136 lines
3.7 KiB
C
136 lines
3.7 KiB
C
/* mpz_bin_ui - compute n over k.
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Copyright 1998, 1999, 2000, 2001, 2002 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 "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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/* This is a poor implementation. Look at bin_uiui.c for improvement ideas.
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In fact consider calling mpz_bin_uiui() when the arguments fit, leaving
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the code here only for big n.
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The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol
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1 section 1.2.6 part G. */
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#define DIVIDE() \
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do { \
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ASSERT (SIZ(r) > 0); \
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MPN_DIVREM_OR_DIVEXACT_1 (PTR(r), PTR(r), (mp_size_t) SIZ(r), kacc); \
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SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0); \
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} while (0)
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void
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mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k)
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{
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mpz_t ni;
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mp_limb_t i;
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mpz_t nacc;
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mp_limb_t kacc;
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mp_size_t negate;
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if (mpz_sgn (n) < 0)
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{
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/* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
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mpz_init (ni);
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mpz_neg (ni, n);
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mpz_sub_ui (ni, ni, 1L);
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negate = (k & 1); /* (-1)^k */
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}
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else
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{
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/* bin(n,k) == 0 if k>n
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(no test for this under the n<0 case, since -n+k-1 >= k there) */
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if (mpz_cmp_ui (n, k) < 0)
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{
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mpz_set_ui (r, 0L);
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return;
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}
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/* set ni = n-k */
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mpz_init (ni);
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mpz_sub_ui (ni, n, k);
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negate = 0;
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}
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/* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
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for positive, 1 for negative). */
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mpz_set_ui (r, 1L);
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/* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. In this case it's
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whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
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= ni, and new ni of ni+k-ni = k. */
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if (mpz_cmp_ui (ni, k) < 0)
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{
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unsigned long tmp;
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tmp = k;
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k = mpz_get_ui (ni);
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mpz_set_ui (ni, tmp);
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}
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kacc = 1;
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mpz_init_set_ui (nacc, 1L);
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for (i = 1; i <= k; i++)
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{
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mp_limb_t k1, k0;
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#if 0
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mp_limb_t nacclow;
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int c;
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nacclow = PTR(nacc)[0];
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for (c = 0; (((kacc | nacclow) & 1) == 0); c++)
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{
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kacc >>= 1;
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nacclow >>= 1;
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}
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mpz_div_2exp (nacc, nacc, c);
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#endif
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mpz_add_ui (ni, ni, 1L);
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mpz_mul (nacc, nacc, ni);
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umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS);
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k0 >>= GMP_NAIL_BITS;
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if (k1 != 0)
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{
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/* Accumulator overflow. Perform bignum step. */
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mpz_mul (r, r, nacc);
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mpz_set_ui (nacc, 1L);
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DIVIDE ();
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kacc = i;
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}
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else
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{
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/* Save new products in accumulators to keep accumulating. */
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kacc = k0;
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}
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}
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mpz_mul (r, r, nacc);
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DIVIDE ();
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SIZ(r) = (SIZ(r) ^ -negate) + negate;
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mpz_clear (nacc);
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mpz_clear (ni);
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}
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