| /* 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); |
| } |