1  /* Return arc tangent of complex float type.
       2     Copyright (C) 1997-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  #include <complex.h>
      20  #include <math.h>
      21  #include <math_private.h>
      22  #include <math-underflow.h>
      23  #include <float.h>
      24  
      25  CFLOAT
      26  M_DECL_FUNC (__catan) (CFLOAT x)
      27  {
      28    CFLOAT res;
      29    int rcls = fpclassify (__real__ x);
      30    int icls = fpclassify (__imag__ x);
      31  
      32    if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
      33      {
      34        if (rcls == FP_INFINITE)
      35  	{
      36  	  __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
      37  	  __imag__ res = M_COPYSIGN (0, __imag__ x);
      38  	}
      39        else if (icls == FP_INFINITE)
      40  	{
      41  	  if (rcls >= FP_ZERO)
      42  	    __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
      43  	  else
      44  	    __real__ res = M_NAN;
      45  	  __imag__ res = M_COPYSIGN (0, __imag__ x);
      46  	}
      47        else if (icls == FP_ZERO || icls == FP_INFINITE)
      48  	{
      49  	  __real__ res = M_NAN;
      50  	  __imag__ res = M_COPYSIGN (0, __imag__ x);
      51  	}
      52        else
      53  	{
      54  	  __real__ res = M_NAN;
      55  	  __imag__ res = M_NAN;
      56  	}
      57      }
      58    else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
      59      {
      60        res = x;
      61      }
      62    else
      63      {
      64        if (M_FABS (__real__ x) >= 16 / M_EPSILON
      65  	  || M_FABS (__imag__ x) >= 16 / M_EPSILON)
      66  	{
      67  	  __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x);
      68  	  if (M_FABS (__real__ x) <= 1)
      69  	    __imag__ res = 1 / __imag__ x;
      70  	  else if (M_FABS (__imag__ x) <= 1)
      71  	    __imag__ res = __imag__ x / __real__ x / __real__ x;
      72  	  else
      73  	    {
      74  	      FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
      75  	      __imag__ res = __imag__ x / h / h / 4;
      76  	    }
      77  	}
      78        else
      79  	{
      80  	  FLOAT den, absx, absy;
      81  
      82  	  absx = M_FABS (__real__ x);
      83  	  absy = M_FABS (__imag__ x);
      84  	  if (absx < absy)
      85  	    {
      86  	      FLOAT t = absx;
      87  	      absx = absy;
      88  	      absy = t;
      89  	    }
      90  
      91  	  if (absy < M_EPSILON / 2)
      92  	    {
      93  	      den = (1 - absx) * (1 + absx);
      94  	      if (den == 0)
      95  		den = 0;
      96  	    }
      97  	  else if (absx >= 1)
      98  	    den = (1 - absx) * (1 + absx) - absy * absy;
      99  	  else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
     100  	    den = -M_SUF (__x2y2m1) (absx, absy);
     101  	  else
     102  	    den = (1 - absx) * (1 + absx) - absy * absy;
     103  
     104  	  __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den);
     105  
     106  	  if (M_FABS (__imag__ x) == 1
     107  	      && M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
     108  	    __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
     109  			    * (M_MLIT (M_LN2)
     110  			       - M_LOG (M_FABS (__real__ x))));
     111  	  else
     112  	    {
     113  	      FLOAT r2 = 0, num, f;
     114  
     115  	      if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON)
     116  		r2 = __real__ x * __real__ x;
     117  
     118  	      num = __imag__ x + 1;
     119  	      num = r2 + num * num;
     120  
     121  	      den = __imag__ x - 1;
     122  	      den = r2 + den * den;
     123  
     124  	      f = num / den;
     125  	      if (f < M_LIT (0.5))
     126  		__imag__ res = M_LIT (0.25) * M_LOG (f);
     127  	      else
     128  		{
     129  		  num = 4 * __imag__ x;
     130  		  __imag__ res = M_LIT (0.25) * M_LOG1P (num / den);
     131  		}
     132  	    }
     133  	}
     134  
     135        math_check_force_underflow_complex (res);
     136      }
     137  
     138    return res;
     139  }
     140  
     141  declare_mgen_alias (__catan, catan)