/* mpn_sbpi1_divappr_q -- Schoolbook division using the Möller-Granlund 3/2

   division algorithm, returning approximate quotient.  The quotient returned

   is either correct, or one too large.

   Contributed to the GNU project by Torbjorn Granlund.

   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY

   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST

   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.

Copyright 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-impl.h"

#include "longlong.h"

mp_limb_t

mpn_sbpi1_divappr_q (mp_ptr qp,

         mp_ptr np, mp_size_t nn,

         mp_srcptr dp, mp_size_t dn,

         mp_limb_t dinv)

{

  mp_limb_t qh;

  mp_size_t qn, i;

  mp_limb_t n1, n0;

  mp_limb_t d1, d0;

  mp_limb_t cy, cy1;

  mp_limb_t q;

  mp_limb_t flag;

  ASSERT (dn > 2);

  ASSERT (nn >= dn);

  ASSERT ((dp[dn-1] & GMP_NUMB_HIGHBIT) != 0);

  np += nn;

  qn = nn - dn;

  if (qn + 1 < dn)

    {

      dp += dn - (qn + 1);

      dn = qn + 1;

    }

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

  if (qh != 0)

    mpn_sub_n (np - dn, np - dn, dp, dn);

  qp += qn;

  dn -= 2;      /* offset dn by 2 for main division loops,

           saving two iterations in mpn_submul_1.  */

  d1 = dp[dn + 1];

  d0 = dp[dn + 0];

  np -= 2;

  n1 = np[1];

  for (i = qn - (dn + 2); i >= 0; i--)

    {

      np--;

      if (UNLIKELY (n1 == d1) && np[1] == d0)

  {

    q = GMP_NUMB_MASK;

    mpn_submul_1 (np - dn, dp, dn + 2, q);

    n1 = np[1];   /* update n1, last loop's value will now be invalid */

  }

      else

  {

    udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);

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

    cy1 = n0 < cy;

    n0 = (n0 - cy) & GMP_NUMB_MASK;

    cy = n1 < cy1;

    n1 -= cy1;

    np[0] = n0;

    if (UNLIKELY (cy != 0))

      {

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

        q--;

      }

  }

      *--qp = q;

    }

  flag = ~CNST_LIMB(0);

  if (dn >= 0)

    {

      for (i = dn; i > 0; i--)

  {

    np--;

    if (UNLIKELY (n1 >= (d1 & flag)))

      {

        q = GMP_NUMB_MASK;

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

        if (UNLIKELY (n1 != cy))

    {

      if (n1 < (cy & flag))

        {

          q--;

          mpn_add_n (np - dn, np - dn, dp, dn + 2);

        }

      else

        flag = 0;

    }

        n1 = np[1];

      }

    else

      {

        udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);

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

        cy1 = n0 < cy;

        n0 = (n0 - cy) & GMP_NUMB_MASK;

        cy = n1 < cy1;

        n1 -= cy1;

        np[0] = n0;

        if (UNLIKELY (cy != 0))

    {

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

      q--;

    }

      }

    *--qp = q;

    /* Truncate operands.  */

    dn--;

    dp++;

  }

      np--;

      if (UNLIKELY (n1 >= (d1 & flag)))

  {

    q = GMP_NUMB_MASK;

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

    if (UNLIKELY (n1 != cy))

      {

        if (n1 < (cy & flag))

    {

      q--;

      add_ssaaaa (np[1], np[0], np[1], np[0], dp[1], dp[0]);

    }

        else

    flag = 0;

      }

    n1 = np[1];

  }

      else

  {

    udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);

    np[1] = n1;

    np[0] = n0;

  }

      *--qp = q;

    }

  ASSERT_ALWAYS (np[1] == n1);

  return qh;

}