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#ifndef lint
34static const char copyright[] =
35"@(#) Copyright (c) 1989, 1993\n\
36	The Regents of the University of California.  All rights reserved.\n";
37#endif /* not lint */
38
39#ifndef lint
40#if 0
41static char sccsid[] = "@(#)primes.c	8.5 (Berkeley) 5/10/95";
42#endif
43static const char rcsid[] =
44 "$FreeBSD: releng/11.0/usr.bin/primes/primes.c 272207 2014-09-27 09:00:38Z cperciva $";
45#endif /* not lint */
46
47/*
48 * primes - generate a table of primes between two values
49 *
50 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
51 *
52 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
53 *
54 * usage:
55 *	primes [-h] [start [stop]]
56 *
57 *	Print primes >= start and < stop.  If stop is omitted,
58 *	the value 4294967295 (2^32-1) is assumed.  If start is
59 *	omitted, start is read from standard input.
60 *
61 * validation check: there are 664579 primes between 0 and 10^7
62 */
63
64#include <ctype.h>
65#include <err.h>
66#include <errno.h>
67#include <inttypes.h>
68#include <limits.h>
69#include <math.h>
70#include <stdio.h>
71#include <stdlib.h>
72#include <string.h>
73#include <unistd.h>
74
75#include "primes.h"
76
77/*
78 * Eratosthenes sieve table
79 *
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.
83 *
84 * We make TABSIZE large to reduce the overhead of inner loop setup.
85 */
86static char table[TABSIZE];	 /* Eratosthenes sieve of odd numbers */
87
88static int	hflag;
89
90static void	primes(ubig, ubig);
91static ubig	read_num_buf(void);
92static void	usage(void);
93
94int
95main(int argc, char *argv[])
96{
97	ubig start;		/* where to start generating */
98	ubig stop;		/* don't generate at or above this value */
99	int ch;
100	char *p;
101
102	while ((ch = getopt(argc, argv, "h")) != -1)
103		switch (ch) {
104		case 'h':
105			hflag++;
106			break;
107		case '?':
108		default:
109			usage();
110		}
111	argc -= optind;
112	argv += optind;
113
114	start = 0;
115	stop = SPSPMAX;
116
117	/*
118	 * Convert low and high args.  Strtoumax(3) sets errno to
119	 * ERANGE if the number is too large, but, if there's
120	 * a leading minus sign it returns the negation of the
121	 * result of the conversion, which we'd rather disallow.
122	 */
123	switch (argc) {
124	case 2:
125		/* Start and stop supplied on the command line. */
126		if (argv[0][0] == '-' || argv[1][0] == '-')
127			errx(1, "negative numbers aren't permitted.");
128
129		errno = 0;
130		start = strtoumax(argv[0], &p, 0);
131		if (errno)
132			err(1, "%s", argv[0]);
133		if (*p != '\0')
134			errx(1, "%s: illegal numeric format.", argv[0]);
135
136		errno = 0;
137		stop = strtoumax(argv[1], &p, 0);
138		if (errno)
139			err(1, "%s", argv[1]);
140		if (*p != '\0')
141			errx(1, "%s: illegal numeric format.", argv[1]);
142		if (stop > SPSPMAX)
143			errx(1, "%s: stop value too large.", argv[1]);
144		break;
145	case 1:
146		/* Start on the command line. */
147		if (argv[0][0] == '-')
148			errx(1, "negative numbers aren't permitted.");
149
150		errno = 0;
151		start = strtoumax(argv[0], &p, 0);
152		if (errno)
153			err(1, "%s", argv[0]);
154		if (*p != '\0')
155			errx(1, "%s: illegal numeric format.", argv[0]);
156		break;
157	case 0:
158		start = read_num_buf();
159		break;
160	default:
161		usage();
162	}
163
164	if (start > stop)
165		errx(1, "start value must be less than stop value.");
166	primes(start, stop);
167	return (0);
168}
169
170/*
171 * read_num_buf --
172 *	This routine returns a number n, where 0 <= n && n <= BIG.
173 */
174static ubig
175read_num_buf(void)
176{
177	ubig val;
178	char *p, buf[LINE_MAX];		/* > max number of digits. */
179
180	for (;;) {
181		if (fgets(buf, sizeof(buf), stdin) == NULL) {
182			if (ferror(stdin))
183				err(1, "stdin");
184			exit(0);
185		}
186		for (p = buf; isblank(*p); ++p);
187		if (*p == '\n' || *p == '\0')
188			continue;
189		if (*p == '-')
190			errx(1, "negative numbers aren't permitted.");
191		errno = 0;
192		val = strtoumax(buf, &p, 0);
193		if (errno)
194			err(1, "%s", buf);
195		if (*p != '\n')
196			errx(1, "%s: illegal numeric format.", buf);
197		return (val);
198	}
199}
200
201/*
202 * primes - sieve and print primes from start up to and but not including stop
203 */
204static void
205primes(ubig start, ubig stop)
206{
207	char *q;		/* sieve spot */
208	ubig factor;		/* index and factor */
209	char *tab_lim;		/* the limit to sieve on the table */
210	const ubig *p;		/* prime table pointer */
211	ubig fact_lim;		/* highest prime for current block */
212	ubig mod;		/* temp storage for mod */
213
214	/*
215	 * A number of systems can not convert double values into unsigned
216	 * longs when the values are larger than the largest signed value.
217	 * We don't have this problem, so we can go all the way to BIG.
218	 */
219	if (start < 3) {
220		start = (ubig)2;
221	}
222	if (stop < 3) {
223		stop = (ubig)2;
224	}
225	if (stop <= start) {
226		return;
227	}
228
229	/*
230	 * be sure that the values are odd, or 2
231	 */
232	if (start != 2 && (start&0x1) == 0) {
233		++start;
234	}
235	if (stop != 2 && (stop&0x1) == 0) {
236		++stop;
237	}
238
239	/*
240	 * quick list of primes <= pr_limit
241	 */
242	if (start <= *pr_limit) {
243		/* skip primes up to the start value */
244		for (p = &prime[0], factor = prime[0];
245		    factor < stop && p <= pr_limit; factor = *(++p)) {
246			if (factor >= start) {
247				printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor);
248			}
249		}
250		/* return early if we are done */
251		if (p <= pr_limit) {
252			return;
253		}
254		start = *pr_limit+2;
255	}
256
257	/*
258	 * we shall sieve a bytemap window, note primes and move the window
259	 * upward until we pass the stop point
260	 */
261	while (start < stop) {
262		/*
263		 * factor out 3, 5, 7, 11 and 13
264		 */
265		/* initial pattern copy */
266		factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
267		memcpy(table, &pattern[factor], pattern_size-factor);
268		/* main block pattern copies */
269		for (fact_lim=pattern_size-factor;
270		    fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
271			memcpy(&table[fact_lim], pattern, pattern_size);
272		}
273		/* final block pattern copy */
274		memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
275
276		/*
277		 * sieve for primes 17 and higher
278		 */
279		/* note highest useful factor and sieve spot */
280		if (stop-start > TABSIZE+TABSIZE) {
281			tab_lim = &table[TABSIZE]; /* sieve it all */
282			fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
283		} else {
284			tab_lim = &table[(stop-start)/2]; /* partial sieve */
285			fact_lim = sqrt(stop+1.0);
286		}
287		/* sieve for factors >= 17 */
288		factor = 17;	/* 17 is first prime to use */
289		p = &prime[7];	/* 19 is next prime, pi(19)=7 */
290		do {
291			/* determine the factor's initial sieve point */
292			mod = start%factor;
293			if (mod & 0x1) {
294				q = &table[(factor-mod)/2];
295			} else {
296				q = &table[mod ? factor-(mod/2) : 0];
297			}
298			/* sive for our current factor */
299			for ( ; q < tab_lim; q += factor) {
300				*q = '\0'; /* sieve out a spot */
301			}
302			factor = *p++;
303		} while (factor <= fact_lim);
304
305		/*
306		 * print generated primes
307		 */
308		for (q = table; q < tab_lim; ++q, start+=2) {
309			if (*q) {
310				if (start > SIEVEMAX) {
311					if (!isprime(start))
312						continue;
313				}
314				printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start);
315			}
316		}
317	}
318}
319
320static void
321usage(void)
322{
323	fprintf(stderr, "usage: primes [-h] [start [stop]]\n");
324	exit(1);
325}
326