bin_ui.c
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上传日期:2022-08-06
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- /* mpz_bin_ui - 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 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"
- /* 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 (mpz_sgn (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_neg (ni, n);
- mpz_sub_ui (ni, ni, 1L);
- 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)
- {
- mpz_set_ui (r, 0L);
- 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). */
- mpz_set_ui (r, 1L);
- /* 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);
- k0 >>= GMP_NAIL_BITS;
- if (k1 != 0)
- {
- /* Accumulator overflow. Perform bignum step. */
- mpz_mul (r, r, nacc);
- mpz_set_ui (nacc, 1L);
- DIVIDE ();
- kacc = i;
- }
- else
- {
- /* Save new products in accumulators to keep accumulating. */
- kacc = k0;
- }
- }
- mpz_mul (r, r, nacc);
- DIVIDE ();
- SIZ(r) = (SIZ(r) ^ -negate) + negate;
- mpz_clear (nacc);
- mpz_clear (ni);
- }