1  /* Return arc hyperbolic tangent for a 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  catanhq (__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 (icls == QUADFP_INFINITE)
      32  	{
      33  	  __real__ res = copysignq (0, __real__ x);
      34  	  __imag__ res = copysignq (M_PI_2q, __imag__ x);
      35  	}
      36        else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO)
      37  	{
      38  	  __real__ res = copysignq (0, __real__ x);
      39  	  if (icls >= QUADFP_ZERO)
      40  	    __imag__ res = copysignq (M_PI_2q, __imag__ x);
      41  	  else
      42  	    __imag__ res = nanq ("");
      43  	}
      44        else
      45  	{
      46  	  __real__ res = nanq ("");
      47  	  __imag__ res = nanq ("");
      48  	}
      49      }
      50    else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
      51      {
      52        res = x;
      53      }
      54    else
      55      {
      56        if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
      57  	  || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
      58  	{
      59  	  __imag__ res = copysignq (M_PI_2q, __imag__ x);
      60  	  if (fabsq (__imag__ x) <= 1)
      61  	    __real__ res = 1 / __real__ x;
      62  	  else if (fabsq (__real__ x) <= 1)
      63  	    __real__ res = __real__ x / __imag__ x / __imag__ x;
      64  	  else
      65  	    {
      66  	      __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
      67  	      __real__ res = __real__ x / h / h / 4;
      68  	    }
      69  	}
      70        else
      71  	{
      72  	  if (fabsq (__real__ x) == 1
      73  	      && fabsq (__imag__ x) < FLT128_EPSILON * FLT128_EPSILON)
      74  	    __real__ res = (copysignq (0.5Q, __real__ x)
      75  			    * ((__float128) M_LN2q
      76  			       - logq (fabsq (__imag__ x))));
      77  	  else
      78  	    {
      79  	      __float128 i2 = 0;
      80  	      if (fabsq (__imag__ x) >= FLT128_EPSILON * FLT128_EPSILON)
      81  		i2 = __imag__ x * __imag__ x;
      82  
      83  	      __float128 num = 1 + __real__ x;
      84  	      num = i2 + num * num;
      85  
      86  	      __float128 den = 1 - __real__ x;
      87  	      den = i2 + den * den;
      88  
      89  	      __float128 f = num / den;
      90  	      if (f < 0.5Q)
      91  		__real__ res = 0.25Q * logq (f);
      92  	      else
      93  		{
      94  		  num = 4 * __real__ x;
      95  		  __real__ res = 0.25Q * log1pq (num / den);
      96  		}
      97  	    }
      98  
      99  	  __float128 absx, absy, den;
     100  
     101  	  absx = fabsq (__real__ x);
     102  	  absy = fabsq (__imag__ x);
     103  	  if (absx < absy)
     104  	    {
     105  	      __float128 t = absx;
     106  	      absx = absy;
     107  	      absy = t;
     108  	    }
     109  
     110  	  if (absy < FLT128_EPSILON / 2)
     111  	    {
     112  	      den = (1 - absx) * (1 + absx);
     113  	      if (den == 0)
     114  		den = 0;
     115  	    }
     116  	  else if (absx >= 1)
     117  	    den = (1 - absx) * (1 + absx) - absy * absy;
     118  	  else if (absx >= 0.75Q || absy >= 0.5Q)
     119  	    den = -__quadmath_x2y2m1q (absx, absy);
     120  	  else
     121  	    den = (1 - absx) * (1 + absx) - absy * absy;
     122  
     123  	  __imag__ res = 0.5Q * atan2q (2 * __imag__ x, den);
     124  	}
     125  
     126        math_check_force_underflow_complex (res);
     127      }
     128  
     129    return res;
     130  }