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32 * @(#) Copyright (c) 1989, 1993 The Regents of the University of California. All rights reserved.
33 * @(#)primes.c 8.5 (Berkeley) 5/10/95
34 * $FreeBSD: src/games/primes/primes.c,v 1.15.2.2 2002/10/23 14:59:14 fanf Exp $
35 * $DragonFly: src/games/primes/primes.c,v 1.2 2003/06/17 04:25:24 dillon Exp $
39 * primes - generate a table of primes between two values
41 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
43 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
46 * primes [-h] [start [stop]]
48 * Print primes >= start and < stop. If stop is omitted,
49 * the value 4294967295 (2^32-1) is assumed. If start is
50 * omitted, start is read from standard input.
52 * validation check: there are 664579 primes between 0 and 10^7
68 * Eratosthenes sieve table
70 * We only sieve the odd numbers. The base of our sieve windows are always
71 * odd. If the base of table is 1, table[i] represents 2*i-1. After the
72 * sieve, table[i] == 1 if and only if 2*i-1 is prime.
74 * We make TABSIZE large to reduce the overhead of inner loop setup.
76 static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
80 static void primes(ubig, ubig);
81 static ubig read_num_buf(void);
82 static void usage(void);
85 main(int argc, char *argv[])
87 ubig start; /* where to start generating */
88 ubig stop; /* don't generate at or above this value */
92 while ((ch = getopt(argc, argv, "h")) != -1)
108 * Convert low and high args. Strtoul(3) sets errno to
109 * ERANGE if the number is too large, but, if there's
110 * a leading minus sign it returns the negation of the
111 * result of the conversion, which we'd rather disallow.
115 /* Start and stop supplied on the command line. */
116 if (argv[0][0] == '-' || argv[1][0] == '-')
117 errx(1, "negative numbers aren't permitted.");
120 start = strtoul(argv[0], &p, 0);
122 err(1, "%s", argv[0]);
124 errx(1, "%s: illegal numeric format.", argv[0]);
127 stop = strtoul(argv[1], &p, 0);
129 err(1, "%s", argv[1]);
131 errx(1, "%s: illegal numeric format.", argv[1]);
134 /* Start on the command line. */
135 if (argv[0][0] == '-')
136 errx(1, "negative numbers aren't permitted.");
139 start = strtoul(argv[0], &p, 0);
141 err(1, "%s", argv[0]);
143 errx(1, "%s: illegal numeric format.", argv[0]);
146 start = read_num_buf();
153 errx(1, "start value must be less than stop value.");
160 * This routine returns a number n, where 0 <= n && n <= BIG.
166 char *p, buf[LINE_MAX]; /* > max number of digits. */
169 if (fgets(buf, sizeof(buf), stdin) == NULL) {
174 for (p = buf; isblank(*p); ++p);
175 if (*p == '\n' || *p == '\0')
178 errx(1, "negative numbers aren't permitted.");
180 val = strtoul(buf, &p, 0);
184 errx(1, "%s: illegal numeric format.", buf);
190 * primes - sieve and print primes from start up to and but not including stop
193 primes(ubig start, ubig stop)
195 char *q; /* sieve spot */
196 ubig factor; /* index and factor */
197 char *tab_lim; /* the limit to sieve on the table */
198 const ubig *p; /* prime table pointer */
199 ubig fact_lim; /* highest prime for current block */
200 ubig mod; /* temp storage for mod */
203 * A number of systems can not convert double values into unsigned
204 * longs when the values are larger than the largest signed value.
205 * We don't have this problem, so we can go all the way to BIG.
218 * be sure that the values are odd, or 2
220 if (start != 2 && (start&0x1) == 0) {
223 if (stop != 2 && (stop&0x1) == 0) {
228 * quick list of primes <= pr_limit
230 if (start <= *pr_limit) {
231 /* skip primes up to the start value */
232 for (p = &prime[0], factor = prime[0];
233 factor < stop && p <= pr_limit; factor = *(++p)) {
234 if (factor >= start) {
235 printf(hflag ? "0x%lx\n" : "%lu\n", factor);
238 /* return early if we are done */
246 * we shall sieve a bytemap window, note primes and move the window
247 * upward until we pass the stop point
249 while (start < stop) {
251 * factor out 3, 5, 7, 11 and 13
253 /* initial pattern copy */
254 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
255 memcpy(table, &pattern[factor], pattern_size-factor);
256 /* main block pattern copies */
257 for (fact_lim=pattern_size-factor;
258 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
259 memcpy(&table[fact_lim], pattern, pattern_size);
261 /* final block pattern copy */
262 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
265 * sieve for primes 17 and higher
267 /* note highest useful factor and sieve spot */
268 if (stop-start > TABSIZE+TABSIZE) {
269 tab_lim = &table[TABSIZE]; /* sieve it all */
270 fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
272 tab_lim = &table[(stop-start)/2]; /* partial sieve */
273 fact_lim = sqrt(stop+1.0);
275 /* sieve for factors >= 17 */
276 factor = 17; /* 17 is first prime to use */
277 p = &prime[7]; /* 19 is next prime, pi(19)=7 */
279 /* determine the factor's initial sieve point */
282 q = &table[(factor-mod)/2];
284 q = &table[mod ? factor-(mod/2) : 0];
286 /* sive for our current factor */
287 for ( ; q < tab_lim; q += factor) {
288 *q = '\0'; /* sieve out a spot */
291 } while (factor <= fact_lim);
294 * print generated primes
296 for (q = table; q < tab_lim; ++q, start+=2) {
298 printf(hflag ? "0x%lx\n" : "%lu\n", start);
307 fprintf(stderr, "usage: primes [-h] [start [stop]]\n");