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Initial revision

/* 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 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 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser 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 ();
}