/* mpn_remove -- divide out all multiples of odd mpn number from another mpn

   number.

   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 2009, 2012-2014, 2017 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"

#if GMP_LIMB_BITS > 50

#define LOG 50

#else

#define LOG GMP_LIMB_BITS

#endif

/* Input: U = {up,un}, V = {vp,vn} must be odd, cap

   Ouput  W = {wp,*wn} allocation need is exactly *wn

   Set W = U / V^k, where k is the largest integer <= cap such that the

   division yields an integer.

   FIXME: We currently allow any operand overlap.  This is quite non mpn-ish

   and might be changed, since it cost significant temporary space.

   * If we require W to have space for un + 1 limbs, we could save qp or qp2

     (but we will still need to copy things into wp 50% of the time).

   * If we allow ourselves to clobber U, we could save the other of qp and qp2,

     and the initial COPY (but also here we would need un + 1 limbs).

*/

/* FIXME: We need to wrap mpn_bdiv_qr due to the itch interface.  This need

   indicates a flaw in the current itch mechanism: Which operands not greater

   than un,un will incur the worst itch?  We need a parallel foo_maxitch set

   of functions.  */

static void

mpn_bdiv_qr_wrap (mp_ptr qp, mp_ptr rp,

      mp_srcptr np, mp_size_t nn,

      mp_srcptr dp, mp_size_t dn)

{

  mp_ptr scratch_out;

  TMP_DECL;

  TMP_MARK;

  scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (nn, dn));

  mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch_out);

  TMP_FREE;

}

mp_bitcnt_t

mpn_remove (mp_ptr wp, mp_size_t *wn,

      mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn,

      mp_bitcnt_t cap)

{

  mp_srcptr pwpsp[LOG];

  mp_size_t pwpsn[LOG];

  mp_size_t npowers;

  mp_ptr tp, qp, np, qp2;

  mp_srcptr pp;

  mp_size_t pn, nn, qn, i;

  mp_bitcnt_t pwr;

  TMP_DECL;

  ASSERT (un > 0);

  ASSERT (vn > 0);

  ASSERT (vp[0] % 2 != 0);  /* 2-adic division wants odd numbers */

  ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */

  TMP_MARK;

  TMP_ALLOC_LIMBS_3 (qp, un + 1, /* quotient, alternating */

         qp2, un + 1, /* quotient, alternating */

         tp, (un + 1 + vn) / 2); /* remainder */

  pp = vp;

  pn = vn;

  MPN_COPY (qp, up, un);

  qn = un;

  npowers = 0;

  while (qn >= pn)

    {

      qp[qn] = 0;

      mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn);

      if (!mpn_zero_p (tp, pn))

  {

    if (mpn_cmp (tp, pp, pn) != 0)

      break;   /* could not divide by V^npowers */

  }

      MP_PTR_SWAP (qp, qp2);

      qn = qn - pn;

      mpn_neg (qp, qp, qn+1);

      qn += qp[qn] != 0;

      pwpsp[npowers] = pp;

      pwpsn[npowers] = pn;

      ++npowers;

      if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)

  break;

      nn = 2 * pn - 1;    /* next power will be at least this large */

      if (nn > qn)

  break;      /* next power would be overlarge */

      if (npowers == 1)    /* Alloc once, but only if it's needed */

  np = TMP_ALLOC_LIMBS (qn + LOG);  /* powers of V */

      else

  np += pn;

      mpn_sqr (np, pp, pn);

      pn = nn + (np[nn] != 0);

      pp = np;

    }

  pwr = ((mp_bitcnt_t) 1 << npowers) - 1;

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

    {

      pn = pwpsn[i];

      if (qn < pn)

  continue;

      if (pwr + ((mp_bitcnt_t) 1 << i) > cap)

  continue;   /* V^i would bring us past cap */

      qp[qn] = 0;

      mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pwpsp[i], pn);

      if (!mpn_zero_p (tp, pn))

  {

    if (mpn_cmp (tp, pwpsp[i], pn) != 0)

      continue;   /* could not divide by V^i */

  }

      MP_PTR_SWAP (qp, qp2);

      qn = qn - pn;

      mpn_neg (qp, qp, qn+1);

      qn += qp[qn] != 0;

      pwr += (mp_bitcnt_t) 1 << i;

    }

  MPN_COPY (wp, qp, qn);

  *wn = qn;

  TMP_FREE;

  return pwr;

}