/* mpn_dcpi1_div_qr_n -- recursive divide-and-conquer division for arbitrary

   size operands.

   Contributed to the GNU project by 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 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"

#include "longlong.h"

mp_limb_t

mpn_dcpi1_div_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n,

		    gmp_pi1_t *dinv, mp_ptr tp)

{

  mp_size_t lo, hi;

  mp_limb_t cy, qh, ql;

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

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

  if (BELOW_THRESHOLD (hi, DC_DIV_QR_THRESHOLD))

    qh = mpn_sbpi1_div_qr (qp + lo, np + 2 * lo, 2 * hi, dp + lo, hi, dinv->inv32);

  else

    qh = mpn_dcpi1_div_qr_n (qp + lo, np + 2 * lo, dp + lo, hi, dinv, tp);

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

  cy = mpn_sub_n (np + lo, np + lo, tp, n);

  if (qh != 0)

    cy += mpn_sub_n (np + n, np + n, dp, lo);

  while (cy != 0)

    {

      qh -= mpn_sub_1 (qp + lo, qp + lo, hi, 1);

      cy -= mpn_add_n (np + lo, np + lo, dp, n);

    }

  if (BELOW_THRESHOLD (lo, DC_DIV_QR_THRESHOLD))

    ql = mpn_sbpi1_div_qr (qp, np + hi, 2 * lo, dp + hi, lo, dinv->inv32);

  else

    ql = mpn_dcpi1_div_qr_n (qp, np + hi, dp + hi, lo, dinv, tp);

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

  cy = mpn_sub_n (np, np, tp, n);

  if (ql != 0)

    cy += mpn_sub_n (np + lo, np + lo, dp, hi);

  while (cy != 0)

    {

      mpn_sub_1 (qp, qp, lo, 1);

      cy -= mpn_add_n (np, np, dp, n);

    }

  return qh;

}

mp_limb_t

mpn_dcpi1_div_qr (mp_ptr qp,

		  mp_ptr np, mp_size_t nn,

		  mp_srcptr dp, mp_size_t dn,

		  gmp_pi1_t *dinv)

{

  mp_size_t qn;

  mp_limb_t qh, cy;

  mp_ptr tp;

  TMP_DECL;

  TMP_MARK;

  ASSERT (dn >= 6);		/* to adhere to mpn_sbpi1_div_qr's limits */

  ASSERT (nn - dn >= 3);	/* to adhere to mpn_sbpi1_div_qr's limits */

  ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);

  tp = TMP_ALLOC_LIMBS (dn);

  qn = nn - dn;

  qp += qn;

  np += nn;

  dp += dn;

  if (qn > dn)

    {

      /* Reduce qn mod dn without division, optimizing small operations.  */

      do

	qn -= dn;

      while (qn > dn);

      qp -= qn;			/* point at low limb of next quotient block */

      np -= qn;			/* point in the middle of partial remainder */

      /* Perform the typically smaller block first.  */

      if (qn == 1)

	{

	  mp_limb_t q, n2, n1, n0, d1, d0;

	  /* Handle qh up front, for simplicity. */

	  qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;

	  if (qh)

	    ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));

	  /* A single iteration of schoolbook: One 3/2 division,

	     followed by the bignum update and adjustment. */

	  n2 = np[0];

	  n1 = np[-1];

	  n0 = np[-2];

	  d1 = dp[-1];

	  d0 = dp[-2];

	  ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));

	  if (UNLIKELY (n2 == d1) && n1 == d0)

	    {

	      q = GMP_NUMB_MASK;

	      cy = mpn_submul_1 (np - dn, dp - dn, dn, q);

	      ASSERT (cy == n2);

	    }

	  else

	    {

	      udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32);

	      if (dn > 2)

		{

		  mp_limb_t cy, cy1;

		  cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);

		  cy1 = n0 < cy;

		  n0 = (n0 - cy) & GMP_NUMB_MASK;

		  cy = n1 < cy1;

		  n1 = (n1 - cy1) & GMP_NUMB_MASK;

		  np[-2] = n0;

		  if (UNLIKELY (cy != 0))

		    {

		      n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);

		      qh -= (q == 0);

		      q = (q - 1) & GMP_NUMB_MASK;

		    }

		}

	      else

		np[-2] = n0;

	      np[-1] = n1;

	    }

	  qp[0] = q;

	}

      else

	{

	  /* Do a 2qn / qn division */

	  if (qn == 2)

	    qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); /* FIXME: obsolete function. Use 5/3 division? */

	  else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))

	    qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);

	  else

	    qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);

	  if (qn != dn)

	    {

	      if (qn > dn - qn)

		mpn_mul (tp, qp, qn, dp - dn, dn - qn);

	      else

		mpn_mul (tp, dp - dn, dn - qn, qp, qn);

	      cy = mpn_sub_n (np - dn, np - dn, tp, dn);

	      if (qh != 0)

		cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);

	      while (cy != 0)

		{

		  qh -= mpn_sub_1 (qp, qp, qn, 1);

		  cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);

		}

	    }

	}

      qn = nn - dn - qn;

      do

	{

	  qp -= dn;

	  np -= dn;

	  mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp);

	  qn -= dn;

	}

      while (qn > 0);

    }

  else

    {

      qp -= qn;			/* point at low limb of next quotient block */

      np -= qn;			/* point in the middle of partial remainder */

      if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))

	qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);

      else

	qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);

      if (qn != dn)

	{

	  if (qn > dn - qn)

	    mpn_mul (tp, qp, qn, dp - dn, dn - qn);

	  else

	    mpn_mul (tp, dp - dn, dn - qn, qp, qn);

	  cy = mpn_sub_n (np - dn, np - dn, tp, dn);

	  if (qh != 0)

	    cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);

	  while (cy != 0)

	    {

	      qh -= mpn_sub_1 (qp, qp, qn, 1);

	      cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);

	    }

	}

    }

  TMP_FREE;

  return qh;

}