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/* Return arc tangent of complex float type.
Copyright (C) 1997-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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 (__catan) (CFLOAT x)
{
CFLOAT res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
{
if (rcls == FP_INFINITE)
{
__real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
else
__real__ res = M_NAN;
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = M_NAN;
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
}
}
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
res = x;
}
else
{
if (M_FABS (__real__ x) >= 16 / M_EPSILON
|| M_FABS (__imag__ x) >= 16 / M_EPSILON)
{
__real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
if (M_FABS (__real__ x) <= 1)
__imag__ res = 1 / __imag__ x;
else if (M_FABS (__imag__ x) <= 1)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
__imag__ res = __imag__ x / h / h / 4;
}
}
else
{
FLOAT den, absx, absy;
absx = M_FABS (__real__ x);
absy = M_FABS (__imag__ x);
if (absx < absy)
{
FLOAT t = absx;
absx = absy;
absy = t;
}
if (absy < M_EPSILON / 2)
{
den = (1 - absx) * (1 + absx);
if (den == 0)
den = 0;
}
else if (absx >= 1)
den = (1 - absx) * (1 + absx) - absy * absy;
else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
den = -M_SUF (__x2y2m1) (absx, absy);
else
den = (1 - absx) * (1 + absx) - absy * absy;
__real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den);
if (M_FABS (__imag__ x) == 1
&& M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
__imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
* (M_MLIT (M_LN2)
- M_LOG (M_FABS (__real__ x))));
else
{
FLOAT r2 = 0, num, f;
if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON)
r2 = __real__ x * __real__ x;
num = __imag__ x + 1;
num = r2 + num * num;
den = __imag__ x - 1;
den = r2 + den * den;
f = num / den;
if (f < M_LIT (0.5))
__imag__ res = M_LIT (0.25) * M_LOG (f);
else
{
num = 4 * __imag__ x;
__imag__ res = M_LIT (0.25) * M_LOG1P (num / den);
}
}
}
math_check_force_underflow_complex (res);
}
return res;
}
declare_mgen_alias (__catan, catan)
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