Annotation of OpenXM_contrib/gmp/mpz/bin_ui.c, Revision 1.1
1.1 ! maekawa 1: /* mpz_bin_uiui - compute n over k.
! 2:
! 3: Copyright (C) 1998, 1999, 2000 Free Software Foundation, Inc.
! 4:
! 5: This file is part of the GNU MP Library.
! 6:
! 7: The GNU MP Library is free software; you can redistribute it and/or modify
! 8: it under the terms of the GNU Lesser General Public License as published by
! 9: the Free Software Foundation; either version 2.1 of the License, or (at your
! 10: option) any later version.
! 11:
! 12: The GNU MP Library is distributed in the hope that it will be useful, but
! 13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
! 14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
! 15: License for more details.
! 16:
! 17: You should have received a copy of the GNU Lesser General Public License
! 18: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
! 19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
! 20: MA 02111-1307, USA. */
! 21:
! 22: #include "gmp.h"
! 23: #include "gmp-impl.h"
! 24: #include "longlong.h"
! 25:
! 26:
! 27: /* This is a poor implementation. Look at bin_uiui.c for improvement ideas.
! 28: In fact consider calling mpz_bin_uiui() when the arguments fit, leaving
! 29: the code here only for big n.
! 30:
! 31: The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol
! 32: 1 section 1.2.6 part G. */
! 33:
! 34:
! 35: /* Enhancement: use mpn_divexact_1 when it exists */
! 36: #define DIVIDE() \
! 37: ASSERT (SIZ(r) > 0); \
! 38: ASSERT_NOCARRY (mpn_divrem_1 (PTR(r), (mp_size_t) 0, \
! 39: PTR(r), SIZ(r), kacc)); \
! 40: SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0);
! 41:
! 42: void
! 43: #if __STDC__
! 44: mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k)
! 45: #else
! 46: mpz_bin_ui (r, n, k)
! 47: mpz_ptr r;
! 48: mpz_srcptr n;
! 49: unsigned long int k;
! 50: #endif
! 51: {
! 52: mpz_t ni;
! 53: mp_limb_t i;
! 54: mpz_t nacc;
! 55: mp_limb_t kacc;
! 56: mp_size_t negate;
! 57:
! 58: if (mpz_sgn (n) < 0)
! 59: {
! 60: /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
! 61: mpz_init (ni);
! 62: mpz_neg (ni, n);
! 63: mpz_sub_ui (ni, ni, 1L);
! 64: negate = (k & 1); /* (-1)^k */
! 65: }
! 66: else
! 67: {
! 68: /* bin(n,k) == 0 if k>n
! 69: (no test for this under the n<0 case, since -n+k-1 >= k there) */
! 70: if (mpz_cmp_ui (n, k) < 0)
! 71: {
! 72: mpz_set_ui (r, 0L);
! 73: return;
! 74: }
! 75:
! 76: /* set ni = n-k */
! 77: mpz_init (ni);
! 78: mpz_sub_ui (ni, n, k);
! 79: negate = 0;
! 80: }
! 81:
! 82: /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
! 83: for positive, 1 for negative). */
! 84: mpz_set_ui (r, 1L);
! 85:
! 86: /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. In this case it's
! 87: whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
! 88: = ni, and new ni of ni+k-ni = k. */
! 89: if (mpz_cmp_ui (ni, k) < 0)
! 90: {
! 91: unsigned long tmp;
! 92: tmp = k;
! 93: k = mpz_get_ui (ni);
! 94: mpz_set_ui (ni, tmp);
! 95: }
! 96:
! 97: kacc = 1;
! 98: mpz_init_set_ui (nacc, 1);
! 99:
! 100: for (i = 1; i <= k; i++)
! 101: {
! 102: mp_limb_t k1, k0;
! 103:
! 104: #if 0
! 105: mp_limb_t nacclow;
! 106: int c;
! 107:
! 108: nacclow = PTR(nacc)[0];
! 109: for (c = 0; (((kacc | nacclow) & 1) == 0); c++)
! 110: {
! 111: kacc >>= 1;
! 112: nacclow >>= 1;
! 113: }
! 114: mpz_div_2exp (nacc, nacc, c);
! 115: #endif
! 116:
! 117: mpz_add_ui (ni, ni, 1);
! 118: mpz_mul (nacc, nacc, ni);
! 119: umul_ppmm (k1, k0, kacc, i);
! 120: if (k1 != 0)
! 121: {
! 122: /* Accumulator overflow. Perform bignum step. */
! 123: mpz_mul (r, r, nacc);
! 124: mpz_set_ui (nacc, 1);
! 125: DIVIDE ();
! 126: kacc = i;
! 127: }
! 128: else
! 129: {
! 130: /* Save new products in accumulators to keep accumulating. */
! 131: kacc = k0;
! 132: }
! 133: }
! 134:
! 135: mpz_mul (r, r, nacc);
! 136: DIVIDE ();
! 137: SIZ(r) = (SIZ(r) ^ -negate) + negate;
! 138:
! 139: mpz_clear (nacc);
! 140: mpz_clear (ni);
! 141: }
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