/* mpz_bin_uiui - compute n over k.

Copyright (C) 1998, 1999, 2000 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 the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.

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 Library General Public
License for more details.

You should have received a copy of the GNU Library General Public License
along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

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


/* Avoid reallocs by rounding up any new size */
#define ROUNDUP_MASK  15

/* Enhancement: use mpn_divexact_1 when it exists */
#define MULDIV()                                                \
  MPZ_REALLOC (r, (SIZ(r)+1)|ROUNDUP_MASK);                     \
  PTR(r)[SIZ(r)] = mpn_mul_1 (PTR(r), PTR(r), SIZ(r), nacc);    \
  ASSERT_NOCARRY (mpn_divrem_1 (PTR(r), (mp_size_t) 0,          \
                                PTR(r), SIZ(r)+1, kacc));       \
  SIZ(r) += (PTR(r)[SIZ(r)] != 0);

void
#if __STDC__
mpz_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)
#else
mpz_bin_uiui (r, n, k)
     mpz_ptr r;
     unsigned long int n;
     unsigned long int k;
#endif
{
  unsigned long int  i, j;
  mp_limb_t          nacc, kacc;
  unsigned long int  cnt;

  /* bin(n,k) = 0 if k>n. */
  if (n < k)
    {
      mpz_set_ui (r, 0);
      return;
    }

  /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. */
  k = MIN (k, n-k);

  /* bin(n,0) = 1 */
  if (k == 0)
    {
      mpz_set_ui (r, 1);
      return;
    }

  j = n - k + 1;
  mpz_set_ui (r, j);

  /* Initialize accumulators.  */
  nacc = 1;
  kacc = 1;

  cnt = 0;
  for (i = 2; i <= k; i++)
    {
      mp_limb_t n1, n0, k1, k0;

      j++;
#if 0
      /* Remove common multiples of 2.  This will allow us to accumulate
         more in nacc and kacc before we need a bignum step.  It would make
         sense to cancel factors of 3, 5, etc too, but this would be best
         handled by sieving out factors.  Alternatively, we could perform a
         gcd of the accumulators just as they have overflown, and keep
         accumulating until the gcd doesn't remove a significant factor.  */
      while (((nacc | kacc) & 1) == 0)
        {
          nacc >>= 1;
          kacc >>= 1;
        }
#else
      cnt = ((nacc | kacc) & 1) ^ 1;
      nacc >>= cnt;
      kacc >>= cnt;
#endif
      /* Accumulate next multiples.  */
      umul_ppmm (n1, n0, nacc, j);
      umul_ppmm (k1, k0, kacc, i);
      if (n1 != 0)
        {
          /* Accumulator overflow.  Perform bignum step.  */
          MULDIV ();
          nacc = j;
          kacc = i;
        }
      else
        {
          if (k1 != 0) abort ();
          /* Save new products in accumulators to keep accumulating.  */
          nacc = n0;
          kacc = k0;
        }
    }

  /* Take care of whatever is left in accumulators.  */
  MULDIV ();
}