mpir/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 2.1 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; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

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


int
mpz_ui_kronecker (mpir_ui 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);
}