mpn/generic/toom33_mul.c

/* mpn_toom33_mul -- Multiply {ap,an} and {p,bn} where an and bn are close in
   size.  Or more accurately, bn <= an < (3/2)bn.

   Contributed to the GNU project by Torbjorn Granlund.
   Additional improvements by Marco Bodrato.

   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 GNU MP RELEASE.

Copyright 2006, 2007, 2008, 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 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.

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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */


#include "gmp.h"
#include "gmp-impl.h"

/* Evaluate in: -1, 0, +1, +2, +inf

  <-s--><--n--><--n--><--n-->
   ____ ______ ______ ______
  |_a3_|___a2_|___a1_|___a0_|
   |b3_|___b2_|___b1_|___b0_|
   <-t-><--n--><--n--><--n-->

  v0  =  a0         * b0          #   A(0)*B(0)
  v1  = (a0+ a1+ a2)*(b0+ b1+ b2) #   A(1)*B(1)      ah  <= 2  bh <= 2
  vm1 = (a0- a1+ a2)*(b0- b1+ b2) #  A(-1)*B(-1)    |ah| <= 1  bh <= 1
  v2  = (a0+2a1+4a2)*(b0+2b1+4b2) #   A(2)*B(2)      ah  <= 6  bh <= 6
  vinf=          a2 *         b2  # A(inf)*B(inf)
*/

#if TUNE_PROGRAM_BUILD
#define MAYBE_mul_basecase 1
#define MAYBE_mul_toom33   1
#else
#define MAYBE_mul_basecase						\
  (MUL_TOOM33_THRESHOLD < 3 * MUL_TOOM22_THRESHOLD)
#define MAYBE_mul_toom33						\
  (MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD)
#endif

/* FIXME: TOOM33_MUL_N_REC is not quite right for a balanced
   multiplication at the infinity point. We may have
   MAYBE_mul_basecase == 0, and still get s just below
   MUL_TOOM22_THRESHOLD. If MUL_TOOM33_THRESHOLD == 7, we can even get
   s == 1 and mpn_toom22_mul will crash.
*/

#define TOOM33_MUL_N_REC(p, a, b, n, ws)				\
  do {									\
    if (MAYBE_mul_basecase						\
	&& BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD))			\
      mpn_mul_basecase (p, a, n, b, n);					\
    else if (! MAYBE_mul_toom33						\
	     || BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD))		\
      mpn_toom22_mul (p, a, n, b, n, ws);				\
    else								\
      mpn_toom33_mul (p, a, n, b, n, ws);				\
  } while (0)

void
mpn_toom33_mul (mp_ptr pp,
		mp_srcptr ap, mp_size_t an,
		mp_srcptr bp, mp_size_t bn,
		mp_ptr scratch)
{
  mp_size_t n, s, t;
  int vm1_neg;
  mp_limb_t cy, vinf0;
  mp_ptr gp;
  mp_ptr as1, asm1, as2;
  mp_ptr bs1, bsm1, bs2;

#define a0  ap
#define a1  (ap + n)
#define a2  (ap + 2*n)
#define b0  bp
#define b1  (bp + n)
#define b2  (bp + 2*n)

  n = (an + 2) / (size_t) 3;

  s = an - 2 * n;
  t = bn - 2 * n;

  ASSERT (an >= bn);

  ASSERT (0 < s && s <= n);
  ASSERT (0 < t && t <= n);

  as1  = scratch + 4 * n + 4;
  asm1 = scratch + 2 * n + 2;
  as2 = pp + n + 1;

  bs1 = pp;
  bsm1 = scratch + 3 * n + 3; /* we need 4n+4 <= 4n+s+t */
  bs2 = pp + 2 * n + 2;

  gp = scratch;

  vm1_neg = 0;

  /* Compute as1 and asm1.  */
  cy = mpn_add (gp, a0, n, a2, s);
#if HAVE_NATIVE_mpn_add_n_sub_n
  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
    {
      cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
      as1[n] = cy >> 1;
      asm1[n] = 0;
      vm1_neg = 1;
    }
  else
    {
      mp_limb_t cy2;
      cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
      as1[n] = cy + (cy2 >> 1);
      asm1[n] = cy - (cy2 & 1);
    }
#else
  as1[n] = cy + mpn_add_n (as1, gp, a1, n);
  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
    {
      mpn_sub_n (asm1, a1, gp, n);
      asm1[n] = 0;
      vm1_neg = 1;
    }
  else
    {
      cy -= mpn_sub_n (asm1, gp, a1, n);
      asm1[n] = cy;
    }
#endif

  /* Compute as2.  */
#if HAVE_NATIVE_mpn_rsblsh1_n
  cy = mpn_add_n (as2, a2, as1, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
  cy += as1[n];
  cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
#else
#if HAVE_NATIVE_mpn_addlsh1_n
  cy  = mpn_addlsh1_n (as2, a1, a2, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
  cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
#else
  cy = mpn_add_n (as2, a2, as1, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
  cy += as1[n];
  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
  cy -= mpn_sub_n (as2, as2, a0, n);
#endif
#endif
  as2[n] = cy;

  /* Compute bs1 and bsm1.  */
  cy = mpn_add (gp, b0, n, b2, t);
#if HAVE_NATIVE_mpn_add_n_sub_n
  if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
    {
      cy = mpn_add_n_sub_n (bs1, bsm1, b1, gp, n);
      bs1[n] = cy >> 1;
      bsm1[n] = 0;
      vm1_neg ^= 1;
    }
  else
    {
      mp_limb_t cy2;
      cy2 = mpn_add_n_sub_n (bs1, bsm1, gp, b1, n);
      bs1[n] = cy + (cy2 >> 1);
      bsm1[n] = cy - (cy2 & 1);
    }
#else
  bs1[n] = cy + mpn_add_n (bs1, gp, b1, n);
  if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
    {
      mpn_sub_n (bsm1, b1, gp, n);
      bsm1[n] = 0;
      vm1_neg ^= 1;
    }
  else
    {
      cy -= mpn_sub_n (bsm1, gp, b1, n);
      bsm1[n] = cy;
    }
#endif

  /* Compute bs2.  */
#if HAVE_NATIVE_mpn_rsblsh1_n
  cy = mpn_add_n (bs2, b2, bs1, t);
  if (t != n)
    cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
  cy += bs1[n];
  cy = 2 * cy + mpn_rsblsh1_n (bs2, b0, bs2, n);
#else
#if HAVE_NATIVE_mpn_addlsh1_n
  cy  = mpn_addlsh1_n (bs2, b1, b2, t);
  if (t != n)
    cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
  cy = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n);
#else
  cy  = mpn_add_n (bs2, bs1, b2, t);
  if (t != n)
    cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
  cy += bs1[n];
  cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1);
  cy -= mpn_sub_n (bs2, bs2, b0, n);
#endif
#endif
  bs2[n] = cy;

  ASSERT (as1[n] <= 2);
  ASSERT (bs1[n] <= 2);
  ASSERT (asm1[n] <= 1);
  ASSERT (bsm1[n] <= 1);
  ASSERT (as2[n] <= 6);
  ASSERT (bs2[n] <= 6);

#define v0    pp				/* 2n */
#define v1    (pp + 2 * n)			/* 2n+1 */
#define vinf  (pp + 4 * n)			/* s+t */
#define vm1   scratch				/* 2n+1 */
#define v2    (scratch + 2 * n + 1)		/* 2n+2 */
#define scratch_out  (scratch + 5 * n + 5)

  /* vm1, 2n+1 limbs */
#ifdef SMALLER_RECURSION
  TOOM33_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
  cy = 0;
  if (asm1[n] != 0)
    cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
  if (bsm1[n] != 0)
    cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
  vm1[2 * n] = cy;
#else
  TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + 1, scratch_out);
#endif

  TOOM33_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out);	/* v2, 2n+1 limbs */

  /* vinf, s+t limbs */
  if (s > t)  mpn_mul (vinf, a2, s, b2, t);
  else        TOOM33_MUL_N_REC (vinf, a2, b2, s, scratch_out);

  vinf0 = vinf[0];				/* v1 overlaps with this */

#ifdef SMALLER_RECURSION
  /* v1, 2n+1 limbs */
  TOOM33_MUL_N_REC (v1, as1, bs1, n, scratch_out);
  if (as1[n] == 1)
    {
      cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
    }
  else if (as1[n] != 0)
    {
#if HAVE_NATIVE_mpn_addlsh1_n
      cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
#else
      cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
#endif
    }
  else
    cy = 0;
  if (bs1[n] == 1)
    {
      cy += mpn_add_n (v1 + n, v1 + n, as1, n);
    }
  else if (bs1[n] != 0)
    {
#if HAVE_NATIVE_mpn_addlsh1_n
      cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
#else
      cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
#endif
    }
  v1[2 * n] = cy;
#else
  cy = vinf[1];
  TOOM33_MUL_N_REC (v1, as1, bs1, n + 1, scratch_out);
  vinf[1] = cy;
#endif

  TOOM33_MUL_N_REC (v0, ap, bp, n, scratch_out);	/* v0, 2n limbs */

  mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);
}