2 * Copyright (c) 1989, 1993
3 * The Regents of the University of California. All rights reserved.
5 * This code is derived from software contributed to Berkeley by
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9 * modification, are permitted provided that the following conditions
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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.
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
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34 static const char copyright[] =
35 "@(#) Copyright (c) 1989, 1993\n\
36 The Regents of the University of California. All rights reserved.\n";
41 static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
46 * primes - generate a table of primes between two values
48 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
50 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
53 * primes [-h] [start [stop]]
55 * Print primes >= start and < stop. If stop is omitted,
56 * the value 18446744073709551615 (2^64-1) is assumed. If
57 * start is omitted, start is read from standard input.
59 * validation check: there are 664579 primes between 0 and 10^7
62 #include <capsicum_helpers.h>
78 * Eratosthenes sieve table
80 * We only sieve the odd numbers. The base of our sieve windows are always
81 * odd. If the base of table is 1, table[i] represents 2*i-1. After the
82 * sieve, table[i] == 1 if and only if 2*i-1 is prime.
84 * We make TABSIZE large to reduce the overhead of inner loop setup.
86 static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
90 static void primes(ubig, ubig);
91 static ubig read_num_buf(void);
92 static void usage(void);
95 main(int argc, char *argv[])
97 ubig start; /* where to start generating */
98 ubig stop; /* don't generate at or above this value */
102 caph_cache_catpages();
103 if (caph_enter() < 0)
106 while ((ch = getopt(argc, argv, "h")) != -1)
119 stop = (uint64_t)(-1);
122 * Convert low and high args. Strtoumax(3) sets errno to
123 * ERANGE if the number is too large, but, if there's
124 * a leading minus sign it returns the negation of the
125 * result of the conversion, which we'd rather disallow.
129 /* Start and stop supplied on the command line. */
130 if (argv[0][0] == '-' || argv[1][0] == '-')
131 errx(1, "negative numbers aren't permitted.");
134 start = strtoumax(argv[0], &p, 0);
136 err(1, "%s", argv[0]);
138 errx(1, "%s: illegal numeric format.", argv[0]);
141 stop = strtoumax(argv[1], &p, 0);
143 err(1, "%s", argv[1]);
145 errx(1, "%s: illegal numeric format.", argv[1]);
148 /* Start on the command line. */
149 if (argv[0][0] == '-')
150 errx(1, "negative numbers aren't permitted.");
153 start = strtoumax(argv[0], &p, 0);
155 err(1, "%s", argv[0]);
157 errx(1, "%s: illegal numeric format.", argv[0]);
160 start = read_num_buf();
167 errx(1, "start value must be less than stop value.");
174 * This routine returns a number n, where 0 <= n && n <= BIG.
180 char *p, buf[LINE_MAX]; /* > max number of digits. */
183 if (fgets(buf, sizeof(buf), stdin) == NULL) {
188 for (p = buf; isblank(*p); ++p);
189 if (*p == '\n' || *p == '\0')
192 errx(1, "negative numbers aren't permitted.");
194 val = strtoumax(buf, &p, 0);
198 errx(1, "%s: illegal numeric format.", buf);
204 * primes - sieve and print primes from start up to and but not including stop
207 primes(ubig start, ubig stop)
209 char *q; /* sieve spot */
210 ubig factor; /* index and factor */
211 char *tab_lim; /* the limit to sieve on the table */
212 const ubig *p; /* prime table pointer */
213 ubig fact_lim; /* highest prime for current block */
214 ubig mod; /* temp storage for mod */
217 * A number of systems can not convert double values into unsigned
218 * longs when the values are larger than the largest signed value.
219 * We don't have this problem, so we can go all the way to BIG.
232 * be sure that the values are odd, or 2
234 if (start != 2 && (start&0x1) == 0) {
237 if (stop != 2 && (stop&0x1) == 0) {
242 * quick list of primes <= pr_limit
244 if (start <= *pr_limit) {
245 /* skip primes up to the start value */
246 for (p = &prime[0], factor = prime[0];
247 factor < stop && p <= pr_limit; factor = *(++p)) {
248 if (factor >= start) {
249 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor);
252 /* return early if we are done */
260 * we shall sieve a bytemap window, note primes and move the window
261 * upward until we pass the stop point
263 while (start < stop) {
265 * factor out 3, 5, 7, 11 and 13
267 /* initial pattern copy */
268 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
269 memcpy(table, &pattern[factor], pattern_size-factor);
270 /* main block pattern copies */
271 for (fact_lim=pattern_size-factor;
272 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
273 memcpy(&table[fact_lim], pattern, pattern_size);
275 /* final block pattern copy */
276 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
279 * sieve for primes 17 and higher
281 /* note highest useful factor and sieve spot */
282 if (stop-start > TABSIZE+TABSIZE) {
283 tab_lim = &table[TABSIZE]; /* sieve it all */
284 fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
286 tab_lim = &table[(stop-start)/2]; /* partial sieve */
287 fact_lim = sqrt(stop+1.0);
289 /* sieve for factors >= 17 */
290 factor = 17; /* 17 is first prime to use */
291 p = &prime[7]; /* 19 is next prime, pi(19)=7 */
293 /* determine the factor's initial sieve point */
296 q = &table[(factor-mod)/2];
298 q = &table[mod ? factor-(mod/2) : 0];
300 /* sive for our current factor */
301 for ( ; q < tab_lim; q += factor) {
302 *q = '\0'; /* sieve out a spot */
305 } while (factor <= fact_lim);
308 * print generated primes
310 for (q = table; q < tab_lim; ++q, start+=2) {
312 if (start > SIEVEMAX) {
316 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start);
325 fprintf(stderr, "usage: primes [-h] [start [stop]]\n");