/* 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 2006-2008, 2010, 2012, 2015, 2021 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"

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

  <-s--><--n--><--n-->

   ____ ______ ______

  |_a2_|___a1_|___a0_|

   |b2_|___b1_|___b0_|

   <-t-><--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 || WANT_FAT_BINARY

#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)

{

  const int __gmpn_cpuvec_initialized = 1;

  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

  vm1[2 * n] = 0;

  TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + (bsm1[n] | asm1[n]), 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_ip1

      cy = 2 * bs1[n] + mpn_addlsh1_n_ip1 (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_ip1

      cy += mpn_addlsh1_n_ip1 (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);

}