/* mpn_dcpi1_bdiv_qr -- divide-and-conquer Hensel division with precomputed

   inverse, returning quotient and remainder.

   Contributed to the GNU project by Niels Möller 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 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.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_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_sub (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_sub_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_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_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_sub (np + qn, np + qn, nn - qn, tp, dn);

      cy = 0;

    }

  TMP_FREE;

  return rr + cy;

}