Annotation of OpenXM_contrib/gmp/mpz/bin_ui.c, Revision 1.1.1.2
1.1 maekawa 1: /* mpz_bin_uiui - compute n over k.
2:
1.1.1.2 ! ohara 3: Copyright 1998, 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
1.1 maekawa 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 */
1.1.1.2 ! ohara 36: #define DIVIDE() \
! 37: do { \
! 38: ASSERT (SIZ(r) > 0); \
! 39: MPN_DIVREM_OR_DIVEXACT_1 (PTR(r), PTR(r), SIZ(r), kacc); \
! 40: SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0); \
! 41: } while (0)
1.1 maekawa 42:
43: void
44: mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k)
45: {
46: mpz_t ni;
47: mp_limb_t i;
48: mpz_t nacc;
49: mp_limb_t kacc;
50: mp_size_t negate;
1.1.1.2 ! ohara 51:
1.1 maekawa 52: if (mpz_sgn (n) < 0)
53: {
54: /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
55: mpz_init (ni);
56: mpz_neg (ni, n);
57: mpz_sub_ui (ni, ni, 1L);
58: negate = (k & 1); /* (-1)^k */
59: }
60: else
61: {
62: /* bin(n,k) == 0 if k>n
63: (no test for this under the n<0 case, since -n+k-1 >= k there) */
64: if (mpz_cmp_ui (n, k) < 0)
65: {
66: mpz_set_ui (r, 0L);
67: return;
68: }
69:
70: /* set ni = n-k */
71: mpz_init (ni);
72: mpz_sub_ui (ni, n, k);
73: negate = 0;
74: }
75:
76: /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
77: for positive, 1 for negative). */
78: mpz_set_ui (r, 1L);
79:
80: /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. In this case it's
81: whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
82: = ni, and new ni of ni+k-ni = k. */
83: if (mpz_cmp_ui (ni, k) < 0)
84: {
85: unsigned long tmp;
86: tmp = k;
87: k = mpz_get_ui (ni);
88: mpz_set_ui (ni, tmp);
89: }
90:
91: kacc = 1;
92: mpz_init_set_ui (nacc, 1);
93:
94: for (i = 1; i <= k; i++)
95: {
96: mp_limb_t k1, k0;
97:
98: #if 0
99: mp_limb_t nacclow;
100: int c;
101:
102: nacclow = PTR(nacc)[0];
103: for (c = 0; (((kacc | nacclow) & 1) == 0); c++)
104: {
105: kacc >>= 1;
106: nacclow >>= 1;
107: }
108: mpz_div_2exp (nacc, nacc, c);
109: #endif
110:
111: mpz_add_ui (ni, ni, 1);
112: mpz_mul (nacc, nacc, ni);
1.1.1.2 ! ohara 113: umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS);
! 114: k0 >>= GMP_NAIL_BITS;
1.1 maekawa 115: if (k1 != 0)
116: {
117: /* Accumulator overflow. Perform bignum step. */
118: mpz_mul (r, r, nacc);
119: mpz_set_ui (nacc, 1);
120: DIVIDE ();
121: kacc = i;
122: }
123: else
124: {
125: /* Save new products in accumulators to keep accumulating. */
126: kacc = k0;
127: }
128: }
129:
130: mpz_mul (r, r, nacc);
131: DIVIDE ();
132: SIZ(r) = (SIZ(r) ^ -negate) + negate;
133:
134: mpz_clear (nacc);
135: mpz_clear (ni);
136: }
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