mpn/generic/dcpi1_bdiv_qr.c

/* mpn_dcpi1_bdiv_qr -- divide-and-conquer Hensel division with precomputed
   inverse, returning quotient and remainder.

   Contributed to the GNU project by Niels Mller and Torbjorn Granlund.

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.

Copyright 2006, 2007, 2009, 2010, 2017 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software
    Foundation; either version 2 of the License, or (at your option) any
    later version.

or both in parallel, as here.

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 General Public License
for more details.

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

#include "gmp-impl.h"


/* Computes Hensel binary division of {np, 2*n} by {dp, n}.

   Output:

      q = -n * d^{-1} mod 2^{qn * GMP_NUMB_BITS},

      r = (n + q * d) * 2^{-qn * GMP_NUMB_BITS}

   Stores q at qp. Stores the n least significant limbs of r at the high half
   of np, and returns the carry from the addition n + q*d.

   d must be odd. dinv is (-d)^-1 mod 2^GMP_NUMB_BITS. */

mp_size_t
mpn_dcpi1_bdiv_qr_n_itch (mp_size_t n)
{
  return n;
}

mp_limb_t
mpn_dcpi1_bdiv_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n,
		     mp_limb_t dinv, mp_ptr tp)
{
  mp_size_t lo, hi;
  mp_limb_t cy;
  mp_limb_t rh;

  lo = n >> 1;			/* floor(n/2) */
  hi = n - lo;			/* ceil(n/2) */

  if (BELOW_THRESHOLD (lo, DC_BDIV_QR_THRESHOLD))
    cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * lo, dp, lo, dinv);
  else
    cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, lo, dinv, tp);

  mpn_mul (tp, dp + lo, hi, qp, lo);

  mpn_incr_u (tp + lo, cy);
  rh = mpn_add (np + lo, np + lo, n + hi, tp, n);

  if (BELOW_THRESHOLD (hi, DC_BDIV_QR_THRESHOLD))
    cy = mpn_sbpi1_bdiv_qr (qp + lo, np + lo, 2 * hi, dp, hi, dinv);
  else
    cy = mpn_dcpi1_bdiv_qr_n (qp + lo, np + lo, dp, hi, dinv, tp);

  mpn_mul (tp, qp + lo, hi, dp + hi, lo);

  mpn_incr_u (tp + hi, cy);
  rh += mpn_add_n (np + n, np + n, tp, n);

  return rh;
}

mp_limb_t
mpn_dcpi1_bdiv_qr (mp_ptr qp, mp_ptr np, mp_size_t nn,
		   mp_srcptr dp, mp_size_t dn, mp_limb_t dinv)
{
  mp_size_t qn;
  mp_limb_t rr, cy;
  mp_ptr tp;
  TMP_DECL;

  TMP_MARK;

  ASSERT (dn >= 2);		/* to adhere to mpn_sbpi1_div_qr's limits */
  ASSERT (nn - dn >= 1);	/* to adhere to mpn_sbpi1_div_qr's limits */
  ASSERT (dp[0] & 1);

  tp = TMP_SALLOC_LIMBS (dn);

  qn = nn - dn;

  if (qn > dn)
    {
      /* Reduce qn mod dn without division, optimizing small operations.  */
      do
	qn -= dn;
      while (qn > dn);

      /* Perform the typically smaller block first.  */
      if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD))
	cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
      else
	cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp);

      rr = 0;
      if (qn != dn)
	{
	  if (qn > dn - qn)
	    mpn_mul (tp, qp, qn, dp + qn, dn - qn);
	  else
	    mpn_mul (tp, dp + qn, dn - qn, qp, qn);
	  mpn_incr_u (tp + qn, cy);

	  rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn);
	  cy = 0;
	}

      np += qn;
      qp += qn;

      qn = nn - dn - qn;
      do
	{
	  rr += mpn_add_1 (np + dn, np + dn, qn, cy);
	  cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, dn, dinv, tp);
	  qp += dn;
	  np += dn;
	  qn -= dn;
	}
      while (qn > 0);
      TMP_FREE;
      return rr + cy;
    }

  if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD))
    cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
  else
    cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp);

  rr = 0;
  if (qn != dn)
    {
      if (qn > dn - qn)
	mpn_mul (tp, qp, qn, dp + qn, dn - qn);
      else
	mpn_mul (tp, dp + qn, dn - qn, qp, qn);
      mpn_incr_u (tp + qn, cy);

      rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn);
      cy = 0;
    }

  TMP_FREE;
  return rr + cy;
}