1  /* Compute complex natural logarithm.
       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  clogq (__complex128 x)
      24  {
      25    __complex128 result;
      26    int rcls = fpclassifyq (__real__ x);
      27    int icls = fpclassifyq (__imag__ x);
      28  
      29    if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
      30      {
      31        /* Real and imaginary part are 0.0.  */
      32        __imag__ result = signbitq (__real__ x) ? (__float128) M_PIq : 0;
      33        __imag__ result = copysignq (__imag__ result, __imag__ x);
      34        /* Yes, the following line raises an exception.  */
      35        __real__ result = -1 / fabsq (__real__ x);
      36      }
      37    else if (__glibc_likely (rcls != QUADFP_NAN && icls != QUADFP_NAN))
      38      {
      39        /* Neither real nor imaginary part is NaN.  */
      40        __float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
      41        int scale = 0;
      42  
      43        if (absx < absy)
      44  	{
      45  	  __float128 t = absx;
      46  	  absx = absy;
      47  	  absy = t;
      48  	}
      49  
      50        if (absx > FLT128_MAX / 2)
      51  	{
      52  	  scale = -1;
      53  	  absx = scalbnq (absx, scale);
      54  	  absy = (absy >= FLT128_MIN * 2 ? scalbnq (absy, scale) : 0);
      55  	}
      56        else if (absx < FLT128_MIN && absy < FLT128_MIN)
      57  	{
      58  	  scale = FLT128_MANT_DIG;
      59  	  absx = scalbnq (absx, scale);
      60  	  absy = scalbnq (absy, scale);
      61  	}
      62  
      63        if (absx == 1 && scale == 0)
      64  	{
      65  	  __real__ result = log1pq (absy * absy) / 2;
      66  	  math_check_force_underflow_nonneg (__real__ result);
      67  	}
      68        else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
      69  	{
      70  	  __float128 d2m1 = (absx - 1) * (absx + 1);
      71  	  if (absy >= FLT128_EPSILON)
      72  	    d2m1 += absy * absy;
      73  	  __real__ result = log1pq (d2m1) / 2;
      74  	}
      75        else if (absx < 1
      76  	       && absx >= 0.5Q
      77  	       && absy < FLT128_EPSILON / 2
      78  	       && scale == 0)
      79  	{
      80  	  __float128 d2m1 = (absx - 1) * (absx + 1);
      81  	  __real__ result = log1pq (d2m1) / 2;
      82  	}
      83        else if (absx < 1
      84  	       && absx >= 0.5Q
      85  	       && scale == 0
      86  	       && absx * absx + absy * absy >= 0.5Q)
      87  	{
      88  	  __float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
      89  	  __real__ result = log1pq (d2m1) / 2;
      90  	}
      91        else
      92  	{
      93  	  __float128 d = hypotq (absx, absy);
      94  	  __real__ result = logq (d) - scale * (__float128) M_LN2q;
      95  	}
      96  
      97        __imag__ result = atan2q (__imag__ x, __real__ x);
      98      }
      99    else
     100      {
     101        __imag__ result = nanq ("");
     102        if (rcls == QUADFP_INFINITE || icls == QUADFP_INFINITE)
     103  	/* Real or imaginary part is infinite.  */
     104  	__real__ result = HUGE_VALQ;
     105        else
     106  	__real__ result = nanq ("");
     107      }
     108  
     109    return result;
     110  }