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/* 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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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"
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. */
mpz_mul_ui (r, r, nacc);
nacc = j;
mpz_tdiv_q_ui (r, r, kacc);
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. */
mpz_mul_ui (r, r, nacc);
mpz_tdiv_q_ui (r, r, kacc);
}
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