mpir/mpz/bin_uiui.c

/* mpz_bin_uiui - compute n over k.

Copyright 1998, 1999, 2000, 2001, 2002, 2003 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., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

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


/* Enhancement: It ought to be possible to calculate the size of the final
   result in advance, to a rough approximation at least, and use it to do
   just one realloc.  Stirling's approximation n! ~= sqrt(2*pi*n)*(n/e)^n
   (Knuth section 1.2.5) might be of use.  */

/* "inc" in the main loop allocates a chunk more space if not already
   enough, so as to avoid repeated reallocs.  The final step on the other
   hand requires only one more limb.  */
#define MULDIV(inc)                                                     \
  do {                                                                  \
    ASSERT (rsize <= ralloc);                                           \
                                                                        \
    if (rsize == ralloc)                                                \
      {                                                                 \
        mp_size_t  new_ralloc = ralloc + (inc);                         \
        rp = __GMP_REALLOCATE_FUNC_LIMBS (rp, ralloc, new_ralloc);      \
        ralloc = new_ralloc;                                            \
      }                                                                 \
                                                                        \
    rp[rsize] = mpn_mul_1 (rp, rp, rsize, nacc);                        \
    MPN_DIVREM_OR_DIVEXACT_1 (rp, rp, rsize+1, kacc);                   \
    rsize += (rp[rsize] != 0);                                          \
                                                                        \
} while (0)

void
mpz_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)
{
  unsigned long int  i, j;
  mp_limb_t          nacc, kacc;
  unsigned long int  cnt;
  mp_size_t          rsize, ralloc;
  mp_ptr             rp;

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

  rp = PTR(r);

  /* 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)
    {
      SIZ(r) = 1;
      rp[0] = 1;
      return;
    }

  j = n - k + 1;
  rp[0] = j;
  rsize = 1;
  ralloc = ALLOC(r);

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

  cnt = 0;
  for (i = 2; i <= k; i++)
    {
      mp_limb_t n1, n0, 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, (mp_limb_t) j << GMP_NAIL_BITS);
      k0 = kacc * i;
      n0 >>= GMP_NAIL_BITS;
      if (n1 != 0)
        {
          /* Accumulator overflow.  Perform bignum step. */
          MULDIV (32);
          nacc = j;
          kacc = i;
        }
      else
        {
          /* k<=n, so should have no overflow from k0 = kacc*i */
          ASSERT (kacc <= GMP_NUMB_MAX / i);

          /* Save new products in accumulators to keep accumulating.  */
          nacc = n0;
          kacc = k0;
        }
    }

  /* Take care of whatever is left in accumulators.  */
  MULDIV (1);

  ALLOC(r) = ralloc;
  SIZ(r) = rsize;
  PTR(r) = rp;
}