/* matrix22_mul.c.

   Contributed by Niels Möller and Marco Bodrato.

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY

   SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST

   GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2003-2005, 2008, 2009 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"

#include "longlong.h"

#define MUL(rp, ap, an, bp, bn) do {   \

  if (an >= bn)         \

    mpn_mul (rp, ap, an, bp, bn);   \

  else            \

    mpn_mul (rp, bp, bn, ap, an);   \

} while (0)

/* Inputs are unsigned. */

static int

abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)

{

  int c;

  MPN_CMP (c, ap, bp, n);

  if (c >= 0)

    {

      mpn_sub_n (rp, ap, bp, n);

      return 0;

    }

  else

    {

      mpn_sub_n (rp, bp, ap, n);

      return 1;

    }

}

static int

add_signed_n (mp_ptr rp,

        mp_srcptr ap, int as, mp_srcptr bp, int bs, mp_size_t n)

{

  if (as != bs)

    return as ^ abs_sub_n (rp, ap, bp, n);

  else

    {

      ASSERT_NOCARRY (mpn_add_n (rp, ap, bp, n));

      return as;

    }

}

mp_size_t

mpn_matrix22_mul_itch (mp_size_t rn, mp_size_t mn)

{

  if (BELOW_THRESHOLD (rn, MATRIX22_STRASSEN_THRESHOLD)

      || BELOW_THRESHOLD (mn, MATRIX22_STRASSEN_THRESHOLD))

    return 3*rn + 2*mn;

  else

    return 3*(rn + mn) + 5;

}

/* Algorithm:

    / s0 \   /  1  0  0  0 \ / r0 \

    | s1 |   |  0  1  0  1 | | r1 |

    | s2 |   |  0  0 -1  1 | | r2 |

    | s3 | = |  0  1 -1  1 | \ r3 /

    | s4 |   | -1  1 -1  1 |

    | s5 |   |  0  1  0  0 |

    \ s6 /   \  0  0  1  0 /

    / t0 \   /  1  0  0  0 \ / m0 \

    | t1 |   |  0  1  0  1 | | m1 |

    | t2 |   |  0  0 -1  1 | | m2 |

    | t3 | = |  0  1 -1  1 | \ m3 /

    | t4 |   | -1  1 -1  1 |

    | t5 |   |  0  1  0  0 |

    \ t6 /   \  0  0  1  0 /

  Note: the two matrices above are the same, but s_i and t_i are used

  in the same product, only for i<4, see "A Strassen-like Matrix

  Multiplication suited for squaring and higher power computation" by

  M. Bodrato, in Proceedings of ISSAC 2010.

    / r0 \   / 1 0  0  0  0  1  0 \ / s0*t0 \

    | r1 | = | 0 0 -1  1 -1  1  0 | | s1*t1 |

    | r2 |   | 0 1  0 -1  0 -1 -1 | | s2*t2 |

    \ r3 /   \ 0 1  1 -1  0 -1  0 / | s3*t3 |

            | s4*t5 |

            | s5*t6 |

            \ s6*t4 /

  The scheduling uses two temporaries U0 and U1 to store products, and

  two, S0 and T0, to store combinations of entries of the two

  operands.

*/

/* Computes R = R * M. Elements are numbers R = (r0, r1; r2, r3).

 *

 * Resulting elements are of size up to rn + mn + 1.

 *

 * Temporary storage: 3 rn + 3 mn + 5. */

static void

mpn_matrix22_mul_strassen (mp_ptr r0, mp_ptr r1, mp_ptr r2, mp_ptr r3, mp_size_t rn,

         mp_srcptr m0, mp_srcptr m1, mp_srcptr m2, mp_srcptr m3, mp_size_t mn,

         mp_ptr tp)

{

  mp_ptr s0, t0, u0, u1;

  int r1s, r3s, s0s, t0s, u1s;

  s0 = tp; tp += rn + 1;

  t0 = tp; tp += mn + 1;

  u0 = tp; tp += rn + mn + 1;

  u1 = tp; /* rn + mn + 2 */

  MUL (u0, r1, rn, m2, mn);    /* u5 = s5 * t6 */

  r3s = abs_sub_n (r3, r3, r2, rn); /* r3 - r2 */

  if (r3s)

    {

      r1s = abs_sub_n (r1, r1, r3, rn);

      r1[rn] = 0;

    }

  else

    {

      r1[rn] = mpn_add_n (r1, r1, r3, rn);

      r1s = 0;        /* r1 - r2 + r3  */

    }

  if (r1s)

    {

      s0[rn] = mpn_add_n (s0, r1, r0, rn);

      s0s = 0;

    }

  else if (r1[rn] != 0)

    {

      s0[rn] = r1[rn] - mpn_sub_n (s0, r1, r0, rn);

      s0s = 1;        /* s4 = -r0 + r1 - r2 + r3 */

          /* Reverse sign! */

    }

  else

    {

      s0s = abs_sub_n (s0, r0, r1, rn);

      s0[rn] = 0;

    }

  MUL (u1, r0, rn, m0, mn);    /* u0 = s0 * t0 */

  r0[rn+mn] = mpn_add_n (r0, u0, u1, rn + mn);

  ASSERT (r0[rn+mn] < 2);   /* u0 + u5 */

  t0s = abs_sub_n (t0, m3, m2, mn);

  u1s = r3s^t0s^1;      /* Reverse sign! */

  MUL (u1, r3, rn, t0, mn);    /* u2 = s2 * t2 */

  u1[rn+mn] = 0;

  if (t0s)

    {

      t0s = abs_sub_n (t0, m1, t0, mn);

      t0[mn] = 0;

    }

  else

    {

      t0[mn] = mpn_add_n (t0, t0, m1, mn);

    }

  /* FIXME: Could be simplified if we had space for rn + mn + 2 limbs

     at r3. I'd expect that for matrices of random size, the high

     words t0[mn] and r1[rn] are non-zero with a pretty small

     probability. If that can be confirmed this should be done as an

     unconditional rn x (mn+1) followed by an if (UNLIKELY (r1[rn]))

     add_n. */

  if (t0[mn] != 0)

    {

      MUL (r3, r1, rn, t0, mn + 1);  /* u3 = s3 * t3 */

      ASSERT (r1[rn] < 2);

      if (r1[rn] != 0)

  mpn_add_n (r3 + rn, r3 + rn, t0, mn + 1);

    }

  else

    {

      MUL (r3, r1, rn + 1, t0, mn);

    }

  ASSERT (r3[rn+mn] < 4);

  u0[rn+mn] = 0;

  if (r1s^t0s)

    {

      r3s = abs_sub_n (r3, u0, r3, rn + mn + 1);

    }

  else

    {

      ASSERT_NOCARRY (mpn_add_n (r3, r3, u0, rn + mn + 1));

      r3s = 0;        /* u3 + u5 */

    }

  if (t0s)

    {

      t0[mn] = mpn_add_n (t0, t0, m0, mn);

    }

  else if (t0[mn] != 0)

    {

      t0[mn] -= mpn_sub_n (t0, t0, m0, mn);

    }

  else

    {

      t0s = abs_sub_n (t0, t0, m0, mn);

    }

  MUL (u0, r2, rn, t0, mn + 1);    /* u6 = s6 * t4 */

  ASSERT (u0[rn+mn] < 2);

  if (r1s)

    {

      ASSERT_NOCARRY (mpn_sub_n (r1, r2, r1, rn));

    }

  else

    {

      r1[rn] += mpn_add_n (r1, r1, r2, rn);

    }

  rn++;

  t0s = add_signed_n (r2, r3, r3s, u0, t0s, rn + mn);

          /* u3 + u5 + u6 */

  ASSERT (r2[rn+mn-1] < 4);

  r3s = add_signed_n (r3, r3, r3s, u1, u1s, rn + mn);

          /* -u2 + u3 + u5  */

  ASSERT (r3[rn+mn-1] < 3);

  MUL (u0, s0, rn, m1, mn);    /* u4 = s4 * t5 */

  ASSERT (u0[rn+mn-1] < 2);

  t0[mn] = mpn_add_n (t0, m3, m1, mn);

  MUL (u1, r1, rn, t0, mn + 1);    /* u1 = s1 * t1 */

  mn += rn;

  ASSERT (u1[mn-1] < 4);

  ASSERT (u1[mn] == 0);

  ASSERT_NOCARRY (add_signed_n (r1, r3, r3s, u0, s0s, mn));

          /* -u2 + u3 - u4 + u5  */

  ASSERT (r1[mn-1] < 2);

  if (r3s)

    {

      ASSERT_NOCARRY (mpn_add_n (r3, u1, r3, mn));

    }

  else

    {

      ASSERT_NOCARRY (mpn_sub_n (r3, u1, r3, mn));

          /* u1 + u2 - u3 - u5  */

    }

  ASSERT (r3[mn-1] < 2);

  if (t0s)

    {

      ASSERT_NOCARRY (mpn_add_n (r2, u1, r2, mn));

    }

  else

    {

      ASSERT_NOCARRY (mpn_sub_n (r2, u1, r2, mn));

          /* u1 - u3 - u5 - u6  */

    }

  ASSERT (r2[mn-1] < 2);

}

void

mpn_matrix22_mul (mp_ptr r0, mp_ptr r1, mp_ptr r2, mp_ptr r3, mp_size_t rn,

      mp_srcptr m0, mp_srcptr m1, mp_srcptr m2, mp_srcptr m3, mp_size_t mn,

      mp_ptr tp)

{

  if (BELOW_THRESHOLD (rn, MATRIX22_STRASSEN_THRESHOLD)

      || BELOW_THRESHOLD (mn, MATRIX22_STRASSEN_THRESHOLD))

    {

      mp_ptr p0, p1;

      unsigned i;

      /* Temporary storage: 3 rn + 2 mn */

      p0 = tp + rn;

      p1 = p0 + rn + mn;

      for (i = 0; i < 2; i++)

  {

    MPN_COPY (tp, r0, rn);

    if (rn >= mn)

      {

        mpn_mul (p0, r0, rn, m0, mn);

        mpn_mul (p1, r1, rn, m3, mn);

        mpn_mul (r0, r1, rn, m2, mn);

        mpn_mul (r1, tp, rn, m1, mn);

      }

    else

      {

        mpn_mul (p0, m0, mn, r0, rn);

        mpn_mul (p1, m3, mn, r1, rn);

        mpn_mul (r0, m2, mn, r1, rn);

        mpn_mul (r1, m1, mn, tp, rn);

      }

    r0[rn+mn] = mpn_add_n (r0, r0, p0, rn + mn);

    r1[rn+mn] = mpn_add_n (r1, r1, p1, rn + mn);

    r0 = r2; r1 = r3;

  }

    }

  else

    mpn_matrix22_mul_strassen (r0, r1, r2, r3, rn,

             m0, m1, m2, m3, mn, tp);

}