github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpz/kronuz.c (about)

     1  /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
     2  
     3  Copyright 1999-2002 Free Software Foundation, Inc.
     4  
     5  This file is part of the GNU MP Library.
     6  
     7  The GNU MP Library is free software; you can redistribute it and/or modify
     8  it under the terms of either:
     9  
    10    * the GNU Lesser General Public License as published by the Free
    11      Software Foundation; either version 3 of the License, or (at your
    12      option) any later version.
    13  
    14  or
    15  
    16    * the GNU General Public License as published by the Free Software
    17      Foundation; either version 2 of the License, or (at your option) any
    18      later version.
    19  
    20  or both in parallel, as here.
    21  
    22  The GNU MP Library is distributed in the hope that it will be useful, but
    23  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    24  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    25  for more details.
    26  
    27  You should have received copies of the GNU General Public License and the
    28  GNU Lesser General Public License along with the GNU MP Library.  If not,
    29  see https://www.gnu.org/licenses/.  */
    30  
    31  #include "gmp.h"
    32  #include "gmp-impl.h"
    33  #include "longlong.h"
    34  
    35  
    36  int
    37  mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
    38  {
    39    mp_srcptr  b_ptr;
    40    mp_limb_t  b_low;
    41    int        b_abs_size;
    42    mp_limb_t  b_rem;
    43    int        twos;
    44    int        result_bit1;
    45  
    46    /* (a/-1)=1 when a>=0, so the sign of b is ignored */
    47    b_abs_size = ABSIZ (b);
    48  
    49    if (b_abs_size == 0)
    50      return JACOBI_U0 (a);  /* (a/0) */
    51  
    52    if (a > GMP_NUMB_MAX)
    53      {
    54        mp_limb_t  alimbs[2];
    55        mpz_t      az;
    56        ALLOC(az) = numberof (alimbs);
    57        PTR(az) = alimbs;
    58        mpz_set_ui (az, a);
    59        return mpz_kronecker (az, b);
    60      }
    61  
    62    b_ptr = PTR(b);
    63    b_low = b_ptr[0];
    64    result_bit1 = 0;
    65  
    66    if (! (b_low & 1))
    67      {
    68        /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
    69        if (! (a & 1))
    70  	return 0;
    71  
    72        /* a odd, b even
    73  
    74  	 Establish shifted b_low with valid bit1 for the RECIP below.  Zero
    75  	 limbs stripped are accounted for, but zero bits on b_low are not
    76  	 because they remain in {b_ptr,b_abs_size} for
    77  	 JACOBI_MOD_OR_MODEXACT_1_ODD. */
    78  
    79        JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
    80        if (! (b_low & 1))
    81  	{
    82  	  if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
    83  	    {
    84  	      /* need b_ptr[1] to get bit1 in b_low */
    85  	      if (b_abs_size == 1)
    86  		{
    87  		  /* (a/0x80...00) == (a/2)^(NUMB-1) */
    88  		  if ((GMP_NUMB_BITS % 2) == 0)
    89  		    {
    90  		      /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
    91  			 when GMP_NUMB_BITS is even, so it's still 0. */
    92  		      ASSERT (result_bit1 == 0);
    93  		      result_bit1 = JACOBI_TWO_U_BIT1 (a);
    94  		    }
    95  		  return JACOBI_BIT1_TO_PN (result_bit1);
    96  		}
    97  
    98  	      /* b_abs_size > 1 */
    99  	      b_low = b_ptr[1] << 1;
   100  	    }
   101  	  else
   102  	    {
   103  	      count_trailing_zeros (twos, b_low);
   104  	      b_low >>= twos;
   105  	    }
   106  	}
   107      }
   108    else
   109      {
   110        if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
   111  	return (b_abs_size == 1 && b_low == 1);
   112  
   113        if (! (a & 1))
   114  	{
   115  	  /* a even, b odd */
   116  	  count_trailing_zeros (twos, a);
   117  	  a >>= twos;
   118  	  /* (a*2^n/b) = (a/b) * (2/a)^n */
   119  	  result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
   120  	}
   121      }
   122  
   123    if (a == 1)
   124      return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
   125  
   126    /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
   127    JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
   128    result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
   129    return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
   130  }