1  /* Complex tangent function 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  ctanq (__complex128 x)
      24  {
      25    __complex128 res;
      26  
      27    if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
      28      {
      29        if (isinfq (__imag__ x))
      30  	{
      31  	  if (finiteq (__real__ x) && fabsq (__real__ x) > 1)
      32  	    {
      33  	      __float128 sinrx, cosrx;
      34  	      sincosq (__real__ x, &sinrx, &cosrx);
      35  	      __real__ res = copysignq (0, sinrx * cosrx);
      36  	    }
      37  	  else
      38  	    __real__ res = copysignq (0, __real__ x);
      39  	  __imag__ res = copysignq (1, __imag__ x);
      40  	}
      41        else if (__real__ x == 0)
      42  	{
      43  	  res = x;
      44  	}
      45        else
      46  	{
      47  	  __real__ res = nanq ("");
      48  	  if (__imag__ x == 0)
      49  	    __imag__ res = __imag__ x;
      50  	  else
      51  	    __imag__ res = nanq ("");
      52  
      53  	  if (isinfq (__real__ x))
      54  	    feraiseexcept (FE_INVALID);
      55  	}
      56      }
      57    else
      58      {
      59        __float128 sinrx, cosrx;
      60        __float128 den;
      61        const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
      62  
      63        /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
      64  	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
      65  
      66        if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN))
      67  	{
      68  	  sincosq (__real__ x, &sinrx, &cosrx);
      69  	}
      70        else
      71  	{
      72  	  sinrx = __real__ x;
      73  	  cosrx = 1;
      74  	}
      75  
      76        if (fabsq (__imag__ x) > t)
      77  	{
      78  	  /* Avoid intermediate overflow when the real part of the
      79  	     result may be subnormal.  Ignoring negligible terms, the
      80  	     imaginary part is +/- 1, the real part is
      81  	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
      82  	  __float128 exp_2t = expq (2 * t);
      83  
      84  	  __imag__ res = copysignq (1, __imag__ x);
      85  	  __real__ res = 4 * sinrx * cosrx;
      86  	  __imag__ x = fabsq (__imag__ x);
      87  	  __imag__ x -= t;
      88  	  __real__ res /= exp_2t;
      89  	  if (__imag__ x > t)
      90  	    {
      91  	      /* Underflow (original imaginary part of x has absolute
      92  		 value > 2t).  */
      93  	      __real__ res /= exp_2t;
      94  	    }
      95  	  else
      96  	    __real__ res /= expq (2 * __imag__ x);
      97  	}
      98        else
      99  	{
     100  	  __float128 sinhix, coshix;
     101  	  if (fabsq (__imag__ x) > FLT128_MIN)
     102  	    {
     103  	      sinhix = sinhq (__imag__ x);
     104  	      coshix = coshq (__imag__ x);
     105  	    }
     106  	  else
     107  	    {
     108  	      sinhix = __imag__ x;
     109  	      coshix = 1;
     110  	    }
     111  
     112  	  if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
     113  	    den = cosrx * cosrx + sinhix * sinhix;
     114  	  else
     115  	    den = cosrx * cosrx;
     116  	  __real__ res = sinrx * cosrx / den;
     117  	  __imag__ res = sinhix * coshix / den;
     118  	}
     119        math_check_force_underflow_complex (res);
     120      }
     121  
     122    return res;
     123  }