/* mpn_toom33_mul -- Multiply {ap,an} and {bp,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.

   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 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/.  */


/*
  Things to work on:

  1. Trim allocation.  The allocations for as1, asm1, bs1, and bsm1 could be
     avoided by instead reusing the pp area and the scratch area.
  2. Use new toom functions for the recursive calls.
*/

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

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

  <-s-><--n--><--n--><--n-->
   ___ ______ ______ ______
  |a3_|___a2_|___a1_|___a0_|
	       |_b1_|___b0_|
	       <-t--><--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_KARATSUBA_THRESHOLD)
#define MAYBE_mul_toom33						\
  (MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD)
#endif

#define TOOM33_MUL_N_REC(p, a, b, n, ws)				\
  do {									\
    if (MAYBE_mul_basecase						\
	&& BELOW_THRESHOLD (n, MUL_KARATSUBA_THRESHOLD))		\
      mpn_mul_basecase (p, a, n, b, n);					\
    else if (! MAYBE_mul_toom33						\
	     || BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD))		\
      mpn_kara_mul_n (p, a, b, n, ws);					\
    else								\
      mpn_toom3_mul_n (p, a, 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;
  TMP_DECL;

#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);

  TMP_MARK;

  as1 = TMP_SALLOC_LIMBS (n + 1);
  asm1 = TMP_SALLOC_LIMBS (n + 1);
  as2 = TMP_SALLOC_LIMBS (n + 1);

  bs1 = TMP_SALLOC_LIMBS (n + 1);
  bsm1 = TMP_SALLOC_LIMBS (n + 1);
  bs2 = TMP_SALLOC_LIMBS (n + 1);

  gp = pp;

  vm1_neg = 0;

  /* Compute as1 and asm1.  */
  cy = mpn_add (gp, a0, n, a2, s);
#if HAVE_NATIVE_mpn_addsub_n
  if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
    {
      cy = mpn_addsub_n (as1, asm1, a1, gp, n);
      as1[n] = 0;
      asm1[n] = 0;
      vm1_neg = 1;
    }
  else
    {
      cy2 = mpn_addsub_n (as1, asm1, gp, a1, n);
      as1[n] = cy + (cy2 >> 1);
      asm1[n] = cy - (cy & 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_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_lshift (as2, a2, s, 1);
  cy += mpn_add_n (as2, a1, as2, s);
  if (s != n)
    cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
  cy += mpn_add_n (as2, a0, as2, n);
#endif
  as2[n] = cy;

  /* Compute bs1 and bsm1.  */
  cy = mpn_add (gp, b0, n, b2, t);
#if HAVE_NATIVE_mpn_addsub_n
  if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
    {
      cy = mpn_addsub_n (bs1, bsm1, b1, gp, n);
      bs1[n] = 0;
      bsm1[n] = 0;
      vm1_neg ^= 1;
    }
  else
    {
      cy2 = mpn_addsub_n (bs1, bsm1, gp, b1, n);
      bs1[n] = cy + (cy2 >> 1);
      bsm1[n] = cy - (cy & 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_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_lshift (bs2, b2, t, 1);
  cy += mpn_add_n (bs2, b1, bs2, t);
  if (t != n)
    cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
  cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1);
  cy += mpn_add_n (bs2, b0, bs2, n);
#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 + 4 * n + 4)

  /* 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, 1^vm1_neg, vinf0, scratch_out);

  TMP_FREE;
}