mpn/generic/mulmid.c

/* mpn_mulmid -- middle product

   Contributed by David Harvey.

   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'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2011 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"


#define CHUNK (200 + MULMID_TOOM42_THRESHOLD)


void
mpn_mulmid (mp_ptr rp,
            mp_srcptr ap, mp_size_t an,
            mp_srcptr bp, mp_size_t bn)
{
  mp_size_t rn, k;
  mp_ptr scratch, temp;

  ASSERT (an >= bn);
  ASSERT (bn >= 1);
  ASSERT (! MPN_OVERLAP_P (rp, an - bn + 3, ap, an));
  ASSERT (! MPN_OVERLAP_P (rp, an - bn + 3, bp, bn));

  if (bn < MULMID_TOOM42_THRESHOLD)
    {
      /* region not tall enough to make toom42 worthwhile for any portion */

      if (an < CHUNK)
	{
	  /* region not too wide either, just call basecase directly */
	  mpn_mulmid_basecase (rp, ap, an, bp, bn);
	  return;
	}

      /* Region quite wide. For better locality, use basecase on chunks:

	 AAABBBCC..
	 .AAABBBCC.
	 ..AAABBBCC
      */

      k = CHUNK - bn + 1;    /* number of diagonals per chunk */

      /* first chunk (marked A in the above diagram) */
      mpn_mulmid_basecase (rp, ap, CHUNK, bp, bn);

      /* remaining chunks (B, C, etc) */
      an -= k;

      while (an >= CHUNK)
	{
	  mp_limb_t t0, t1, cy;
	  ap += k, rp += k;
	  t0 = rp[0], t1 = rp[1];
	  mpn_mulmid_basecase (rp, ap, CHUNK, bp, bn);
	  ADDC_LIMB (cy, rp[0], rp[0], t0);    /* add back saved limbs */
	  MPN_INCR_U (rp + 1, k + 1, t1 + cy);
	  an -= k;
	}

      if (an >= bn)
	{
	  /* last remaining chunk */
	  mp_limb_t t0, t1, cy;
	  ap += k, rp += k;
	  t0 = rp[0], t1 = rp[1];
	  mpn_mulmid_basecase (rp, ap, an, bp, bn);
	  ADDC_LIMB (cy, rp[0], rp[0], t0);
	  MPN_INCR_U (rp + 1, an - bn + 2, t1 + cy);
	}

      return;
    }

  /* region is tall enough for toom42 */

  rn = an - bn + 1;

  if (rn < MULMID_TOOM42_THRESHOLD)
    {
      /* region not wide enough to make toom42 worthwhile for any portion */

      TMP_DECL;

      if (bn < CHUNK)
	{
	  /* region not too tall either, just call basecase directly */
	  mpn_mulmid_basecase (rp, ap, an, bp, bn);
	  return;
	}

      /* Region quite tall. For better locality, use basecase on chunks:

	 AAAAA....
	 .AAAAA...
	 ..BBBBB..
	 ...BBBBB.
	 ....CCCCC
      */

      TMP_MARK;

      temp = TMP_ALLOC_LIMBS (rn + 2);

      /* first chunk (marked A in the above diagram) */
      bp += bn - CHUNK, an -= bn - CHUNK;
      mpn_mulmid_basecase (rp, ap, an, bp, CHUNK);

      /* remaining chunks (B, C, etc) */
      bn -= CHUNK;

      while (bn >= CHUNK)
	{
	  ap += CHUNK, bp -= CHUNK;
	  mpn_mulmid_basecase (temp, ap, an, bp, CHUNK);
	  mpn_add_n (rp, rp, temp, rn + 2);
	  bn -= CHUNK;
	}

      if (bn)
	{
	  /* last remaining chunk */
	  ap += CHUNK, bp -= bn;
	  mpn_mulmid_basecase (temp, ap, rn + bn - 1, bp, bn);
	  mpn_add_n (rp, rp, temp, rn + 2);
	}

      TMP_FREE;
      return;
    }

  /* we're definitely going to use toom42 somewhere */

  if (bn > rn)
    {
      /* slice region into chunks, use toom42 on all chunks except possibly
	 the last:

         AA....
         .AA...
         ..BB..
         ...BB.
         ....CC
      */

      TMP_DECL;
      TMP_MARK;

      temp = TMP_ALLOC_LIMBS (rn + 2 + mpn_toom42_mulmid_itch (rn));
      scratch = temp + rn + 2;

      /* first chunk (marked A in the above diagram) */
      bp += bn - rn;
      mpn_toom42_mulmid (rp, ap, bp, rn, scratch);

      /* remaining chunks (B, C, etc) */
      bn -= rn;

      while (bn >= rn)
        {
          ap += rn, bp -= rn;
	  mpn_toom42_mulmid (temp, ap, bp, rn, scratch);
          mpn_add_n (rp, rp, temp, rn + 2);
          bn -= rn;
        }

      if (bn)
        {
          /* last remaining chunk */
          ap += rn, bp -= bn;
	  mpn_mulmid (temp, ap, rn + bn - 1, bp, bn);
          mpn_add_n (rp, rp, temp, rn + 2);
        }

      TMP_FREE;
    }
  else
    {
      /* slice region into chunks, use toom42 on all chunks except possibly
	 the last:

         AAABBBCC..
         .AAABBBCC.
         ..AAABBBCC
      */

      TMP_DECL;
      TMP_MARK;

      scratch = TMP_ALLOC_LIMBS (mpn_toom42_mulmid_itch (bn));

      /* first chunk (marked A in the above diagram) */
      mpn_toom42_mulmid (rp, ap, bp, bn, scratch);

      /* remaining chunks (B, C, etc) */
      rn -= bn;

      while (rn >= bn)
        {
	  mp_limb_t t0, t1, cy;
          ap += bn, rp += bn;
          t0 = rp[0], t1 = rp[1];
          mpn_toom42_mulmid (rp, ap, bp, bn, scratch);
	  ADDC_LIMB (cy, rp[0], rp[0], t0);     /* add back saved limbs */
	  MPN_INCR_U (rp + 1, bn + 1, t1 + cy);
	  rn -= bn;
        }

      TMP_FREE;

      if (rn)
        {
          /* last remaining chunk */
	  mp_limb_t t0, t1, cy;
          ap += bn, rp += bn;
          t0 = rp[0], t1 = rp[1];
          mpn_mulmid (rp, ap, rn + bn - 1, bp, bn);
	  ADDC_LIMB (cy, rp[0], rp[0], t0);
	  MPN_INCR_U (rp + 1, rn + 1, t1 + cy);
        }
    }
}