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      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 (at) 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 }
    111