/* mpn_toom53_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 5/3

   times as large as bn.  Or more accurately, (4/3)bn < an < (5/2)bn.

   Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.

   The idea of applying toom to unbalanced multiplication is due to Marco

   Bodrato and Alberto Zanoni.

   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, 2012, 2014, 2015 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: 0, +1, -1, +2, -2, 1/2, +inf

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

   ___ ______ ______ ______ ______

  |a4_|___a3_|___a2_|___a1_|___a0_|

         |__b2|___b1_|___b0_|

         <-t--><--n--><--n-->

  v0  =    a0                  *  b0          #    A(0)*B(0)

  v1  = (  a0+ a1+ a2+ a3+  a4)*( b0+ b1+ b2) #    A(1)*B(1)      ah  <= 4   bh <= 2

  vm1 = (  a0- a1+ a2- a3+  a4)*( b0- b1+ b2) #   A(-1)*B(-1)    |ah| <= 2   bh <= 1

  v2  = (  a0+2a1+4a2+8a3+16a4)*( b0+2b1+4b2) #    A(2)*B(2)      ah  <= 30  bh <= 6

  vm2 = (  a0-2a1+4a2-8a3+16a4)*( b0-2b1+4b2) #    A(2)*B(2)     -9<=ah<=20 -1<=bh<=4

  vh  = (16a0+8a1+4a2+2a3+  a4)*(4b0+2b1+ b2) #  A(1/2)*B(1/2)    ah  <= 30  bh <= 6

  vinf=                     a4 *          b2  #  A(inf)*B(inf)

*/

void

mpn_toom53_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;

  mp_limb_t cy;

  mp_ptr gp;

  mp_ptr as1, asm1, as2, asm2, ash;

  mp_ptr bs1, bsm1, bs2, bsm2, bsh;

  mp_ptr tmp;

  enum toom7_flags flags;

  TMP_DECL;

#define a0  ap

#define a1  (ap + n)

#define a2  (ap + 2*n)

#define a3  (ap + 3*n)

#define a4  (ap + 4*n)

#define b0  bp

#define b1  (bp + n)

#define b2  (bp + 2*n)

  n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);

  s = an - 4 * n;

  t = bn - 2 * n;

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

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

  TMP_MARK;

  tmp = TMP_ALLOC_LIMBS (10 * (n + 1));

  as1  = tmp; tmp += n + 1;

  asm1 = tmp; tmp += n + 1;

  as2  = tmp; tmp += n + 1;

  asm2 = tmp; tmp += n + 1;

  ash  = tmp; tmp += n + 1;

  bs1  = tmp; tmp += n + 1;

  bsm1 = tmp; tmp += n + 1;

  bs2  = tmp; tmp += n + 1;

  bsm2 = tmp; tmp += n + 1;

  bsh  = tmp; tmp += n + 1;

  gp = pp;

  /* Compute as1 and asm1.  */

  flags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, gp));

  /* Compute as2 and asm2. */

  flags = (enum toom7_flags) (flags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, gp)));

  /* Compute ash = 16 a0 + 8 a1 + 4 a2 + 2 a3 + a4

     = 2*(2*(2*(2*a0 + a1) + a2) + a3) + a4  */

#if HAVE_NATIVE_mpn_addlsh1_n

  cy = mpn_addlsh1_n (ash, a1, a0, n);

  cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n);

  cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n);

  if (s < n)

    {

      mp_limb_t cy2;

      cy2 = mpn_addlsh1_n (ash, a4, ash, s);

      ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1);

      MPN_INCR_U (ash + s, n+1-s, cy2);

    }

  else

    ash[n] = 2*cy + mpn_addlsh1_n (ash, a4, ash, n);

#else

  cy = mpn_lshift (ash, a0, n, 1);

  cy += mpn_add_n (ash, ash, a1, n);

  cy = 2*cy + mpn_lshift (ash, ash, n, 1);

  cy += mpn_add_n (ash, ash, a2, n);

  cy = 2*cy + mpn_lshift (ash, ash, n, 1);

  cy += mpn_add_n (ash, ash, a3, n);

  cy = 2*cy + mpn_lshift (ash, ash, n, 1);

  ash[n] = cy + mpn_add (ash, ash, n, a4, s);

#endif

  /* Compute bs1 and bsm1.  */

  bs1[n] = mpn_add (bs1, b0, n, b2, t);   /* b0 + b2 */

#if HAVE_NATIVE_mpn_add_n_sub_n

  if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)

    {

      bs1[n] = mpn_add_n_sub_n (bs1, bsm1, b1, bs1, n) >> 1;

      bsm1[n] = 0;

      flags = (enum toom7_flags) (flags ^ toom7_w3_neg);

    }

  else

    {

      cy = mpn_add_n_sub_n (bs1, bsm1, bs1, b1, n);

      bsm1[n] = bs1[n] - (cy & 1);

      bs1[n] += (cy >> 1);

    }

#else

  if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)

    {

      mpn_sub_n (bsm1, b1, bs1, n);

      bsm1[n] = 0;

      flags = (enum toom7_flags) (flags ^ toom7_w3_neg);

    }

  else

    {

      bsm1[n] = bs1[n] - mpn_sub_n (bsm1, bs1, b1, n);

    }

  bs1[n] += mpn_add_n (bs1, bs1, b1, n);  /* b0+b1+b2 */

#endif

  /* Compute bs2 and bsm2. */

#if HAVE_NATIVE_mpn_addlsh_n || HAVE_NATIVE_mpn_addlsh2_n

#if HAVE_NATIVE_mpn_addlsh2_n

  cy = mpn_addlsh2_n (bs2, b0, b2, t);

#else /* HAVE_NATIVE_mpn_addlsh_n */

  cy = mpn_addlsh_n (bs2, b0, b2, t, 2);

#endif

  if (t < n)

    cy = mpn_add_1 (bs2 + t, b0 + t, n - t, cy);

  bs2[n] = cy;

#else

  cy = mpn_lshift (gp, b2, t, 2);

  bs2[n] = mpn_add (bs2, b0, n, gp, t);

  MPN_INCR_U (bs2 + t, n+1-t, cy);

#endif

  gp[n] = mpn_lshift (gp, b1, n, 1);

#if HAVE_NATIVE_mpn_add_n_sub_n

  if (mpn_cmp (bs2, gp, n+1) < 0)

    {

      ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, gp, bs2, n+1));

      flags = (enum toom7_flags) (flags ^ toom7_w1_neg);

    }

  else

    {

      ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, bs2, gp, n+1));

    }

#else

  if (mpn_cmp (bs2, gp, n+1) < 0)

    {

      ASSERT_NOCARRY (mpn_sub_n (bsm2, gp, bs2, n+1));

      flags = (enum toom7_flags) (flags ^ toom7_w1_neg);

    }

  else

    {

      ASSERT_NOCARRY (mpn_sub_n (bsm2, bs2, gp, n+1));

    }

  mpn_add_n (bs2, bs2, gp, n+1);

#endif

  /* Compute bsh = 4 b0 + 2 b1 + b2 = 2*(2*b0 + b1)+b2.  */

#if HAVE_NATIVE_mpn_addlsh1_n

  cy = mpn_addlsh1_n (bsh, b1, b0, n);

  if (t < n)

    {

      mp_limb_t cy2;

      cy2 = mpn_addlsh1_n (bsh, b2, bsh, t);

      bsh[n] = 2*cy + mpn_lshift (bsh + t, bsh + t, n - t, 1);

      MPN_INCR_U (bsh + t, n+1-t, cy2);

    }

  else

    bsh[n] = 2*cy + mpn_addlsh1_n (bsh, b2, bsh, n);

#else

  cy = mpn_lshift (bsh, b0, n, 1);

  cy += mpn_add_n (bsh, bsh, b1, n);

  cy = 2*cy + mpn_lshift (bsh, bsh, n, 1);

  bsh[n] = cy + mpn_add (bsh, bsh, n, b2, t);

#endif

  ASSERT (as1[n] <= 4);

  ASSERT (bs1[n] <= 2);

  ASSERT (asm1[n] <= 2);

  ASSERT (bsm1[n] <= 1);

  ASSERT (as2[n] <= 30);

  ASSERT (bs2[n] <= 6);

  ASSERT (asm2[n] <= 20);

  ASSERT (bsm2[n] <= 4);

  ASSERT (ash[n] <= 30);

  ASSERT (bsh[n] <= 6);

#define v0    pp        /* 2n */

#define v1    (pp + 2 * n)      /* 2n+1 */

#define vinf  (pp + 6 * n)      /* s+t */

#define v2    scratch        /* 2n+1 */

#define vm2   (scratch + 2 * n + 1)    /* 2n+1 */

#define vh    (scratch + 4 * n + 2)    /* 2n+1 */

#define vm1   (scratch + 6 * n + 3)    /* 2n+1 */

#define scratch_out (scratch + 8 * n + 4)    /* 2n+1 */

  /* Total scratch need: 10*n+5 */

  /* Must be in allocation order, as they overwrite one limb beyond

   * 2n+1. */

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

  mpn_mul_n (vm2, asm2, bsm2, n + 1);   /* vm2, 2n+1 limbs */

  mpn_mul_n (vh, ash, bsh, n + 1);   /* vh, 2n+1 limbs */

  /* vm1, 2n+1 limbs */

#ifdef SMALLER_RECURSION

  mpn_mul_n (vm1, asm1, bsm1, n);

  if (asm1[n] == 1)

    {

      cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);

    }

  else if (asm1[n] == 2)

    {

#if HAVE_NATIVE_mpn_addlsh1_n_ip1

      cy = 2 * bsm1[n] + mpn_addlsh1_n_ip1 (vm1 + n, bsm1, n);

#else

      cy = 2 * bsm1[n] + mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2));

#endif

    }

  else

    cy = 0;

  if (bsm1[n] != 0)

    cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);

  vm1[2 * n] = cy;

#else /* SMALLER_RECURSION */

  vm1[2 * n] = 0;

  mpn_mul_n (vm1, asm1, bsm1, n + ((asm1[n] | bsm1[n]) != 0));

#endif /* SMALLER_RECURSION */

  /* v1, 2n+1 limbs */

#ifdef SMALLER_RECURSION

  mpn_mul_n (v1, as1, bs1, n);

  if (as1[n] == 1)

    {

      cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);

    }

  else if (as1[n] == 2)

    {

#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 if (as1[n] != 0)

    {

      cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]);

    }

  else

    cy = 0;

  if (bs1[n] == 1)

    {

      cy += mpn_add_n (v1 + n, v1 + n, as1, n);

    }

  else if (bs1[n] == 2)

    {

#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 /* SMALLER_RECURSION */

  v1[2 * n] = 0;

  mpn_mul_n (v1, as1, bs1, n + ((as1[n] | bs1[n]) != 0));

#endif /* SMALLER_RECURSION */

  mpn_mul_n (v0, a0, b0, n);     /* v0, 2n limbs */

  /* vinf, s+t limbs */

  if (s > t)  mpn_mul (vinf, a4, s, b2, t);

  else        mpn_mul (vinf, b2, t, a4, s);

  mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t,

           scratch_out);

  TMP_FREE;

}