Annotation of OpenXM_contrib/gmp/mpz/bin_ui.c, Revision 1.1.1.1
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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