mpn/generic/dcpi1_divappr_q.c

/* mpn_dcpi1_divappr_q -- divide-and-conquer division, returning approximate
   quotient.  The quotient returned is either correct, or one too large.

   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, 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-impl.h"
#include "longlong.h"


static mp_limb_t
mpn_dcpi1_divappr_q_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_DIVAPPR_Q_THRESHOLD))
    ql = mpn_sbpi1_divappr_q (qp, np + hi, 2 * lo, dp + hi, lo, dinv->inv32);
  else
    ql = mpn_dcpi1_divappr_q_n (qp, np + hi, dp + hi, lo, dinv, tp);

  if (UNLIKELY (ql != 0))
    {
      mp_size_t i;
      for (i = 0; i < lo; i++)
          qp[i] = GMP_NUMB_MASK;
    }

  return qh;
}

mp_limb_t
mpn_dcpi1_divappr_q (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, qsave;
  mp_ptr tp;
  TMP_DECL;

  TMP_MARK;

  ASSERT (dn >= 6);
  ASSERT (nn > dn);
  ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);

  qn = nn - dn;
  qp += qn;
  np += nn;
  dp += dn;

  if (qn >= dn)
    {
      qn++;                             /* pretend we'll need an extra limb */
      /* 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 */

      tp = TMP_SALLOC_LIMBS (dn);

      /* 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
          {
            if (qn == 2)
              qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2);
            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 + 1;
      while (qn > dn)
          {
            qp -= dn;
            np -= dn;
            mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp);
            qn -= dn;
          }

      /* Since we pretended we'd need an extra quotient limb before, we now
           have made sure the code above left just dn-1=qn quotient limbs to
           develop.  Develop that plus a guard limb. */
      qn--;
      qp -= qn;
      np -= dn;
      qsave = qp[qn];
      mpn_dcpi1_divappr_q_n (qp, np - dn, dp - dn, dn, dinv, tp);
      MPN_COPY_INCR (qp, qp + 1, qn);
      qp[qn] = qsave;
    }
  else    /* (qn < dn) */
    {
      mp_ptr q2p;
#if 0                                   /* not possible since we demand nn > dn */
      if (qn == 0)
          {
            qh = mpn_cmp (np - dn, dp - dn, dn) >= 0;
            if (qh)
              mpn_sub_n (np - dn, np - dn, dp - dn, dn);
            TMP_FREE;
            return qh;
          }
#endif

      qp -= qn;                         /* point at low limb of next quotient block */
      np -= qn;                         /* point in the middle of partial remainder */

      q2p = TMP_SALLOC_LIMBS (qn + 1);
      /* Should we at all check DC_DIVAPPR_Q_THRESHOLD here, or reply on
           callers not to be silly?  */
      if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD))
          {
            qh = mpn_sbpi1_divappr_q (q2p, np - qn - 2, 2 * (qn + 1),
                                            dp - (qn + 1), qn + 1, dinv->inv32);
          }
      else
          {
            /* It is tempting to use qp for recursive scratch and put quotient in
               tp, but the recursive scratch needs one limb too many.  */
            tp = TMP_SALLOC_LIMBS (qn + 1);
            qh = mpn_dcpi1_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv, tp);
          }
      MPN_COPY (qp, q2p + 1, qn);
    }

  TMP_FREE;
  return qh;
}