1  /* Compute complex natural 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  CFLOAT
      26  M_DECL_FUNC (__clog) (CFLOAT x)
      27  {
      28    CFLOAT result;
      29    int rcls = fpclassify (__real__ x);
      30    int icls = fpclassify (__imag__ x);
      31  
      32    if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
      33      {
      34        /* Real and imaginary part are 0.0.  */
      35        __imag__ result = signbit (__real__ x) ? M_MLIT (M_PI) : 0;
      36        __imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
      37        /* Yes, the following line raises an exception.  */
      38        __real__ result = -1 / M_FABS (__real__ x);
      39      }
      40    else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
      41      {
      42        /* Neither real nor imaginary part is NaN.  */
      43        FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
      44        int scale = 0;
      45  
      46        if (absx < absy)
      47  	{
      48  	  FLOAT t = absx;
      49  	  absx = absy;
      50  	  absy = t;
      51  	}
      52  
      53        if (absx > M_MAX / 2)
      54  	{
      55  	  scale = -1;
      56  	  absx = M_SCALBN (absx, scale);
      57  	  absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
      58  	}
      59        else if (absx < M_MIN && absy < M_MIN)
      60  	{
      61  	  scale = M_MANT_DIG;
      62  	  absx = M_SCALBN (absx, scale);
      63  	  absy = M_SCALBN (absy, scale);
      64  	}
      65  
      66        if (absx == 1 && scale == 0)
      67  	{
      68  	  __real__ result = M_LOG1P (absy * absy) / 2;
      69  	  math_check_force_underflow_nonneg (__real__ result);
      70  	}
      71        else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
      72  	{
      73  	  FLOAT d2m1 = (absx - 1) * (absx + 1);
      74  	  if (absy >= M_EPSILON)
      75  	    d2m1 += absy * absy;
      76  	  __real__ result = M_LOG1P (d2m1) / 2;
      77  	}
      78        else if (absx < 1
      79  	       && absx >= M_LIT (0.5)
      80  	       && absy < M_EPSILON / 2
      81  	       && scale == 0)
      82  	{
      83  	  FLOAT d2m1 = (absx - 1) * (absx + 1);
      84  	  __real__ result = M_LOG1P (d2m1) / 2;
      85  	}
      86        else if (absx < 1
      87  	       && absx >= M_LIT (0.5)
      88  	       && scale == 0
      89  	       && absx * absx + absy * absy >= M_LIT (0.5))
      90  	{
      91  	  FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
      92  	  __real__ result = M_LOG1P (d2m1) / 2;
      93  	}
      94        else
      95  	{
      96  	  FLOAT d = M_HYPOT (absx, absy);
      97  	  __real__ result = M_LOG (d) - scale * M_MLIT (M_LN2);
      98  	}
      99  
     100        __imag__ result = M_ATAN2 (__imag__ x, __real__ x);
     101      }
     102    else
     103      {
     104        __imag__ result = M_NAN;
     105        if (rcls == FP_INFINITE || icls == FP_INFINITE)
     106  	/* Real or imaginary part is infinite.  */
     107  	__real__ result = M_HUGE_VAL;
     108        else
     109  	__real__ result = M_NAN;
     110      }
     111  
     112    return result;
     113  }
     114  
     115  declare_mgen_alias (__clog, clog)