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 "$FreeBSD$";
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 <limits.h>
68#include <math.h>
69#include <stdio.h>
70#include <stdlib.h>
71#include <string.h>
72#include <unistd.h>
73
74#include "primes.h"
75
76/*
77 * Eratosthenes sieve table
78 *
79 * We only sieve the odd numbers.  The base of our sieve windows are always
80 * odd.  If the base of table is 1, table[i] represents 2*i-1.  After the
81 * sieve, table[i] == 1 if and only if 2*i-1 is prime.
82 *
83 * We make TABSIZE large to reduce the overhead of inner loop setup.
84 */
85static char table[TABSIZE];	 /* Eratosthenes sieve of odd numbers */
86
87static int	hflag;
88
89static void	primes(ubig, ubig);
90static ubig	read_num_buf(void);
91static void	usage(void);
92
93int
94main(int argc, char *argv[])
95{
96	ubig start;		/* where to start generating */
97	ubig stop;		/* don't generate at or above this value */
98	int ch;
99	char *p;
100
101	while ((ch = getopt(argc, argv, "h")) != -1)
102		switch (ch) {
103		case 'h':
104			hflag++;
105			break;
106		case '?':
107		default:
108			usage();
109		}
110	argc -= optind;
111	argv += optind;
112
113	start = 0;
114	stop = BIG;
115
116	/*
117	 * Convert low and high args.  Strtoul(3) sets errno to
118	 * ERANGE if the number is too large, but, if there's
119	 * a leading minus sign it returns the negation of the
120	 * result of the conversion, which we'd rather disallow.
121	 */
122	switch (argc) {
123	case 2:
124		/* Start and stop supplied on the command line. */
125		if (argv[0][0] == '-' || argv[1][0] == '-')
126			errx(1, "negative numbers aren't permitted.");
127
128		errno = 0;
129		start = strtoul(argv[0], &p, 0);
130		if (errno)
131			err(1, "%s", argv[0]);
132		if (*p != '\0')
133			errx(1, "%s: illegal numeric format.", argv[0]);
134
135		errno = 0;
136		stop = strtoul(argv[1], &p, 0);
137		if (errno)
138			err(1, "%s", argv[1]);
139		if (*p != '\0')
140			errx(1, "%s: illegal numeric format.", argv[1]);
141		break;
142	case 1:
143		/* Start on the command line. */
144		if (argv[0][0] == '-')
145			errx(1, "negative numbers aren't permitted.");
146
147		errno = 0;
148		start = strtoul(argv[0], &p, 0);
149		if (errno)
150			err(1, "%s", argv[0]);
151		if (*p != '\0')
152			errx(1, "%s: illegal numeric format.", argv[0]);
153		break;
154	case 0:
155		start = read_num_buf();
156		break;
157	default:
158		usage();
159	}
160
161	if (start > stop)
162		errx(1, "start value must be less than stop value.");
163	primes(start, stop);
164	return (0);
165}
166
167/*
168 * read_num_buf --
169 *	This routine returns a number n, where 0 <= n && n <= BIG.
170 */
171static ubig
172read_num_buf(void)
173{
174	ubig val;
175	char *p, buf[LINE_MAX];		/* > max number of digits. */
176
177	for (;;) {
178		if (fgets(buf, sizeof(buf), stdin) == NULL) {
179			if (ferror(stdin))
180				err(1, "stdin");
181			exit(0);
182		}
183		for (p = buf; isblank(*p); ++p);
184		if (*p == '\n' || *p == '\0')
185			continue;
186		if (*p == '-')
187			errx(1, "negative numbers aren't permitted.");
188		errno = 0;
189		val = strtoul(buf, &p, 0);
190		if (errno)
191			err(1, "%s", buf);
192		if (*p != '\n')
193			errx(1, "%s: illegal numeric format.", buf);
194		return (val);
195	}
196}
197
198/*
199 * primes - sieve and print primes from start up to and but not including stop
200 */
201static void
202primes(ubig start, ubig stop)
203{
204	char *q;		/* sieve spot */
205	ubig factor;		/* index and factor */
206	char *tab_lim;		/* the limit to sieve on the table */
207	const ubig *p;		/* prime table pointer */
208	ubig fact_lim;		/* highest prime for current block */
209	ubig mod;		/* temp storage for mod */
210
211	/*
212	 * A number of systems can not convert double values into unsigned
213	 * longs when the values are larger than the largest signed value.
214	 * We don't have this problem, so we can go all the way to BIG.
215	 */
216	if (start < 3) {
217		start = (ubig)2;
218	}
219	if (stop < 3) {
220		stop = (ubig)2;
221	}
222	if (stop <= start) {
223		return;
224	}
225
226	/*
227	 * be sure that the values are odd, or 2
228	 */
229	if (start != 2 && (start&0x1) == 0) {
230		++start;
231	}
232	if (stop != 2 && (stop&0x1) == 0) {
233		++stop;
234	}
235
236	/*
237	 * quick list of primes <= pr_limit
238	 */
239	if (start <= *pr_limit) {
240		/* skip primes up to the start value */
241		for (p = &prime[0], factor = prime[0];
242		    factor < stop && p <= pr_limit; factor = *(++p)) {
243			if (factor >= start) {
244				printf(hflag ? "0x%lx\n" : "%lu\n", factor);
245			}
246		}
247		/* return early if we are done */
248		if (p <= pr_limit) {
249			return;
250		}
251		start = *pr_limit+2;
252	}
253
254	/*
255	 * we shall sieve a bytemap window, note primes and move the window
256	 * upward until we pass the stop point
257	 */
258	while (start < stop) {
259		/*
260		 * factor out 3, 5, 7, 11 and 13
261		 */
262		/* initial pattern copy */
263		factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
264		memcpy(table, &pattern[factor], pattern_size-factor);
265		/* main block pattern copies */
266		for (fact_lim=pattern_size-factor;
267		    fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
268			memcpy(&table[fact_lim], pattern, pattern_size);
269		}
270		/* final block pattern copy */
271		memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
272
273		/*
274		 * sieve for primes 17 and higher
275		 */
276		/* note highest useful factor and sieve spot */
277		if (stop-start > TABSIZE+TABSIZE) {
278			tab_lim = &table[TABSIZE]; /* sieve it all */
279			fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
280		} else {
281			tab_lim = &table[(stop-start)/2]; /* partial sieve */
282			fact_lim = sqrt(stop+1.0);
283		}
284		/* sieve for factors >= 17 */
285		factor = 17;	/* 17 is first prime to use */
286		p = &prime[7];	/* 19 is next prime, pi(19)=7 */
287		do {
288			/* determine the factor's initial sieve point */
289			mod = start%factor;
290			if (mod & 0x1) {
291				q = &table[(factor-mod)/2];
292			} else {
293				q = &table[mod ? factor-(mod/2) : 0];
294			}
295			/* sive for our current factor */
296			for ( ; q < tab_lim; q += factor) {
297				*q = '\0'; /* sieve out a spot */
298			}
299			factor = *p++;
300		} while (factor <= fact_lim);
301
302		/*
303		 * print generated primes
304		 */
305		for (q = table; q < tab_lim; ++q, start+=2) {
306			if (*q) {
307				printf(hflag ? "0x%lx\n" : "%lu\n", start);
308			}
309		}
310	}
311}
312
313static void
314usage(void)
315{
316	fprintf(stderr, "usage: primes [-h] [start [stop]]\n");
317	exit(1);
318}
319