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/* mpz_bin_uiui - 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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, 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, 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 << GMP_NAIL_BITS);
umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS);
n0 >>= GMP_NAIL_BITS;
k0 >>= GMP_NAIL_BITS;
if (n1 != 0)
{
/* Accumulator overflow. Perform bignum step. */
MULDIV (32);
nacc = j;
kacc = i;
}
else
{
ASSERT (k1 == 0); /* n>=k, so high k zero when high n zero */
/* 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;
}
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