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@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  }