1  /* Return arc tangent of complex float type.
       2     Copyright (C) 1997-2018 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4     Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
       5  
       6     The GNU C Library is free software; you can redistribute it and/or
       7     modify it under the terms of the GNU Lesser General Public
       8     License as published by the Free Software Foundation; either
       9     version 2.1 of the License, or (at your option) any later version.
      10  
      11     The GNU C Library is distributed in the hope that it will be useful,
      12     but WITHOUT ANY WARRANTY; without even the implied warranty of
      13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      14     Lesser General Public License for more details.
      15  
      16     You should have received a copy of the GNU Lesser General Public
      17     License along with the GNU C Library; if not, see
      18     <http://www.gnu.org/licenses/>.  */
      19  
      20  #include "quadmath-imp.h"
      21  
      22  __complex128
      23  catanq (__complex128 x)
      24  {
      25    __complex128 res;
      26    int rcls = fpclassifyq (__real__ x);
      27    int icls = fpclassifyq (__imag__ x);
      28  
      29    if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
      30      {
      31        if (rcls == QUADFP_INFINITE)
      32  	{
      33  	  __real__ res = copysignq (M_PI_2q, __real__ x);
      34  	  __imag__ res = copysignq (0, __imag__ x);
      35  	}
      36        else if (icls == QUADFP_INFINITE)
      37  	{
      38  	  if (rcls >= QUADFP_ZERO)
      39  	    __real__ res = copysignq (M_PI_2q, __real__ x);
      40  	  else
      41  	    __real__ res = nanq ("");
      42  	  __imag__ res = copysignq (0, __imag__ x);
      43  	}
      44        else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
      45  	{
      46  	  __real__ res = nanq ("");
      47  	  __imag__ res = copysignq (0, __imag__ x);
      48  	}
      49        else
      50  	{
      51  	  __real__ res = nanq ("");
      52  	  __imag__ res = nanq ("");
      53  	}
      54      }
      55    else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
      56      {
      57        res = x;
      58      }
      59    else
      60      {
      61        if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
      62  	  || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
      63  	{
      64  	  __real__ res = copysignq (M_PI_2q, __real__ x);
      65  	  if (fabsq (__real__ x) <= 1)
      66  	    __imag__ res = 1 / __imag__ x;
      67  	  else if (fabsq (__imag__ x) <= 1)
      68  	    __imag__ res = __imag__ x / __real__ x / __real__ x;
      69  	  else
      70  	    {
      71  	      __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
      72  	      __imag__ res = __imag__ x / h / h / 4;
      73  	    }
      74  	}
      75        else
      76  	{
      77  	  __float128 den, absx, absy;
      78  
      79  	  absx = fabsq (__real__ x);
      80  	  absy = fabsq (__imag__ x);
      81  	  if (absx < absy)
      82  	    {
      83  	      __float128 t = absx;
      84  	      absx = absy;
      85  	      absy = t;
      86  	    }
      87  
      88  	  if (absy < FLT128_EPSILON / 2)
      89  	    {
      90  	      den = (1 - absx) * (1 + absx);
      91  	      if (den == 0)
      92  		den = 0;
      93  	    }
      94  	  else if (absx >= 1)
      95  	    den = (1 - absx) * (1 + absx) - absy * absy;
      96  	  else if (absx >= 0.75Q || absy >= 0.5Q)
      97  	    den = -__quadmath_x2y2m1q (absx, absy);
      98  	  else
      99  	    den = (1 - absx) * (1 + absx) - absy * absy;
     100  
     101  	  __real__ res = 0.5Q * atan2q (2 * __real__ x, den);
     102  
     103  	  if (fabsq (__imag__ x) == 1
     104  	      && fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
     105  	    __imag__ res = (copysignq (0.5Q, __imag__ x)
     106  			    * ((__float128) M_LN2q
     107  			       - logq (fabsq (__real__ x))));
     108  	  else
     109  	    {
     110  	      __float128 r2 = 0, num, f;
     111  
     112  	      if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON)
     113  		r2 = __real__ x * __real__ x;
     114  
     115  	      num = __imag__ x + 1;
     116  	      num = r2 + num * num;
     117  
     118  	      den = __imag__ x - 1;
     119  	      den = r2 + den * den;
     120  
     121  	      f = num / den;
     122  	      if (f < 0.5Q)
     123  		__imag__ res = 0.25Q * logq (f);
     124  	      else
     125  		{
     126  		  num = 4 * __imag__ x;
     127  		  __imag__ res = 0.25Q * log1pq (num / den);
     128  		}
     129  	    }
     130  	}
     131  
     132        math_check_force_underflow_complex (res);
     133      }
     134  
     135    return res;
     136  }