1 /*
2 * Copyright (c) 1989, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * This code is derived from software contributed to Berkeley by
6 * Landon Curt Noll.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 * 3. Neither the name of the University nor the names of its contributors
17 * may be used to endorse or promote products derived from this software
18 * without specific prior written permission.
19 *
20 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
21 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30 * SUCH DAMAGE.
31 */
32
33 /*
34 * primes - generate a table of primes between two values
35 *
36 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
37 *
38 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
39 *
40 * usage:
41 * primes [-h] [start [stop]]
42 *
43 * Print primes >= start and < stop. If stop is omitted,
44 * the value 18446744073709551615 (2^64-1) is assumed. If
45 * start is omitted, start is read from standard input.
46 *
47 * validation check: there are 664579 primes between 0 and 10^7
48 */
49
50 #include <capsicum_helpers.h>
51 #include <ctype.h>
52 #include <err.h>
53 #include <errno.h>
54 #include <inttypes.h>
55 #include <limits.h>
56 #include <math.h>
57 #include <stdio.h>
58 #include <stdlib.h>
59 #include <string.h>
60 #include <nl_types.h>
61 #include <unistd.h>
62
63 #include "primes.h"
64
65 /*
66 * Eratosthenes sieve table
67 *
68 * We only sieve the odd numbers. The base of our sieve windows are always
69 * odd. If the base of table is 1, table[i] represents 2*i-1. After the
70 * sieve, table[i] == 1 if and only if 2*i-1 is prime.
71 *
72 * We make TABSIZE large to reduce the overhead of inner loop setup.
73 */
74 static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
75
76 static int hflag;
77
78 static void primes(ubig, ubig);
79 static ubig read_num_buf(void);
80 static void usage(void);
81
82 int
main(int argc,char * argv[])83 main(int argc, char *argv[])
84 {
85 ubig start; /* where to start generating */
86 ubig stop; /* don't generate at or above this value */
87 int ch;
88 char *p;
89
90 caph_cache_catpages();
91 if (caph_enter() < 0)
92 err(1, "cap_enter");
93
94 while ((ch = getopt(argc, argv, "h")) != -1)
95 switch (ch) {
96 case 'h':
97 hflag++;
98 break;
99 case '?':
100 default:
101 usage();
102 }
103 argc -= optind;
104 argv += optind;
105
106 start = 0;
107 stop = (uint64_t)(-1);
108
109 /*
110 * Convert low and high args. Strtoumax(3) sets errno to
111 * ERANGE if the number is too large, but, if there's
112 * a leading minus sign it returns the negation of the
113 * result of the conversion, which we'd rather disallow.
114 */
115 switch (argc) {
116 case 2:
117 /* Start and stop supplied on the command line. */
118 if (argv[0][0] == '-' || argv[1][0] == '-')
119 errx(1, "negative numbers aren't permitted.");
120
121 errno = 0;
122 start = strtoumax(argv[0], &p, 0);
123 if (errno)
124 err(1, "%s", argv[0]);
125 if (*p != '\0')
126 errx(1, "%s: illegal numeric format.", argv[0]);
127
128 errno = 0;
129 stop = strtoumax(argv[1], &p, 0);
130 if (errno)
131 err(1, "%s", argv[1]);
132 if (*p != '\0')
133 errx(1, "%s: illegal numeric format.", argv[1]);
134 break;
135 case 1:
136 /* Start on the command line. */
137 if (argv[0][0] == '-')
138 errx(1, "negative numbers aren't permitted.");
139
140 errno = 0;
141 start = strtoumax(argv[0], &p, 0);
142 if (errno)
143 err(1, "%s", argv[0]);
144 if (*p != '\0')
145 errx(1, "%s: illegal numeric format.", argv[0]);
146 break;
147 case 0:
148 start = read_num_buf();
149 break;
150 default:
151 usage();
152 }
153
154 if (start > stop)
155 errx(1, "start value must be less than stop value.");
156 primes(start, stop);
157 return (0);
158 }
159
160 /*
161 * read_num_buf --
162 * This routine returns a number n, where 0 <= n && n <= BIG.
163 */
164 static ubig
read_num_buf(void)165 read_num_buf(void)
166 {
167 ubig val;
168 char *p, buf[LINE_MAX]; /* > max number of digits. */
169
170 for (;;) {
171 if (fgets(buf, sizeof(buf), stdin) == NULL) {
172 if (ferror(stdin))
173 err(1, "stdin");
174 exit(0);
175 }
176 for (p = buf; isblank(*p); ++p);
177 if (*p == '\n' || *p == '\0')
178 continue;
179 if (*p == '-')
180 errx(1, "negative numbers aren't permitted.");
181 errno = 0;
182 val = strtoumax(buf, &p, 0);
183 if (errno)
184 err(1, "%s", buf);
185 if (*p != '\n')
186 errx(1, "%s: illegal numeric format.", buf);
187 return (val);
188 }
189 }
190
191 /*
192 * primes - sieve and print primes from start up to and but not including stop
193 */
194 static void
primes(ubig start,ubig stop)195 primes(ubig start, ubig stop)
196 {
197 char *q; /* sieve spot */
198 ubig factor; /* index and factor */
199 char *tab_lim; /* the limit to sieve on the table */
200 const ubig *p; /* prime table pointer */
201 ubig fact_lim; /* highest prime for current block */
202 ubig mod; /* temp storage for mod */
203
204 /*
205 * A number of systems can not convert double values into unsigned
206 * longs when the values are larger than the largest signed value.
207 * We don't have this problem, so we can go all the way to BIG.
208 */
209 if (start < 3) {
210 start = (ubig)2;
211 }
212 if (stop < 3) {
213 stop = (ubig)2;
214 }
215 if (stop <= start) {
216 return;
217 }
218
219 /*
220 * be sure that the values are odd, or 2
221 */
222 if (start != 2 && (start&0x1) == 0) {
223 ++start;
224 }
225 if (stop != 2 && (stop&0x1) == 0) {
226 ++stop;
227 }
228
229 /*
230 * quick list of primes <= pr_limit
231 */
232 if (start <= *pr_limit) {
233 /* skip primes up to the start value */
234 for (p = &prime[0], factor = prime[0];
235 factor < stop && p <= pr_limit; factor = *(++p)) {
236 if (factor >= start) {
237 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor);
238 }
239 }
240 /* return early if we are done */
241 if (p <= pr_limit) {
242 return;
243 }
244 start = *pr_limit+2;
245 }
246
247 /*
248 * we shall sieve a bytemap window, note primes and move the window
249 * upward until we pass the stop point
250 */
251 while (start < stop) {
252 /*
253 * factor out 3, 5, 7, 11 and 13
254 */
255 /* initial pattern copy */
256 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
257 memcpy(table, &pattern[factor], pattern_size-factor);
258 /* main block pattern copies */
259 for (fact_lim=pattern_size-factor;
260 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
261 memcpy(&table[fact_lim], pattern, pattern_size);
262 }
263 /* final block pattern copy */
264 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
265
266 /*
267 * sieve for primes 17 and higher
268 */
269 /* note highest useful factor and sieve spot */
270 if (stop-start > TABSIZE+TABSIZE) {
271 tab_lim = &table[TABSIZE]; /* sieve it all */
272 fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
273 } else {
274 tab_lim = &table[(stop-start)/2]; /* partial sieve */
275 fact_lim = sqrt(stop+1.0);
276 }
277 /* sieve for factors >= 17 */
278 factor = 17; /* 17 is first prime to use */
279 p = &prime[7]; /* 19 is next prime, pi(19)=7 */
280 do {
281 /* determine the factor's initial sieve point */
282 mod = start%factor;
283 if (mod & 0x1) {
284 q = &table[(factor-mod)/2];
285 } else {
286 q = &table[mod ? factor-(mod/2) : 0];
287 }
288 /* sive for our current factor */
289 for ( ; q < tab_lim; q += factor) {
290 *q = '\0'; /* sieve out a spot */
291 }
292 factor = *p++;
293 } while (factor <= fact_lim);
294
295 /*
296 * print generated primes
297 */
298 for (q = table; q < tab_lim; ++q, start+=2) {
299 if (*q) {
300 if (start > SIEVEMAX) {
301 if (!isprime(start))
302 continue;
303 }
304 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start);
305 }
306 }
307 }
308 }
309
310 static void
usage(void)311 usage(void)
312 {
313 fprintf(stderr, "usage: primes [-h] [start [stop]]\n");
314 exit(1);
315 }
316