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/* Return arc tangent of complex float type.
Copyright (C) 1997-2018 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 "quadmath-imp.h"
__complex128
catanq (__complex128 x)
{
__complex128 res;
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
{
if (rcls == QUADFP_INFINITE)
{
__real__ res = copysignq (M_PI_2q, __real__ x);
__imag__ res = copysignq (0, __imag__ x);
}
else if (icls == QUADFP_INFINITE)
{
if (rcls >= QUADFP_ZERO)
__real__ res = copysignq (M_PI_2q, __real__ x);
else
__real__ res = nanq ("");
__imag__ res = copysignq (0, __imag__ x);
}
else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
{
__real__ res = nanq ("");
__imag__ res = copysignq (0, __imag__ x);
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
}
}
else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
{
res = x;
}
else
{
if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
|| fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
{
__real__ res = copysignq (M_PI_2q, __real__ x);
if (fabsq (__real__ x) <= 1)
__imag__ res = 1 / __imag__ x;
else if (fabsq (__imag__ x) <= 1)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
__float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
__imag__ res = __imag__ x / h / h / 4;
}
}
else
{
__float128 den, absx, absy;
absx = fabsq (__real__ x);
absy = fabsq (__imag__ x);
if (absx < absy)
{
__float128 t = absx;
absx = absy;
absy = t;
}
if (absy < FLT128_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 >= 0.75Q || absy >= 0.5Q)
den = -__quadmath_x2y2m1q (absx, absy);
else
den = (1 - absx) * (1 + absx) - absy * absy;
__real__ res = 0.5Q * atan2q (2 * __real__ x, den);
if (fabsq (__imag__ x) == 1
&& fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
__imag__ res = (copysignq (0.5Q, __imag__ x)
* ((__float128) M_LN2q
- logq (fabsq (__real__ x))));
else
{
__float128 r2 = 0, num, f;
if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_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 < 0.5Q)
__imag__ res = 0.25Q * logq (f);
else
{
num = 4 * __imag__ x;
__imag__ res = 0.25Q * log1pq (num / den);
}
}
}
math_check_force_underflow_complex (res);
}
return res;
}
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