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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
|
/*
* sieve.c
*
* Finds prime numbers using the Sieve of Eratosthenes
*
* This implementation uses a bitmap to represent all odd integers in a
* given range. We iterate over this bitmap, crossing off the
* multiples of each prime we find. At the end, all the remaining set
* bits correspond to prime integers.
*
* Here, we make two passes -- once we have generated a sieve-ful of
* primes, we copy them out, reset the sieve using the highest
* generated prime from the first pass as a base. Then we cross out
* all the multiples of all the primes we found the first time through,
* and re-sieve. In this way, we get double use of the memory we
* allocated for the sieve the first time though. Since we also
* implicitly ignore multiples of 2, this amounts to 4 times the
* values.
*
* This could (and probably will) be generalized to re-use the sieve a
* few more times.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
typedef unsigned char byte;
typedef struct {
int size;
byte *bits;
long base;
int next;
int nbits;
} sieve;
void sieve_init(sieve *sp, long base, int nbits);
void sieve_grow(sieve *sp, int nbits);
long sieve_next(sieve *sp);
void sieve_reset(sieve *sp, long base);
void sieve_cross(sieve *sp, long val);
void sieve_clear(sieve *sp);
#define S_ISSET(S, B) (((S)->bits[(B) / CHAR_BIT] >> ((B) % CHAR_BIT)) & 1)
#define S_SET(S, B) ((S)->bits[(B) / CHAR_BIT] |= (1 << ((B) % CHAR_BIT)))
#define S_CLR(S, B) ((S)->bits[(B) / CHAR_BIT] &= ~(1 << ((B) % CHAR_BIT)))
#define S_VAL(S, B) ((S)->base + (2 * (B)))
#define S_BIT(S, V) (((V) - ((S)->base)) / 2)
int
main(int argc, char *argv[])
{
sieve s;
long pr, *p;
int c, ix, cur = 0;
if (argc < 2) {
fprintf(stderr, "Usage: %s <width>\n", argv[0]);
return 1;
}
c = atoi(argv[1]);
if (c < 0)
c = -c;
fprintf(stderr, "%s: sieving to %d positions\n", argv[0], c);
sieve_init(&s, 3, c);
c = 0;
while ((pr = sieve_next(&s)) > 0) {
++c;
}
p = calloc(c, sizeof(long));
if (!p) {
fprintf(stderr, "%s: out of memory after first half\n", argv[0]);
sieve_clear(&s);
exit(1);
}
fprintf(stderr, "%s: half done ... \n", argv[0]);
for (ix = 0; ix < s.nbits; ix++) {
if (S_ISSET(&s, ix)) {
p[cur] = S_VAL(&s, ix);
printf("%ld\n", p[cur]);
++cur;
}
}
sieve_reset(&s, p[cur - 1]);
fprintf(stderr, "%s: crossing off %d found primes ... \n", argv[0], cur);
for (ix = 0; ix < cur; ix++) {
sieve_cross(&s, p[ix]);
if (!(ix % 1000))
fputc('.', stderr);
}
fputc('\n', stderr);
free(p);
fprintf(stderr, "%s: sieving again from %ld ... \n", argv[0], p[cur - 1]);
c = 0;
while ((pr = sieve_next(&s)) > 0) {
++c;
}
fprintf(stderr, "%s: done!\n", argv[0]);
for (ix = 0; ix < s.nbits; ix++) {
if (S_ISSET(&s, ix)) {
printf("%ld\n", S_VAL(&s, ix));
}
}
sieve_clear(&s);
return 0;
}
void
sieve_init(sieve *sp, long base, int nbits)
{
sp->size = (nbits / CHAR_BIT);
if (nbits % CHAR_BIT)
++sp->size;
sp->bits = calloc(sp->size, sizeof(byte));
memset(sp->bits, UCHAR_MAX, sp->size);
if (!(base & 1))
++base;
sp->base = base;
sp->next = 0;
sp->nbits = sp->size * CHAR_BIT;
}
void
sieve_grow(sieve *sp, int nbits)
{
int ns = (nbits / CHAR_BIT);
if (nbits % CHAR_BIT)
++ns;
if (ns > sp->size) {
byte *tmp;
int ix;
tmp = calloc(ns, sizeof(byte));
if (tmp == NULL) {
fprintf(stderr, "Error: out of memory in sieve_grow\n");
return;
}
memcpy(tmp, sp->bits, sp->size);
for (ix = sp->size; ix < ns; ix++) {
tmp[ix] = UCHAR_MAX;
}
free(sp->bits);
sp->bits = tmp;
sp->size = ns;
sp->nbits = sp->size * CHAR_BIT;
}
}
long
sieve_next(sieve *sp)
{
long out;
int ix = 0;
long val;
if (sp->next > sp->nbits)
return -1;
out = S_VAL(sp, sp->next);
#ifdef DEBUG
fprintf(stderr, "Sieving %ld\n", out);
#endif
/* Sieve out all multiples of the current prime */
val = out;
while (ix < sp->nbits) {
val += out;
ix = S_BIT(sp, val);
if ((val & 1) && ix < sp->nbits) { /* && S_ISSET(sp, ix)) { */
S_CLR(sp, ix);
#ifdef DEBUG
fprintf(stderr, "Crossing out %ld (bit %d)\n", val, ix);
#endif
}
}
/* Scan ahead to the next prime */
++sp->next;
while (sp->next < sp->nbits && !S_ISSET(sp, sp->next))
++sp->next;
return out;
}
void
sieve_cross(sieve *sp, long val)
{
int ix = 0;
long cur = val;
while (cur < sp->base)
cur += val;
ix = S_BIT(sp, cur);
while (ix < sp->nbits) {
if (cur & 1)
S_CLR(sp, ix);
cur += val;
ix = S_BIT(sp, cur);
}
}
void
sieve_reset(sieve *sp, long base)
{
memset(sp->bits, UCHAR_MAX, sp->size);
sp->base = base;
sp->next = 0;
}
void
sieve_clear(sieve *sp)
{
if (sp->bits)
free(sp->bits);
sp->bits = NULL;
}
|
