/* Compute {up,n}^(-1) mod B^n.

   Contributed to the GNU project by Torbjorn Granlund.

   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 WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.

Copyright (C) 2004-2007, 2009, 2012, 2017 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"

/*

  r[k+1] = r[k] - r[k] * (u*r[k] - 1)

  r[k+1] = r[k] + r[k] - r[k]*(u*r[k])

*/

#if TUNE_PROGRAM_BUILD

#define NPOWS \

 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)))

#else

#define NPOWS \

 ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)) - LOG2C (BINV_NEWTON_THRESHOLD))

#endif

mp_size_t

mpn_binvert_itch (mp_size_t n)

{

  mp_size_t itch_local = mpn_mulmod_bnm1_next_size (n);

  mp_size_t itch_out = mpn_mulmod_bnm1_itch (itch_local, n, (n + 1) >> 1);

  return itch_local + itch_out;

}

void

mpn_binvert (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr scratch)

{

  mp_ptr xp;

  mp_size_t rn, newrn;

  mp_size_t sizes[NPOWS], *sizp;

  mp_limb_t di;

  /* Compute the computation precisions from highest to lowest, leaving the

     base case size in 'rn'.  */

  sizp = sizes;

  for (rn = n; ABOVE_THRESHOLD (rn, BINV_NEWTON_THRESHOLD); rn = (rn + 1) >> 1)

    *sizp++ = rn;

  xp = scratch;

  /* Compute a base value of rn limbs.  */

  MPN_ZERO (xp, rn);

  xp[0] = 1;

  binvert_limb (di, up[0]);

  if (BELOW_THRESHOLD (rn, DC_BDIV_Q_THRESHOLD))

    mpn_sbpi1_bdiv_q (rp, xp, rn, up, rn, -di);

  else

    mpn_dcpi1_bdiv_q (rp, xp, rn, up, rn, -di);

  mpn_neg (rp, rp, rn);

  /* Use Newton iterations to get the desired precision.  */

  for (; rn < n; rn = newrn)

    {

      mp_size_t m;

      newrn = *--sizp;

      /* X <- UR. */

      m = mpn_mulmod_bnm1_next_size (newrn);

      mpn_mulmod_bnm1 (xp, m, up, newrn, rp, rn, xp + m);

      mpn_sub_1 (xp + m, xp, rn - (m - newrn), 1);

      /* R = R(X/B^rn) */

      mpn_mullo_n (rp + rn, rp, xp + rn, newrn - rn);

      mpn_neg (rp + rn, rp + rn, newrn - rn);

    }

}