1  /* Complex hyperbolic tangent for float types.
       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 <fenv.h>
      21  #include <math.h>
      22  #include <math_private.h>
      23  #include <math-underflow.h>
      24  #include <float.h>
      25  
      26  CFLOAT
      27  M_DECL_FUNC (__ctanh) (CFLOAT x)
      28  {
      29    CFLOAT res;
      30  
      31    if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
      32      {
      33        if (isinf (__real__ x))
      34  	{
      35  	  __real__ res = M_COPYSIGN (1, __real__ x);
      36  	  if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
      37  	    {
      38  	      FLOAT sinix, cosix;
      39  	      M_SINCOS (__imag__ x, &sinix, &cosix);
      40  	      __imag__ res = M_COPYSIGN (0, sinix * cosix);
      41  	    }
      42  	  else
      43  	    __imag__ res = M_COPYSIGN (0, __imag__ x);
      44  	}
      45        else if (__imag__ x == 0)
      46  	{
      47  	  res = x;
      48  	}
      49        else
      50  	{
      51  	  if (__real__ x == 0)
      52  	    __real__ res = __real__ x;
      53  	  else
      54  	    __real__ res = M_NAN;
      55  	  __imag__ res = M_NAN;
      56  
      57  	  if (isinf (__imag__ x))
      58  	    feraiseexcept (FE_INVALID);
      59  	}
      60      }
      61    else
      62      {
      63        FLOAT sinix, cosix;
      64        FLOAT den;
      65        const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
      66  
      67        /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
      68  	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
      69  
      70        if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
      71  	{
      72  	  M_SINCOS (__imag__ x, &sinix, &cosix);
      73  	}
      74        else
      75  	{
      76  	  sinix = __imag__ x;
      77  	  cosix = 1;
      78  	}
      79  
      80        if (M_FABS (__real__ x) > t)
      81  	{
      82  	  /* Avoid intermediate overflow when the imaginary part of
      83  	     the result may be subnormal.  Ignoring negligible terms,
      84  	     the real part is +/- 1, the imaginary part is
      85  	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
      86  	  FLOAT exp_2t = M_EXP (2 * t);
      87  
      88  	  __real__ res = M_COPYSIGN (1, __real__ x);
      89  	  __imag__ res = 4 * sinix * cosix;
      90  	  __real__ x = M_FABS (__real__ x);
      91  	  __real__ x -= t;
      92  	  __imag__ res /= exp_2t;
      93  	  if (__real__ x > t)
      94  	    {
      95  	      /* Underflow (original real part of x has absolute value
      96  		 > 2t).  */
      97  	      __imag__ res /= exp_2t;
      98  	    }
      99  	  else
     100  	    __imag__ res /= M_EXP (2 * __real__ x);
     101  	}
     102        else
     103  	{
     104  	  FLOAT sinhrx, coshrx;
     105  	  if (M_FABS (__real__ x) > M_MIN)
     106  	    {
     107  	      sinhrx = M_SINH (__real__ x);
     108  	      coshrx = M_COSH (__real__ x);
     109  	    }
     110  	  else
     111  	    {
     112  	      sinhrx = __real__ x;
     113  	      coshrx = 1;
     114  	    }
     115  
     116  	  if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
     117  	    den = sinhrx * sinhrx + cosix * cosix;
     118  	  else
     119  	    den = cosix * cosix;
     120  	  __real__ res = sinhrx * coshrx / den;
     121  	  __imag__ res = sinix * cosix / den;
     122  	}
     123        math_check_force_underflow_complex (res);
     124      }
     125  
     126    return res;
     127  }
     128  
     129  declare_mgen_alias (__ctanh, ctanh)