1  /* Compute complex base 10 logarithm.
       2     Copyright (C) 1997-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  #include <complex.h>
      20  #include <math.h>
      21  #include <math_private.h>
      22  #include <math-underflow.h>
      23  #include <float.h>
      24  
      25  /* log_10 (2).  */
      26  #define LOG10_2 M_LIT (0.3010299956639811952137388947244930267682)
      27  
      28  /* pi * log10 (e).  */
      29  #define PI_LOG10E M_LIT (1.364376353841841347485783625431355770210)
      30  
      31  CFLOAT
      32  M_DECL_FUNC (__clog10) (CFLOAT x)
      33  {
      34    CFLOAT result;
      35    int rcls = fpclassify (__real__ x);
      36    int icls = fpclassify (__imag__ x);
      37  
      38    if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
      39      {
      40        /* Real and imaginary part are 0.0.  */
      41        __imag__ result = signbit (__real__ x) ? PI_LOG10E : 0;
      42        __imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
      43        /* Yes, the following line raises an exception.  */
      44        __real__ result = -1 / M_FABS (__real__ x);
      45      }
      46    else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
      47      {
      48        /* Neither real nor imaginary part is NaN.  */
      49        FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
      50        int scale = 0;
      51  
      52        if (absx < absy)
      53  	{
      54  	  FLOAT t = absx;
      55  	  absx = absy;
      56  	  absy = t;
      57  	}
      58  
      59        if (absx > M_MAX / 2)
      60  	{
      61  	  scale = -1;
      62  	  absx = M_SCALBN (absx, scale);
      63  	  absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
      64  	}
      65        else if (absx < M_MIN && absy < M_MIN)
      66  	{
      67  	  scale = M_MANT_DIG;
      68  	  absx = M_SCALBN (absx, scale);
      69  	  absy = M_SCALBN (absy, scale);
      70  	}
      71  
      72        if (absx == 1 && scale == 0)
      73  	{
      74  	  __real__ result = (M_LOG1P (absy * absy)
      75  			     * (M_MLIT (M_LOG10E) / 2));
      76  	  math_check_force_underflow_nonneg (__real__ result);
      77  	}
      78        else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
      79  	{
      80  	  FLOAT d2m1 = (absx - 1) * (absx + 1);
      81  	  if (absy >= M_EPSILON)
      82  	    d2m1 += absy * absy;
      83  	  __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
      84  	}
      85        else if (absx < 1
      86  	       && absx >= M_LIT (0.5)
      87  	       && absy < M_EPSILON / 2
      88  	       && scale == 0)
      89  	{
      90  	  FLOAT d2m1 = (absx - 1) * (absx + 1);
      91  	  __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
      92  	}
      93        else if (absx < 1
      94  	       && absx >= M_LIT (0.5)
      95  	       && scale == 0
      96  	       && absx * absx + absy * absy >= M_LIT (0.5))
      97  	{
      98  	  FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
      99  	  __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
     100  	}
     101        else
     102  	{
     103  	  FLOAT d = M_HYPOT (absx, absy);
     104  	  __real__ result = M_SUF (__ieee754_log10) (d) - scale * LOG10_2;
     105  	}
     106  
     107        __imag__ result = M_MLIT (M_LOG10E) * M_ATAN2 (__imag__ x, __real__ x);
     108      }
     109    else
     110      {
     111        __imag__ result = M_NAN;
     112        if (rcls == FP_INFINITE || icls == FP_INFINITE)
     113  	/* Real or imaginary part is infinite.  */
     114  	__real__ result = M_HUGE_VAL;
     115        else
     116  	__real__ result = M_NAN;
     117      }
     118  
     119    return result;
     120  }
     121  
     122  declare_mgen_alias (__clog10, clog10)