1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
|
/* 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 2.1 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; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#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);
}
|
