gcc/gmp/mpn/generic/dc_bdiv_qr.c

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

   Contributed to the GNU project by Niels Möller and Torbjörn Granlund.

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH A MUTABLE INTERFACE.  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 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"


/* 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 borrow from the subtraction n - q*d.

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

mp_size_t
mpn_dc_bdiv_qr_n_itch (mp_size_t n)
{
  return n;
}

mp_limb_t
mpn_dc_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_sb_bdiv_qr (qp, np, 2 * lo, dp, lo, dinv);
  else
    cy = mpn_dc_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_sub (np + lo, np + lo, n + hi, tp, n);

  if (BELOW_THRESHOLD (hi, DC_BDIV_QR_THRESHOLD))
    cy = mpn_sb_bdiv_qr (qp + lo, np + lo, 2 * hi, dp, hi, dinv);
  else
    cy = mpn_dc_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_sub_n (np + n, np + n, tp, n);

  return rh;
}

mp_limb_t
mpn_dc_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;

  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_sb_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
      else
	cy = mpn_dc_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_sub (np + qn, np + qn, nn - qn, tp, dn);
	  cy = 0;
	}

      np += qn;
      qp += qn;

      qn = nn - dn - qn;
      do
	{
	  rr += mpn_sub_1 (np + dn, np + dn, qn, cy);
	  cy = mpn_dc_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_sb_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
  else
    cy = mpn_dc_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_sub (np + qn, np + qn, nn - qn, tp, dn);
      cy = 0;
    }

  TMP_FREE;
  return rr + cy;
}