/* mpz_bin_ui - compute n over k.

Copyright 1998-2002, 2012, 2013 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software
    Foundation; either version 2 of the License, or (at your option) any
    later version.

or both in parallel, as here.

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 General Public License
for more details.

You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library.  If not,
see https://www.gnu.org/licenses/.  */

#include "gmp.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, unsigned long int 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_add_ui (ni, n, 1L);
      mpz_neg (ni, ni);
      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);
}