mpir/mpz/bin_ui.c

/* mpz_bin_ui - compute n over k.

Copyright 1998, 1999, 2000, 2001, 2002, 2012 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 3 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.  If not, see http://www.gnu.org/licenses/.  */

#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 (SIZ (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)
	{
	  SIZ (r) = 0;
	  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). */
  SIZ (r) = 1; PTR (r)[0] = 1;

  /* 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)
    {
      unsigned long  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);
      if (k1 != 0)
	{
	  /* Accumulator overflow.  Perform bignum step.  */
	  mpz_mul (r, r, nacc);
	  SIZ (nacc) = 1; PTR (nacc)[0] = 1;
	  DIVIDE ();
	  kacc = i;
	}
      else
	{
	  /* Save new products in accumulators to keep accumulating.  */
	  kacc = k0 >> GMP_NAIL_BITS;
	}
    }

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

  mpz_clear (nacc);
  mpz_clear (ni);
}