text: /* 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 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"
  
  /* 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
    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);
  }
  