mpir/mpn/generic/gcdext_lehmer.c

/* mpn_gcdext -- Extended Greatest Common Divisor.

Copyright 1996, 1998, 2000, 2001, 2002, 2003, 2004, 2005, 2008, 2009 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 "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"

/* Temporary storage: 3*(n+1) for u. n+1 for the matrix-vector
   multiplications (if hgcd2 succeeds). If hgcd fails, n+1 limbs are
   needed for the division, with most n for the quotient, and n+1 for
   the product q u0. In all, 4n + 3. */

mp_size_t
mpn_gcdext_lehmer_n (mp_ptr gp, mp_ptr up, mp_size_t *usize,
             mp_ptr ap, mp_ptr bp, mp_size_t n,
             mp_ptr tp)
{
  mp_size_t ualloc = n + 1;

  /* Keeps track of the second row of the reduction matrix
   *
   *   M = (v0, v1 ; u0, u1)
   *
   * which correspond to the first column of the inverse
   *
   *   M^{-1} = (u1, -v1; -u0, v0)
   */

  mp_size_t un;
  mp_ptr u0;
  mp_ptr u1;
  mp_ptr u2;

  MPN_ZERO (tp, 3*ualloc);
  u0 = tp; tp += ualloc;
  u1 = tp; tp += ualloc;
  u2 = tp; tp += ualloc;

  u1[0] = 1; un = 1;

  /* FIXME: Handle n == 2 differently, after the loop? */
  while (n >= 2)
    {
      struct hgcd_matrix1 M;
      mp_limb_t ah, al, bh, bl;
      mp_limb_t mask;

      mask = ap[n-1] | bp[n-1];
      ASSERT (mask > 0);

      if (mask & GMP_NUMB_HIGHBIT)
    {
      ah = ap[n-1]; al = ap[n-2];
      bh = bp[n-1]; bl = bp[n-2];
    }
      else if (n == 2)
    {
      /* We use the full inputs without truncation, so we can
         safely shift left. */
      int shift;

      count_leading_zeros (shift, mask);
      ah = MPN_EXTRACT_NUMB (shift, ap[1], ap[0]);
      al = ap[0] << shift;
      bh = MPN_EXTRACT_NUMB (shift, bp[1], bp[0]);
      bl = bp[0] << shift;
    }
      else
    {
      int shift;

      count_leading_zeros (shift, mask);
      ah = MPN_EXTRACT_NUMB (shift, ap[n-1], ap[n-2]);
      al = MPN_EXTRACT_NUMB (shift, ap[n-2], ap[n-3]);
      bh = MPN_EXTRACT_NUMB (shift, bp[n-1], bp[n-2]);
      bl = MPN_EXTRACT_NUMB (shift, bp[n-2], bp[n-3]);
    }

      /* Try an mpn_nhgcd2 step */
      if (mpn_hgcd2 (ah, al, bh, bl, &M))
    {
      n = mpn_hgcd_mul_matrix1_inverse_vector (&M, tp, ap, bp, n);
      MP_PTR_SWAP (ap, tp);
      un = mpn_hgcd_mul_matrix1_vector(&M, u2, u0, u1, un);
      MP_PTR_SWAP (u0, u2);
    }
      else
    {
      /* mpn_hgcd2 has failed. Then either one of a or b is very
         small, or the difference is very small. Perform one
         subtraction followed by one division. */
      mp_size_t gn;
      mp_size_t updated_un = un;

      /* Temporary storage n for the quotient and ualloc for the
         new cofactor. */
      n = mpn_gcdext_subdiv_step (gp, &gn, up, usize, ap, bp, n,
                      u0, u1, &updated_un, tp, u2);
      if (n == 0)
        return gn;

      un = updated_un;
    }
    }
  ASSERT_ALWAYS (ap[0] > 0);
  ASSERT_ALWAYS (bp[0] > 0);

  if (ap[0] == bp[0])
    {
      int c;

      /* Which cofactor to return now? Candidates are +u1 and -u0,
     depending on which of a and b was most recently reduced,
     which we don't keep track of. So compare and get the smallest
     one. */

      gp[0] = ap[0];

      MPN_CMP (c, u0, u1, un);
      ASSERT (c != 0 || (un == 1 && u0[0] == 1 && u1[0] == 1));
      if (c < 0)
    {
      MPN_NORMALIZE (u0, un);
      MPN_COPY (up, u0, un);
      *usize = -un;
    }
      else
    {
      MPN_NORMALIZE_NOT_ZERO (u1, un);
      MPN_COPY (up, u1, un);
      *usize = un;
    }
      return 1;
    }
  else
    {
      mp_limb_t uh, vh;
      mp_limb_signed_t u;
      mp_limb_signed_t v;
      int negate;

      gp[0] = mpn_gcdext_1 (&u, &v, ap[0], bp[0]);

      /* Set up = u u1 - v u0. Keep track of size, un grows by one or
     two limbs. */

      if (u == 0)
    {
      ASSERT (v == 1);
      MPN_NORMALIZE (u0, un);
      MPN_COPY (up, u0, un);
      *usize = -un;
      return 1;
    }
      else if (v == 0)
    {
      ASSERT (u == 1);
      MPN_NORMALIZE (u1, un);
      MPN_COPY (up, u1, un);
      *usize = un;
      return 1;
    }
      else if (u > 0)
    {
      negate = 0;
      ASSERT (v < 0);
      v = -v;
    }
      else
    {
      negate = 1;
      ASSERT (v > 0);
      u = -u;
    }

      uh = mpn_mul_1 (up, u1, un, u);
      vh = mpn_addmul_1 (up, u0, un, v);

      if ( (uh | vh) > 0)
    {
      uh += vh;
      up[un++] = uh;
      if (uh < vh)
        up[un++] = 1;
    }

      MPN_NORMALIZE_NOT_ZERO (up, un);

      *usize = negate ? -un : un;
      return 1;
    }
}