mpir/mpz/bin_ui.c

/* mpz_bin_ui - compute n over k.

Copyright 1998, 1999, 2000, 2001, 2002 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 "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"


/* This is a poor implementation.  Look at bin_uiui.c for improvement ideas.
   In fact consider calling mpz_bin_uiui() when the arguments fit, leaving
   the code here only for big n.

   The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol
   1 section 1.2.6 part G. */


#define DIVIDE()                                                              \
  do {                                                                        \
    ASSERT (SIZ(r) > 0);                                                      \
    MPN_DIVREM_OR_DIVEXACT_1 (PTR(r), PTR(r), (mp_size_t) SIZ(r), kacc);      \
    SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0);                                        \
  } while (0)

void
mpz_bin_ui (mpz_ptr r, mpz_srcptr n, mpir_ui k)
{
  mpz_t      ni;
  mp_limb_t  i;
  mpz_t      nacc;
  mp_limb_t  kacc;
  mp_size_t  negate;

  if (mpz_sgn (n) < 0)
    {
      /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
      mpz_init (ni);
      mpz_neg (ni, n);
      mpz_sub_ui (ni, ni, 1L);
      negate = (k & 1);   /* (-1)^k */
    }
  else
    {
      /* bin(n,k) == 0 if k>n
         (no test for this under the n<0 case, since -n+k-1 >= k there) */
      if (mpz_cmp_ui (n, k) < 0)
        {
          mpz_set_ui (r, 0L);
          return;
        }

      /* set ni = n-k */
      mpz_init (ni);
      mpz_sub_ui (ni, n, k);
      negate = 0;
    }

  /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
     for positive, 1 for negative). */
  mpz_set_ui (r, 1L);

  /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller.  In this case it's
     whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
     = ni, and new ni of ni+k-ni = k.  */
  if (mpz_cmp_ui (ni, k) < 0)
    {
      mpir_ui  tmp;
      tmp = k;
      k = mpz_get_ui (ni);
      mpz_set_ui (ni, tmp);
    }

  kacc = 1;
  mpz_init_set_ui (nacc, 1L);

  for (i = 1; i <= k; i++)
    {
      mp_limb_t k1, k0;

#if 0
      mp_limb_t nacclow;
      int c;

      nacclow = PTR(nacc)[0];
      for (c = 0; (((kacc | nacclow) & 1) == 0); c++)
	{
	  kacc >>= 1;
	  nacclow >>= 1;
	}
      mpz_div_2exp (nacc, nacc, c);
#endif

      mpz_add_ui (ni, ni, 1L);
      mpz_mul (nacc, nacc, ni);
      umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS);
      k0 >>= GMP_NAIL_BITS;
      if (k1 != 0)
	{
	  /* Accumulator overflow.  Perform bignum step.  */
	  mpz_mul (r, r, nacc);
	  mpz_set_ui (nacc, 1L);
          DIVIDE ();
	  kacc = i;
	}
      else
	{
	  /* Save new products in accumulators to keep accumulating.  */
	  kacc = k0;
	}
    }

  mpz_mul (r, r, nacc);
  DIVIDE ();
  SIZ(r) = (SIZ(r) ^ -negate) + negate;

  mpz_clear (nacc);
  mpz_clear (ni);
}