/* hgcd2_jacobi.c

   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 1996, 1998, 2000-2004, 2008, 2011, 2020 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"

#include "mpn/generic/hgcd2-div.h"

#if GMP_NAIL_BITS != 0

#error Nails not implemented

#endif

int

mpn_hgcd2_jacobi (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,

      struct hgcd_matrix1 *M, unsigned *bitsp)

{

  mp_limb_t u00, u01, u10, u11;

  unsigned bits = *bitsp;

  if (ah < 2 || bh < 2)

    return 0;

  if (ah > bh || (ah == bh && al > bl))

    {

      sub_ddmmss (ah, al, ah, al, bh, bl);

      if (ah < 2)

  return 0;

      u00 = u01 = u11 = 1;

      u10 = 0;

      bits = mpn_jacobi_update (bits, 1, 1);

    }

  else

    {

      sub_ddmmss (bh, bl, bh, bl, ah, al);

      if (bh < 2)

  return 0;

      u00 = u10 = u11 = 1;

      u01 = 0;

      bits = mpn_jacobi_update (bits, 0, 1);

    }

  if (ah < bh)

    goto subtract_a;

  for (;;)

    {

      ASSERT (ah >= bh);

      if (ah == bh)

  goto done;

      if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))

  {

    ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));

    bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

    break;

  }

      /* Subtract a -= q b, and multiply M from the right by (1 q ; 0

   1), affecting the second column of M. */

      ASSERT (ah > bh);

      sub_ddmmss (ah, al, ah, al, bh, bl);

      if (ah < 2)

  goto done;

      if (ah <= bh)

  {

    /* Use q = 1 */

    u01 += u00;

    u11 += u10;

    bits = mpn_jacobi_update (bits, 1, 1);

  }

      else

  {

    mp_limb_t r[2];

    mp_limb_t q = div2 (r, ah, al, bh, bl);

    al = r[0]; ah = r[1];

    if (ah < 2)

      {

        /* A is too small, but q is correct. */

        u01 += q * u00;

        u11 += q * u10;

        bits = mpn_jacobi_update (bits, 1, q & 3);

        goto done;

      }

    q++;

    u01 += q * u00;

    u11 += q * u10;

    bits = mpn_jacobi_update (bits, 1, q & 3);

  }

    subtract_a:

      ASSERT (bh >= ah);

      if (ah == bh)

  goto done;

      if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))

  {

    ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));

    bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

    goto subtract_a1;

  }

      /* Subtract b -= q a, and multiply M from the right by (1 0 ; q

   1), affecting the first column of M. */

      sub_ddmmss (bh, bl, bh, bl, ah, al);

      if (bh < 2)

  goto done;

      if (bh <= ah)

  {

    /* Use q = 1 */

    u00 += u01;

    u10 += u11;

    bits = mpn_jacobi_update (bits, 0, 1);

  }

      else

  {

    mp_limb_t r[2];

    mp_limb_t q = div2 (r, bh, bl, ah, al);

    bl = r[0]; bh = r[1];

    if (bh < 2)

      {

        /* B is too small, but q is correct. */

        u00 += q * u01;

        u10 += q * u11;

        bits = mpn_jacobi_update (bits, 0, q & 3);

        goto done;

      }

    q++;

    u00 += q * u01;

    u10 += q * u11;

    bits = mpn_jacobi_update (bits, 0, q & 3);

  }

    }

  /* NOTE: Since we discard the least significant half limb, we don't get a

     truly maximal M (corresponding to |a - b| < 2^{GMP_LIMB_BITS +1}). */

  /* Single precision loop */

  for (;;)

    {

      ASSERT (ah >= bh);

      ah -= bh;

      if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))

  break;

      if (ah <= bh)

  {

    /* Use q = 1 */

    u01 += u00;

    u11 += u10;

    bits = mpn_jacobi_update (bits, 1, 1);

  }

      else

  {

    mp_double_limb_t rq = div1 (ah, bh);

    mp_limb_t q = rq.d1;

    ah = rq.d0;

    if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))

      {

        /* A is too small, but q is correct. */

        u01 += q * u00;

        u11 += q * u10;

        bits = mpn_jacobi_update (bits, 1, q & 3);

        break;

      }

    q++;

    u01 += q * u00;

    u11 += q * u10;

    bits = mpn_jacobi_update (bits, 1, q & 3);

  }

    subtract_a1:

      ASSERT (bh >= ah);

      bh -= ah;

      if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))

  break;

      if (bh <= ah)

  {

    /* Use q = 1 */

    u00 += u01;

    u10 += u11;

    bits = mpn_jacobi_update (bits, 0, 1);

  }

      else

  {

    mp_double_limb_t rq = div1 (bh, ah);

    mp_limb_t q = rq.d1;

    bh = rq.d0;

    if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))

      {

        /* B is too small, but q is correct. */

        u00 += q * u01;

        u10 += q * u11;

        bits = mpn_jacobi_update (bits, 0, q & 3);

        break;

      }

    q++;

    u00 += q * u01;

    u10 += q * u11;

    bits = mpn_jacobi_update (bits, 0, q & 3);

  }

    }

 done:

  M->u[0][0] = u00; M->u[0][1] = u01;

  M->u[1][0] = u10; M->u[1][1] = u11;

  *bitsp = bits;

  return 1;

}