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1 /* $NetBSD: primes.c,v 1.4 1995/03/23 08:35:55 cgd Exp $ */
4 * Copyright (c) 1989, 1993
5 * The Regents of the University of California. All rights reserved.
7 * This code is derived from software contributed to Berkeley by
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in the
17 * documentation and/or other materials provided with the distribution.
18 * 3. All advertising materials mentioning features or use of this software
19 * must display the following acknowledgement:
20 * This product includes software developed by the University of
21 * California, Berkeley and its contributors.
22 * 4. Neither the name of the University nor the names of its contributors
23 * may be used to endorse or promote products derived from this software
24 * without specific prior written permission.
26 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
27 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
28 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
29 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
30 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
31 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
32 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
33 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
34 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
35 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
40 static char copyright
[] =
41 "@(#) Copyright (c) 1989, 1993\n\
42 The Regents of the University of California. All rights reserved.\n";
47 static char sccsid
[] = "@(#)primes.c 8.4 (Berkeley) 3/21/94";
49 static char rcsid
[] = "$NetBSD: primes.c,v 1.4 1995/03/23 08:35:55 cgd Exp $";
54 * primes - generate a table of primes between two values
56 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
58 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
61 * primes [start [stop]]
63 * Print primes >= start and < stop. If stop is omitted,
64 * the value 4294967295 (2^32-1) is assumed. If start is
65 * omitted, start is read from standard input.
67 * validation check: there are 664579 primes between 0 and 10^7
82 * Eratosthenes sieve table
84 * We only sieve the odd numbers. The base of our sieve windows are always
85 * odd. If the base of table is 1, table[i] represents 2*i-1. After the
86 * sieve, table[i] == 1 if and only iff 2*i-1 is prime.
88 * We make TABSIZE large to reduce the overhead of inner loop setup.
90 char table
[TABSIZE
]; /* Eratosthenes sieve of odd numbers */
93 * prime[i] is the (i-1)th prime.
95 * We are able to sieve 2^32-1 because this byte table yields all primes
96 * up to 65537 and 65537^2 > 2^32-1.
99 extern ubig
*pr_limit
; /* largest prime in the prime array */
102 * To avoid excessive sieves for small factors, we use the table below to
103 * setup our sieve blocks. Each element represents a odd number starting
104 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13.
106 extern char pattern
[];
107 extern int pattern_size
; /* length of pattern array */
109 void primes
__P((ubig
, ubig
));
110 ubig read_num_buf
__P((void));
111 void usage
__P((void));
118 ubig start
; /* where to start generating */
119 ubig stop
; /* don't generate at or above this value */
123 while ((ch
= getopt(argc
, argv
, "")) != EOF
)
136 * Convert low and high args. Strtoul(3) sets errno to
137 * ERANGE if the number is too large, but, if there's
138 * a leading minus sign it returns the negation of the
139 * result of the conversion, which we'd rather disallow.
143 /* Start and stop supplied on the command line. */
144 if (argv
[0][0] == '-' || argv
[1][0] == '-')
145 errx(1, "negative numbers aren't permitted.");
148 start
= strtoul(argv
[0], &p
, 10);
150 err(1, "%s", argv
[0]);
152 errx(1, "%s: illegal numeric format.", argv
[0]);
155 stop
= strtoul(argv
[1], &p
, 10);
157 err(1, "%s", argv
[1]);
159 errx(1, "%s: illegal numeric format.", argv
[1]);
162 /* Start on the command line. */
163 if (argv
[0][0] == '-')
164 errx(1, "negative numbers aren't permitted.");
167 start
= strtoul(argv
[0], &p
, 10);
169 err(1, "%s", argv
[0]);
171 errx(1, "%s: illegal numeric format.", argv
[0]);
174 start
= read_num_buf();
181 errx(1, "start value must be less than stop value.");
188 * This routine returns a number n, where 0 <= n && n <= BIG.
194 char *p
, buf
[100]; /* > max number of digits. */
197 if (fgets(buf
, sizeof(buf
), stdin
) == NULL
) {
202 for (p
= buf
; isblank(*p
); ++p
);
203 if (*p
== '\n' || *p
== '\0')
206 errx(1, "negative numbers aren't permitted.");
208 val
= strtoul(buf
, &p
, 10);
212 errx(1, "%s: illegal numeric format.", buf
);
218 * primes - sieve and print primes from start up to and but not including stop
222 ubig start
; /* where to start generating */
223 ubig stop
; /* don't generate at or above this value */
225 register char *q
; /* sieve spot */
226 register ubig factor
; /* index and factor */
227 register char *tab_lim
; /* the limit to sieve on the table */
228 register ubig
*p
; /* prime table pointer */
229 register ubig fact_lim
; /* highest prime for current block */
232 * A number of systems can not convert double values into unsigned
233 * longs when the values are larger than the largest signed value.
234 * We don't have this problem, so we can go all the way to BIG.
247 * be sure that the values are odd, or 2
249 if (start
!= 2 && (start
&0x1) == 0) {
252 if (stop
!= 2 && (stop
&0x1) == 0) {
257 * quick list of primes <= pr_limit
259 if (start
<= *pr_limit
) {
260 /* skip primes up to the start value */
261 for (p
= &prime
[0], factor
= prime
[0];
262 factor
< stop
&& p
<= pr_limit
; factor
= *(++p
)) {
263 if (factor
>= start
) {
264 printf("%u\n", factor
);
267 /* return early if we are done */
275 * we shall sieve a bytemap window, note primes and move the window
276 * upward until we pass the stop point
278 while (start
< stop
) {
280 * factor out 3, 5, 7, 11 and 13
282 /* initial pattern copy */
283 factor
= (start
%(2*3*5*7*11*13))/2; /* starting copy spot */
284 memcpy(table
, &pattern
[factor
], pattern_size
-factor
);
285 /* main block pattern copies */
286 for (fact_lim
=pattern_size
-factor
;
287 fact_lim
+pattern_size
<=TABSIZE
; fact_lim
+=pattern_size
) {
288 memcpy(&table
[fact_lim
], pattern
, pattern_size
);
290 /* final block pattern copy */
291 memcpy(&table
[fact_lim
], pattern
, TABSIZE
-fact_lim
);
294 * sieve for primes 17 and higher
296 /* note highest useful factor and sieve spot */
297 if (stop
-start
> TABSIZE
+TABSIZE
) {
298 tab_lim
= &table
[TABSIZE
]; /* sieve it all */
299 fact_lim
= (int)sqrt(
300 (double)(start
)+TABSIZE
+TABSIZE
+1.0);
302 tab_lim
= &table
[(stop
-start
)/2]; /* partial sieve */
303 fact_lim
= (int)sqrt((double)(stop
)+1.0);
305 /* sieve for factors >= 17 */
306 factor
= 17; /* 17 is first prime to use */
307 p
= &prime
[7]; /* 19 is next prime, pi(19)=7 */
309 /* determine the factor's initial sieve point */
310 q
= (char *)(start%factor
); /* temp storage for mod */
312 q
= &table
[(factor
-(int)q
)/2];
314 q
= &table
[q
? factor
-((int)q
/2) : 0];
316 /* sive for our current factor */
317 for ( ; q
< tab_lim
; q
+= factor
) {
318 *q
= '\0'; /* sieve out a spot */
320 } while ((factor
=(ubig
)(*(p
++))) <= fact_lim
);
323 * print generated primes
325 for (q
= table
; q
< tab_lim
; ++q
, start
+=2) {
327 printf("%u\n", start
);
336 (void)fprintf(stderr
, "usage: primes [start [stop]]\n");