/*
Copyright 2009 Jason Moxham

This file is part of the MPIR Library.

The MPIR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 2.1 of the License, or (at
your option) any later version.

The MPIR 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPIR Library; see the file COPYING.LIB.  If not, write
to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.
*/

#include "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"

/* 
   using a two limb inverse of a one limb divisor 
   (xp, n) = (qp, n)*d - ret*B^n and 0 <= ret < d
*/
mp_limb_t mpn_divrem_hensel_qr_1_2(mp_ptr qp, mp_srcptr xp, mp_size_t n, mp_limb_t d)
{
   mp_size_t j;
   mp_limb_t c, h, q, dummy, h1, t, ml, mh, xl, xh, ql, qh;

   ASSERT(n >= 2);
   ASSERT_MPN(xp, n);
   ASSERT(MPN_SAME_OR_SEPARATE_P(qp, xp, n));
   ASSERT(d%2 == 1);

   modlimb_invert(ml, d);

   umul_ppmm(h, dummy, d, ml);
   
   ASSERT(dummy == 1);

   h = -h;
   mh = ml*h; /* (mh, ml) is our two limb inverse */
   c = 0;
   h = 0;

   for (j = 0; j + 1 <= n - 1; j += 2)
   {
      xl = xp[j];
      xh = xp[j + 1];
      t = h + c;
      
      if (xh == 0 && t > xl) c = 1;
      else c = 0;
    
      sub_ddmmss(xh, xl, xh, xl, 0, t);
      umul_ppmm(qh, ql, xl, ml);
      qh = qh + xh*ml + xl*mh;
      qp[j] = ql;
      qp[j + 1] = qh;
      umul_ppmm(h, h1, qh, d);
    
      if (h1 > xh)
         h++;
   }

   if (j <= n - 1)
   {
      h1 = xp[j];
      t = h + c;
      
      if (t > h1)
      {
         h1 = h1 - t;
         c = 1;
      }
      else
      {
         h1 = h1 - t;
         c = 0;
      }
   
      q = h1*ml;
      qp[j] = q;
      umul_ppmm(h, dummy, q, d);
   
      ASSERT(dummy == h1);
   }
 
   return h + c;
}