res = 1.0 / __imag__ x;
else if (fabs (__imag__ x) <= 1.0)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__imag__ res = __imag__ x / h / h / 4.0;
}
}
else
{
double den, absx, absy;
absx = fabs (__real__ x);
absy = fabs (__imag__ x);
if (absx < absy)
{
double t = absx;
absx = absy;
absy = t;
}
if (absy < DBL_EPSILON / 2.0)
den = (1.0 - absx) * (1.0 + absx);
else if (absx >= 1.0)
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
else if (absx >= 0.75 || absy >= 0.5)
den = -__x2y2m1 (absx, absy);
else
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
__real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
if (fabs (__imag__ x) == 1.0
&& fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
__imag__ res = (__copysign (0.5, __imag__ x)
* (M_LN2 - __ieee754_log (fabs (__real__ x))));
else
{
double r2 = 0.0, num, f;
if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
r2 = __real__ x * __real__ x;
num = __imag__ x + 1.0;
num = r2 + num * num;
den = __imag__ x - 1.0;
den = r2 + den * den;
f = num / den;
if (f < 0.5)
__imag__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __imag__ x;
__imag__ res = 0.25 * __log1p (num / den);
}
}
}
if (fabs (__real__ res) < DBL_MIN)
{
volatile double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
if (fabs (__imag__ res) < DBL_MIN)
{
volatile double force_underflow = __imag__ res * __imag__ res;
(void) force_underflow;
}
}
return res;
}
weak_alias (__catan, catan)
#ifdef NO_LONG_DOUBLE
strong_alias (__catan, __catanl)
weak_alias (__catan, catanl)
#endif
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