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
136
137
138
139
140
|
/* Prime number generation
Copyright (C) 1994, 1996, 1999 Free Software Foundation
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2, or (at
your option) any later version.
This program 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
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
#include <stdlib.h>
#include <limits.h>
#include <string.h>
#include <assert.h>
#include <spin-lock.h>
#include "priv.h"
#define BITS_PER_UNSIGNED (8 * sizeof (unsigned))
#define SQRT_INT_MAX (1 << (BITS_PER_UNSIGNED / 2))
static spin_lock_t table_lock = SPIN_LOCK_INITIALIZER;
/* Return the next prime greater than or equal to N. */
int
_ihash_nextprime (unsigned n)
{
/* Among other things, We guarantee that, for all i (0 <= i < primes_len),
primes[i] is a prime,
next_multiple[i] is a multiple of primes[i],
next_multiple[i] > primes[primes_len - 1],
next_multiple[i] is not a multiple of two unless primes[i] == 2, and
next_multiple[i] is the smallest such value. */
static unsigned *primes, *next_multiple;
static int primes_len;
static int primes_size;
static unsigned next_sieve; /* always even */
unsigned max_prime;
spin_lock (&table_lock);
if (! primes)
{
primes_size = 128;
primes = (unsigned *) malloc (primes_size * sizeof (*primes));
next_multiple = (unsigned *) malloc (primes_size
* sizeof (*next_multiple));
primes[0] = 2; next_multiple[0] = 6;
primes[1] = 3; next_multiple[1] = 9;
primes[2] = 5; next_multiple[2] = 15;
primes_len = 3;
next_sieve = primes[primes_len - 1] + 1;
}
if (n <= primes[0])
{
spin_unlock (&table_lock);
return primes[0];
}
while (n > (max_prime = primes[primes_len - 1]))
{
/* primes doesn't contain any prime large enough. Sieve from
max_prime + 1 to 2 * max_prime, looking for more primes. */
unsigned start = next_sieve;
unsigned end = start + max_prime + 1;
char sieve[end - start];
int i;
bzero (sieve, (end - start) * sizeof (*sieve));
/* Make the sieve indexed by prime number, rather than
distance-from-start-to-the-prime-number. When we're done,
sieve[P] will be zero iff P is prime. */
#define sieve (sieve - start)
/* Set sieve[i] for all composites i, start <= i < end.
Ignore multiples of 2. */
for (i = 1; i < primes_len; i++)
{
unsigned twice_prime = 2 * primes[i];
unsigned multiple;
for (multiple = next_multiple[i];
multiple < end;
multiple += twice_prime)
sieve[multiple] = 1;
next_multiple[i] = multiple;
}
for (i = start + 1; i < end; i += 2)
if (! sieve[i])
{
if (primes_len >= primes_size)
{
primes_size *= 2;
primes = (int *) realloc (primes,
primes_size * sizeof (*primes));
next_multiple
= (int *) realloc (next_multiple,
primes_size * sizeof (*next_multiple));
}
primes[primes_len] = i;
if (i >= SQRT_INT_MAX)
next_multiple[primes_len] = INT_MAX;
else
next_multiple[primes_len] = i * i;
primes_len++;
}
next_sieve = end;
}
/* Now we have at least one prime >= n. Find the smallest such. */
{
int bottom = 0;
int top = primes_len;
while (bottom < top)
{
int mid = (bottom + top) / 2;
if (primes[mid] < n)
bottom = mid + 1;
else
top = mid;
}
spin_unlock (&table_lock);
return primes[top];
}
}
|
