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      1 /* Compute complex base 10 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 /* log_10 (2).  */
     23 #define LOG10_2 0.3010299956639811952137388947244930267682Q
     24 
     25 /* pi * log10 (e).  */
     26 #define PI_LOG10E 1.364376353841841347485783625431355770210Q
     27 
     28 __complex128
     29 clog10q (__complex128 x)
     30 {
     31   __complex128 result;
     32   int rcls = fpclassifyq (__real__ x);
     33   int icls = fpclassifyq (__imag__ x);
     34 
     35   if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
     36     {
     37       /* Real and imaginary part are 0.0.  */
     38       __imag__ result = signbitq (__real__ x) ? PI_LOG10E : 0;
     39       __imag__ result = copysignq (__imag__ result, __imag__ x);
     40       /* Yes, the following line raises an exception.  */
     41       __real__ result = -1 / fabsq (__real__ x);
     42     }
     43   else if (__glibc_likely (rcls != QUADFP_NAN && icls != QUADFP_NAN))
     44     {
     45       /* Neither real nor imaginary part is NaN.  */
     46       __float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
     47       int scale = 0;
     48 
     49       if (absx < absy)
     50 	{
     51 	  __float128 t = absx;
     52 	  absx = absy;
     53 	  absy = t;
     54 	}
     55 
     56       if (absx > FLT128_MAX / 2)
     57 	{
     58 	  scale = -1;
     59 	  absx = scalbnq (absx, scale);
     60 	  absy = (absy >= FLT128_MIN * 2 ? scalbnq (absy, scale) : 0);
     61 	}
     62       else if (absx < FLT128_MIN && absy < FLT128_MIN)
     63 	{
     64 	  scale = FLT128_MANT_DIG;
     65 	  absx = scalbnq (absx, scale);
     66 	  absy = scalbnq (absy, scale);
     67 	}
     68 
     69       if (absx == 1 && scale == 0)
     70 	{
     71 	  __real__ result = (log1pq (absy * absy)
     72 			     * ((__float128) M_LOG10Eq / 2));
     73 	  math_check_force_underflow_nonneg (__real__ result);
     74 	}
     75       else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
     76 	{
     77 	  __float128 d2m1 = (absx - 1) * (absx + 1);
     78 	  if (absy >= FLT128_EPSILON)
     79 	    d2m1 += absy * absy;
     80 	  __real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
     81 	}
     82       else if (absx < 1
     83 	       && absx >= 0.5Q
     84 	       && absy < FLT128_EPSILON / 2
     85 	       && scale == 0)
     86 	{
     87 	  __float128 d2m1 = (absx - 1) * (absx + 1);
     88 	  __real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
     89 	}
     90       else if (absx < 1
     91 	       && absx >= 0.5Q
     92 	       && scale == 0
     93 	       && absx * absx + absy * absy >= 0.5Q)
     94 	{
     95 	  __float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
     96 	  __real__ result = log1pq (d2m1) * ((__float128) M_LOG10Eq / 2);
     97 	}
     98       else
     99 	{
    100 	  __float128 d = hypotq (absx, absy);
    101 	  __real__ result = log10q (d) - scale * LOG10_2;
    102 	}
    103 
    104       __imag__ result = M_LOG10Eq * atan2q (__imag__ x, __real__ x);
    105     }
    106   else
    107     {
    108       __imag__ result = nanq ("");
    109       if (rcls == QUADFP_INFINITE || icls == QUADFP_INFINITE)
    110 	/* Real or imaginary part is infinite.  */
    111 	__real__ result = HUGE_VALQ;
    112       else
    113 	__real__ result = nanq ("");
    114     }
    115 
    116   return result;
    117 }
    118