gcc/gmp/mpz/kronuz.c

/* mpz_ui_kronecker -- ulong+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_ui_kronecker (unsigned long a, mpz_srcptr b)
{
  mp_srcptr  b_ptr;
  mp_limb_t  b_low;
  int        b_abs_size;
  mp_limb_t  b_rem;
  int        twos;
  int        result_bit1;

  /* (a/-1)=1 when a>=0, so the sign of b is ignored */
  b_abs_size = ABSIZ (b);

  if (b_abs_size == 0)
    return JACOBI_U0 (a);  /* (a/0) */

  if (a > GMP_NUMB_MAX)
    {
      mp_limb_t  alimbs[2];
      mpz_t      az;
      ALLOC(az) = numberof (alimbs);
      PTR(az) = alimbs;
      mpz_set_ui (az, a);
      return mpz_kronecker (az, b);
    }

  b_ptr = PTR(b);
  b_low = b_ptr[0];
  result_bit1 = 0;

  if (! (b_low & 1))
    {
      /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
      if (! (a & 1))
        return 0;

      /* a odd, b even

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

      JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
      if (! (b_low & 1))
        {
          if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
            {
              /* need b_ptr[1] to get bit1 in b_low */
              if (b_abs_size == 1)
                {
                  /* (a/0x80...00) == (a/2)^(NUMB-1) */
                  if ((GMP_NUMB_BITS % 2) == 0)
                    {
                      /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
                         when GMP_NUMB_BITS is even, so it's still 0. */
                      ASSERT (result_bit1 == 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;
            }
        }
    }
  else
    {
      if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
        return (b_abs_size == 1 && b_low == 1);

      if (! (a & 1))
        {
          /* a even, b odd */
          count_trailing_zeros (twos, a);
          a >>= twos;
          /* (a*2^n/b) = (a/b) * (2/a)^n */
          result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
        }
    }

  if (a == 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);
  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
  return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
}