/* mpn/bdivmod.c: mpn_bdivmod for computing U/V mod 2^d.

Copyright 1991, 1993, 1994, 1995, 1996, 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/.  */

/* q_high = mpn_bdivmod (qp, up, usize, vp, vsize, d).

   Puts the low d/BITS_PER_MP_LIMB limbs of Q = U / V mod 2^d at qp, and
   returns the high d%BITS_PER_MP_LIMB bits of Q as the result.

   Also, U - Q * V mod 2^(usize*BITS_PER_MP_LIMB) is placed at up.  Since the
   low d/BITS_PER_MP_LIMB limbs of this difference are zero, the code allows
   the limb vectors at qp to overwrite the low limbs at up, provided qp <= up.

   Preconditions:
   1.  V is odd.
   2.  usize * BITS_PER_MP_LIMB >= d.
   3.  If Q and U overlap, qp <= up.

   Ken Weber (kweber@mat.ufrgs.br, kweber@mcs.kent.edu)

   Funding for this work has been partially provided by Conselho Nacional
   de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq) do Brazil, Grant
   301314194-2, and was done while I was a visiting reseacher in the Instituto
   de Matema'tica at Universidade Federal do Rio Grande do Sul (UFRGS).

   References:
       T. Jebelean, An algorithm for exact division, Journal of Symbolic
       Computation, v. 15, 1993, pp. 169-180.

       K. Weber, The accelerated integer GCD algorithm, ACM Transactions on
       Mathematical Software, v. 21 (March), 1995, pp. 111-122.  */

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


mp_limb_t
mpn_bdivmod (mp_ptr qp, mp_ptr up, mp_size_t usize,
	     mp_srcptr vp, mp_size_t vsize, unsigned long int d)
{
  mp_limb_t v_inv;

  ASSERT (usize >= 1);
  ASSERT (vsize >= 1);
  ASSERT (usize * GMP_NUMB_BITS >= d);
  ASSERT (! MPN_OVERLAP_P (up, usize, vp, vsize));
  ASSERT (! MPN_OVERLAP_P (qp, d/GMP_NUMB_BITS, vp, vsize));
  ASSERT (MPN_SAME_OR_INCR2_P (qp, d/GMP_NUMB_BITS, up, usize));
  ASSERT_MPN (up, usize);
  ASSERT_MPN (vp, vsize);

  /* 1/V mod 2^GMP_NUMB_BITS. */
  modlimb_invert (v_inv, vp[0]);

  /* Fast code for two cases previously used by the accel part of mpn_gcd.
     (Could probably remove this now it's inlined there.) */
  if (usize == 2 && vsize == 2 &&
      (d == GMP_NUMB_BITS || d == 2*GMP_NUMB_BITS))
    {
      mp_limb_t hi, lo;
      mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
      umul_ppmm (hi, lo, q, vp[0] << GMP_NAIL_BITS);
      up[0] = 0;
      up[1] -= hi + q*vp[1];
      qp[0] = q;
      if (d == 2*GMP_NUMB_BITS)
        {
          q = (up[1] * v_inv) & GMP_NUMB_MASK;
          up[1] = 0;
          qp[1] = q;
        }
      return 0;
    }

  /* Main loop.  */
  while (d >= GMP_NUMB_BITS)
    {
      mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
      mp_limb_t b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
      if (usize > vsize)
	mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
      d -= GMP_NUMB_BITS;
      up += 1, usize -= 1;
      *qp++ = q;
    }

  if (d)
    {
      mp_limb_t b;
      mp_limb_t q = (up[0] * v_inv) & (((mp_limb_t)1<<d) - 1);
      if (q <= 1)
	{
	  if (q == 0)
	    return 0;
	  else
	    b = mpn_sub_n (up, up, vp, MIN (usize, vsize));
	}
      else
	b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);

      if (usize > vsize)
	mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
      return q;
    }

  return 0;
}