1  /* Return arc hyperbolic tangent for a 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 (__catanh) (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 (icls == FP_INFINITE)
      35  	{
      36  	  __real__ res = M_COPYSIGN (0, __real__ x);
      37  	  __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
      38  	}
      39        else if (rcls == FP_INFINITE || rcls == FP_ZERO)
      40  	{
      41  	  __real__ res = M_COPYSIGN (0, __real__ x);
      42  	  if (icls >= FP_ZERO)
      43  	    __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
      44  	  else
      45  	    __imag__ res = M_NAN;
      46  	}
      47        else
      48  	{
      49  	  __real__ res = M_NAN;
      50  	  __imag__ res = M_NAN;
      51  	}
      52      }
      53    else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
      54      {
      55        res = x;
      56      }
      57    else
      58      {
      59        if (M_FABS (__real__ x) >= 16 / M_EPSILON
      60  	  || M_FABS (__imag__ x) >= 16 / M_EPSILON)
      61  	{
      62  	  __imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
      63  	  if (M_FABS (__imag__ x) <= 1)
      64  	    __real__ res = 1 / __real__ x;
      65  	  else if (M_FABS (__real__ x) <= 1)
      66  	    __real__ res = __real__ x / __imag__ x / __imag__ x;
      67  	  else
      68  	    {
      69  	      FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
      70  	      __real__ res = __real__ x / h / h / 4;
      71  	    }
      72  	}
      73        else
      74  	{
      75  	  if (M_FABS (__real__ x) == 1
      76  	      && M_FABS (__imag__ x) < M_EPSILON * M_EPSILON)
      77  	    __real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x)
      78  			    * (M_MLIT (M_LN2)
      79  			       - M_LOG (M_FABS (__imag__ x))));
      80  	  else
      81  	    {
      82  	      FLOAT i2 = 0;
      83  	      if (M_FABS (__imag__ x) >= M_EPSILON * M_EPSILON)
      84  		i2 = __imag__ x * __imag__ x;
      85  
      86  	      FLOAT num = 1 + __real__ x;
      87  	      num = i2 + num * num;
      88  
      89  	      FLOAT den = 1 - __real__ x;
      90  	      den = i2 + den * den;
      91  
      92  	      FLOAT f = num / den;
      93  	      if (f < M_LIT (0.5))
      94  		__real__ res = M_LIT (0.25) * M_LOG (f);
      95  	      else
      96  		{
      97  		  num = 4 * __real__ x;
      98  		  __real__ res = M_LIT (0.25) * M_LOG1P (num / den);
      99  		}
     100  	    }
     101  
     102  	  FLOAT absx, absy, den;
     103  
     104  	  absx = M_FABS (__real__ x);
     105  	  absy = M_FABS (__imag__ x);
     106  	  if (absx < absy)
     107  	    {
     108  	      FLOAT t = absx;
     109  	      absx = absy;
     110  	      absy = t;
     111  	    }
     112  
     113  	  if (absy < M_EPSILON / 2)
     114  	    {
     115  	      den = (1 - absx) * (1 + absx);
     116  	      if (den == 0)
     117  		den = 0;
     118  	    }
     119  	  else if (absx >= 1)
     120  	    den = (1 - absx) * (1 + absx) - absy * absy;
     121  	  else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
     122  	    den = -M_SUF (__x2y2m1) (absx, absy);
     123  	  else
     124  	    den = (1 - absx) * (1 + absx) - absy * absy;
     125  
     126  	  __imag__ res = M_LIT (0.5) * M_ATAN2 (2 * __imag__ x, den);
     127  	}
     128  
     129        math_check_force_underflow_complex (res);
     130      }
     131  
     132    return res;
     133  }
     134  
     135  declare_mgen_alias (__catanh, catanh)