142 lines
4.5 KiB
C
142 lines
4.5 KiB
C
/* mpz_bin_uiui - compute n over k.
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Copyright 1998, 1999, 2000, 2001, 2002, 2003 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "mpir.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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/* Enhancement: It ought to be possible to calculate the size of the final
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result in advance, to a rough approximation at least, and use it to do
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just one realloc. Stirling's approximation n! ~= sqrt(2*pi*n)*(n/e)^n
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(Knuth section 1.2.5) might be of use. */
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/* "inc" in the main loop allocates a chunk more space if not already
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enough, so as to avoid repeated reallocs. The final step on the other
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hand requires only one more limb. */
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#define MULDIV(inc) \
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do { \
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ASSERT (rsize <= ralloc); \
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\
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if (rsize == ralloc) \
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{ \
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mp_size_t new_ralloc = ralloc + (inc); \
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rp = __GMP_REALLOCATE_FUNC_LIMBS (rp, ralloc, new_ralloc); \
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ralloc = new_ralloc; \
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} \
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\
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rp[rsize] = mpn_mul_1 (rp, rp, rsize, nacc); \
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MPN_DIVREM_OR_DIVEXACT_1 (rp, rp, rsize+1, kacc); \
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rsize += (rp[rsize] != 0); \
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\
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} while (0)
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void
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mpz_bin_uiui (mpz_ptr r, gmp_ui n, gmp_ui k)
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{
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gmp_ui i, j;
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mp_limb_t nacc, kacc;
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gmp_ui cnt;
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mp_size_t rsize, ralloc;
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mp_ptr rp;
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/* bin(n,k) = 0 if k>n. */
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if (n < k)
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{
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SIZ(r) = 0;
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return;
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}
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rp = PTR(r);
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/* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. */
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k = MIN (k, n-k);
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/* bin(n,0) = 1 */
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if (k == 0)
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{
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SIZ(r) = 1;
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rp[0] = 1;
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return;
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}
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j = n - k + 1;
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rp[0] = j;
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rsize = 1;
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ralloc = ALLOC(r);
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/* Initialize accumulators. */
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nacc = 1;
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kacc = 1;
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cnt = 0;
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for (i = 2; i <= k; i++)
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{
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mp_limb_t n1, n0, k0;
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j++;
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#if 0
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/* Remove common multiples of 2. This will allow us to accumulate
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more in nacc and kacc before we need a bignum step. It would make
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sense to cancel factors of 3, 5, etc too, but this would be best
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handled by sieving out factors. Alternatively, we could perform a
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gcd of the accumulators just as they have overflown, and keep
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accumulating until the gcd doesn't remove a significant factor. */
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while (((nacc | kacc) & 1) == 0)
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{
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nacc >>= 1;
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kacc >>= 1;
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}
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#else
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cnt = ((nacc | kacc) & 1) ^ 1;
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nacc >>= cnt;
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kacc >>= cnt;
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#endif
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/* Accumulate next multiples. */
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umul_ppmm (n1, n0, nacc, (mp_limb_t) j << GMP_NAIL_BITS);
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k0 = kacc * i;
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n0 >>= GMP_NAIL_BITS;
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if (n1 != 0)
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{
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/* Accumulator overflow. Perform bignum step. */
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MULDIV (32);
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nacc = j;
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kacc = i;
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}
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else
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{
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/* k<=n, so should have no overflow from k0 = kacc*i */
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ASSERT (kacc <= GMP_NUMB_MAX / i);
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/* Save new products in accumulators to keep accumulating. */
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nacc = n0;
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kacc = k0;
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}
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}
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/* Take care of whatever is left in accumulators. */
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MULDIV (1);
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ALLOC(r) = ralloc;
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SIZ(r) = rsize;
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PTR(r) = rp;
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}
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