gcc/gmp/mpz/kronsz.c

/* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol.

Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */

#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"


int
mpz_si_kronecker (long a, mpz_srcptr b)
{
  mp_srcptr  b_ptr;
  mp_limb_t  b_low;
  mp_size_t  b_size;
  mp_size_t  b_abs_size;
  mp_limb_t  a_limb, b_rem;
  unsigned   twos;
  int        result_bit1;

#if GMP_NUMB_BITS < BITS_PER_ULONG
  if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX)
    {
      mp_limb_t  alimbs[2];
      mpz_t      az;
      ALLOC(az) = numberof (alimbs);
      PTR(az) = alimbs;
      mpz_set_si (az, a);
      return mpz_kronecker (az, b);
    }
#endif

  b_size = SIZ (b);
  if (b_size == 0)
    return JACOBI_S0 (a);  /* (a/0) */

  /* account for the effect of the sign of b, then ignore it */
  result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);

  b_ptr = PTR(b);
  b_low = b_ptr[0];
  b_abs_size = ABS (b_size);

  if ((b_low & 1) != 0)
    {
      /* b odd */

      result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
      a_limb = (unsigned long) ABS(a);

      if ((a_limb & 1) == 0)
        {
          /* (0/b)=1 for b=+/-1, 0 otherwise */
          if (a_limb == 0)
            return (b_abs_size == 1 && b_low == 1);

          /* a even, b odd */
          count_trailing_zeros (twos, a_limb);
          a_limb >>= twos;
          /* (a*2^n/b) = (a/b) * twos(n,a) */
          result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
        }
    }
  else
    {
      /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
      if ((a & 1) == 0)
        return 0;

      /* a odd, b even

         Establish shifted b_low with valid bit1 for ASGN and RECIP below.
         Zero limbs stripped are acounted for, but zero bits on b_low are
         not because they remain in {b_ptr,b_abs_size} for the
         JACOBI_MOD_OR_MODEXACT_1_ODD. */

      JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
      if ((b_low & 1) == 0)
        {
          if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
            {
              /* need b_ptr[1] to get bit1 in b_low */
              if (b_abs_size == 1)
                {
                  /* (a/0x80000000) = (a/2)^(BPML-1) */
                  if ((GMP_NUMB_BITS % 2) == 0)
                    result_bit1 ^= JACOBI_TWO_U_BIT1 (a);
                  return JACOBI_BIT1_TO_PN (result_bit1);
                }

              /* b_abs_size > 1 */
              b_low = b_ptr[1] << 1;
            }
          else
            {
              count_trailing_zeros (twos, b_low);
              b_low >>= twos;
            }
        }

      result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
      a_limb = (unsigned long) ABS(a);
    }

  if (a_limb == 1)
    return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */

  /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb);
  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low);
  return mpn_jacobi_base (b_rem, a_limb, result_bit1);
}