bin_uiui.c
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上传日期:2022-08-06
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- /* mpz_bin_uiui - compute n over k.
- Copyright 1998, 1999, 2000, 2001, 2002, 2003, 2006 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 "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;
- for (i = 2; i <= k; i++)
- {
- mp_limb_t n1, n0;
- /* Remove common 2 factors. */
- cnt = ((nacc | kacc) & 1) ^ 1;
- nacc >>= cnt;
- kacc >>= cnt;
- j++;
- /* Accumulate next multiples. */
- umul_ppmm (n1, n0, nacc, (mp_limb_t) j << GMP_NAIL_BITS);
- n0 >>= GMP_NAIL_BITS;
- if (n1 == 0)
- {
- /* Save new products in accumulators to keep accumulating. */
- nacc = n0;
- kacc = kacc * i;
- }
- else
- {
- /* Accumulator overflow. Perform bignum step. */
- MULDIV (32);
- nacc = j;
- kacc = i;
- }
- }
- /* Take care of whatever is left in accumulators. */
- MULDIV (1);
- ALLOC(r) = ralloc;
- SIZ(r) = rsize;
- PTR(r) = rp;
- }