1994-09-04 04:03:31 +00:00
|
|
|
/*
|
|
|
|
* Copyright (c) 1989, 1993
|
|
|
|
* The Regents of the University of California. All rights reserved.
|
|
|
|
*
|
|
|
|
* This code is derived from software contributed to Berkeley by
|
|
|
|
* Landon Curt Noll.
|
|
|
|
*
|
|
|
|
* Redistribution and use in source and binary forms, with or without
|
|
|
|
* modification, are permitted provided that the following conditions
|
|
|
|
* are met:
|
|
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
|
|
* notice, this list of conditions and the following disclaimer.
|
|
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
|
|
* documentation and/or other materials provided with the distribution.
|
2010-02-15 18:46:02 +00:00
|
|
|
* 3. Neither the name of the University nor the names of its contributors
|
1994-09-04 04:03:31 +00:00
|
|
|
* may be used to endorse or promote products derived from this software
|
|
|
|
* without specific prior written permission.
|
|
|
|
*
|
|
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
|
|
* SUCH DAMAGE.
|
|
|
|
*/
|
|
|
|
|
|
|
|
#ifndef lint
|
1999-11-30 03:50:02 +00:00
|
|
|
static const char copyright[] =
|
1994-09-04 04:03:31 +00:00
|
|
|
"@(#) Copyright (c) 1989, 1993\n\
|
|
|
|
The Regents of the University of California. All rights reserved.\n";
|
|
|
|
#endif /* not lint */
|
|
|
|
|
|
|
|
#ifndef lint
|
1999-11-30 03:50:02 +00:00
|
|
|
#if 0
|
1997-03-11 17:25:32 +00:00
|
|
|
static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
|
1999-11-30 03:50:02 +00:00
|
|
|
#endif
|
|
|
|
static const char rcsid[] =
|
|
|
|
"$FreeBSD$";
|
1994-09-04 04:03:31 +00:00
|
|
|
#endif /* not lint */
|
|
|
|
|
|
|
|
/*
|
|
|
|
* primes - generate a table of primes between two values
|
|
|
|
*
|
|
|
|
* By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
|
|
|
|
*
|
|
|
|
* chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
|
|
|
|
*
|
|
|
|
* usage:
|
2002-10-09 19:38:55 +00:00
|
|
|
* primes [-h] [start [stop]]
|
1994-09-04 04:03:31 +00:00
|
|
|
*
|
|
|
|
* Print primes >= start and < stop. If stop is omitted,
|
|
|
|
* the value 4294967295 (2^32-1) is assumed. If start is
|
|
|
|
* omitted, start is read from standard input.
|
|
|
|
*
|
|
|
|
* validation check: there are 664579 primes between 0 and 10^7
|
|
|
|
*/
|
|
|
|
|
2016-09-30 13:50:59 +00:00
|
|
|
#include <sys/capsicum.h>
|
1994-09-04 04:03:31 +00:00
|
|
|
#include <ctype.h>
|
|
|
|
#include <err.h>
|
|
|
|
#include <errno.h>
|
2014-09-27 09:00:38 +00:00
|
|
|
#include <inttypes.h>
|
1994-09-04 04:03:31 +00:00
|
|
|
#include <limits.h>
|
|
|
|
#include <math.h>
|
|
|
|
#include <stdio.h>
|
|
|
|
#include <stdlib.h>
|
2002-10-09 20:42:40 +00:00
|
|
|
#include <string.h>
|
2016-09-30 13:50:59 +00:00
|
|
|
#include <nl_types.h>
|
1997-03-11 17:25:32 +00:00
|
|
|
#include <unistd.h>
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
#include "primes.h"
|
|
|
|
|
|
|
|
/*
|
|
|
|
* Eratosthenes sieve table
|
|
|
|
*
|
|
|
|
* We only sieve the odd numbers. The base of our sieve windows are always
|
|
|
|
* odd. If the base of table is 1, table[i] represents 2*i-1. After the
|
2001-12-27 13:33:10 +00:00
|
|
|
* sieve, table[i] == 1 if and only if 2*i-1 is prime.
|
1994-09-04 04:03:31 +00:00
|
|
|
*
|
|
|
|
* We make TABSIZE large to reduce the overhead of inner loop setup.
|
|
|
|
*/
|
2002-02-21 18:13:31 +00:00
|
|
|
static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
|
1994-09-04 04:03:31 +00:00
|
|
|
|
2002-02-21 18:13:31 +00:00
|
|
|
static int hflag;
|
1999-01-06 08:14:26 +00:00
|
|
|
|
2002-02-21 18:13:31 +00:00
|
|
|
static void primes(ubig, ubig);
|
|
|
|
static ubig read_num_buf(void);
|
|
|
|
static void usage(void);
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
int
|
2002-02-21 18:13:31 +00:00
|
|
|
main(int argc, char *argv[])
|
1994-09-04 04:03:31 +00:00
|
|
|
{
|
|
|
|
ubig start; /* where to start generating */
|
|
|
|
ubig stop; /* don't generate at or above this value */
|
|
|
|
int ch;
|
|
|
|
char *p;
|
|
|
|
|
2016-09-30 13:50:59 +00:00
|
|
|
/* Cache NLS data, for strerror, for err(3), before cap_enter. */
|
|
|
|
(void)catopen("libc", NL_CAT_LOCALE);
|
|
|
|
|
|
|
|
if (cap_enter() < 0 && errno != ENOSYS)
|
|
|
|
err(1, "cap_enter");
|
|
|
|
|
1999-01-06 08:14:26 +00:00
|
|
|
while ((ch = getopt(argc, argv, "h")) != -1)
|
1994-09-04 04:03:31 +00:00
|
|
|
switch (ch) {
|
1999-01-06 08:14:26 +00:00
|
|
|
case 'h':
|
|
|
|
hflag++;
|
|
|
|
break;
|
1994-09-04 04:03:31 +00:00
|
|
|
case '?':
|
|
|
|
default:
|
|
|
|
usage();
|
|
|
|
}
|
|
|
|
argc -= optind;
|
|
|
|
argv += optind;
|
|
|
|
|
|
|
|
start = 0;
|
2017-06-04 02:36:37 +00:00
|
|
|
stop = (uint64_t)(-1);
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
/*
|
2014-09-27 09:00:38 +00:00
|
|
|
* Convert low and high args. Strtoumax(3) sets errno to
|
1994-09-04 04:03:31 +00:00
|
|
|
* ERANGE if the number is too large, but, if there's
|
|
|
|
* a leading minus sign it returns the negation of the
|
|
|
|
* result of the conversion, which we'd rather disallow.
|
|
|
|
*/
|
|
|
|
switch (argc) {
|
|
|
|
case 2:
|
|
|
|
/* Start and stop supplied on the command line. */
|
|
|
|
if (argv[0][0] == '-' || argv[1][0] == '-')
|
|
|
|
errx(1, "negative numbers aren't permitted.");
|
|
|
|
|
|
|
|
errno = 0;
|
2014-09-27 09:00:38 +00:00
|
|
|
start = strtoumax(argv[0], &p, 0);
|
1994-09-04 04:03:31 +00:00
|
|
|
if (errno)
|
|
|
|
err(1, "%s", argv[0]);
|
|
|
|
if (*p != '\0')
|
|
|
|
errx(1, "%s: illegal numeric format.", argv[0]);
|
|
|
|
|
|
|
|
errno = 0;
|
2014-09-27 09:00:38 +00:00
|
|
|
stop = strtoumax(argv[1], &p, 0);
|
1994-09-04 04:03:31 +00:00
|
|
|
if (errno)
|
|
|
|
err(1, "%s", argv[1]);
|
|
|
|
if (*p != '\0')
|
|
|
|
errx(1, "%s: illegal numeric format.", argv[1]);
|
|
|
|
break;
|
|
|
|
case 1:
|
|
|
|
/* Start on the command line. */
|
|
|
|
if (argv[0][0] == '-')
|
|
|
|
errx(1, "negative numbers aren't permitted.");
|
|
|
|
|
|
|
|
errno = 0;
|
2014-09-27 09:00:38 +00:00
|
|
|
start = strtoumax(argv[0], &p, 0);
|
1994-09-04 04:03:31 +00:00
|
|
|
if (errno)
|
|
|
|
err(1, "%s", argv[0]);
|
|
|
|
if (*p != '\0')
|
|
|
|
errx(1, "%s: illegal numeric format.", argv[0]);
|
|
|
|
break;
|
|
|
|
case 0:
|
1998-08-09 10:36:25 +00:00
|
|
|
start = read_num_buf();
|
1994-09-04 04:03:31 +00:00
|
|
|
break;
|
|
|
|
default:
|
|
|
|
usage();
|
|
|
|
}
|
|
|
|
|
|
|
|
if (start > stop)
|
|
|
|
errx(1, "start value must be less than stop value.");
|
1998-08-09 10:36:25 +00:00
|
|
|
primes(start, stop);
|
2002-02-21 18:13:31 +00:00
|
|
|
return (0);
|
1994-09-04 04:03:31 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
* read_num_buf --
|
|
|
|
* This routine returns a number n, where 0 <= n && n <= BIG.
|
|
|
|
*/
|
2002-02-21 18:13:31 +00:00
|
|
|
static ubig
|
|
|
|
read_num_buf(void)
|
1994-09-04 04:03:31 +00:00
|
|
|
{
|
|
|
|
ubig val;
|
2002-10-09 19:38:55 +00:00
|
|
|
char *p, buf[LINE_MAX]; /* > max number of digits. */
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
for (;;) {
|
|
|
|
if (fgets(buf, sizeof(buf), stdin) == NULL) {
|
|
|
|
if (ferror(stdin))
|
|
|
|
err(1, "stdin");
|
|
|
|
exit(0);
|
|
|
|
}
|
|
|
|
for (p = buf; isblank(*p); ++p);
|
|
|
|
if (*p == '\n' || *p == '\0')
|
|
|
|
continue;
|
|
|
|
if (*p == '-')
|
|
|
|
errx(1, "negative numbers aren't permitted.");
|
|
|
|
errno = 0;
|
2014-09-27 09:00:38 +00:00
|
|
|
val = strtoumax(buf, &p, 0);
|
1994-09-04 04:03:31 +00:00
|
|
|
if (errno)
|
|
|
|
err(1, "%s", buf);
|
|
|
|
if (*p != '\n')
|
|
|
|
errx(1, "%s: illegal numeric format.", buf);
|
|
|
|
return (val);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
* primes - sieve and print primes from start up to and but not including stop
|
|
|
|
*/
|
2002-02-21 18:13:31 +00:00
|
|
|
static void
|
|
|
|
primes(ubig start, ubig stop)
|
1994-09-04 04:03:31 +00:00
|
|
|
{
|
1999-11-16 02:58:06 +00:00
|
|
|
char *q; /* sieve spot */
|
|
|
|
ubig factor; /* index and factor */
|
|
|
|
char *tab_lim; /* the limit to sieve on the table */
|
2002-10-09 19:38:55 +00:00
|
|
|
const ubig *p; /* prime table pointer */
|
1999-11-16 02:58:06 +00:00
|
|
|
ubig fact_lim; /* highest prime for current block */
|
2002-10-09 19:38:55 +00:00
|
|
|
ubig mod; /* temp storage for mod */
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
/*
|
|
|
|
* A number of systems can not convert double values into unsigned
|
|
|
|
* longs when the values are larger than the largest signed value.
|
|
|
|
* We don't have this problem, so we can go all the way to BIG.
|
|
|
|
*/
|
|
|
|
if (start < 3) {
|
|
|
|
start = (ubig)2;
|
|
|
|
}
|
|
|
|
if (stop < 3) {
|
|
|
|
stop = (ubig)2;
|
|
|
|
}
|
|
|
|
if (stop <= start) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
* be sure that the values are odd, or 2
|
|
|
|
*/
|
|
|
|
if (start != 2 && (start&0x1) == 0) {
|
|
|
|
++start;
|
|
|
|
}
|
|
|
|
if (stop != 2 && (stop&0x1) == 0) {
|
|
|
|
++stop;
|
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
* quick list of primes <= pr_limit
|
|
|
|
*/
|
|
|
|
if (start <= *pr_limit) {
|
|
|
|
/* skip primes up to the start value */
|
|
|
|
for (p = &prime[0], factor = prime[0];
|
|
|
|
factor < stop && p <= pr_limit; factor = *(++p)) {
|
|
|
|
if (factor >= start) {
|
2014-09-27 09:00:38 +00:00
|
|
|
printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor);
|
1994-09-04 04:03:31 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
/* return early if we are done */
|
|
|
|
if (p <= pr_limit) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
start = *pr_limit+2;
|
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
* we shall sieve a bytemap window, note primes and move the window
|
|
|
|
* upward until we pass the stop point
|
|
|
|
*/
|
|
|
|
while (start < stop) {
|
|
|
|
/*
|
|
|
|
* factor out 3, 5, 7, 11 and 13
|
|
|
|
*/
|
|
|
|
/* initial pattern copy */
|
|
|
|
factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
|
|
|
|
memcpy(table, &pattern[factor], pattern_size-factor);
|
|
|
|
/* main block pattern copies */
|
|
|
|
for (fact_lim=pattern_size-factor;
|
|
|
|
fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
|
|
|
|
memcpy(&table[fact_lim], pattern, pattern_size);
|
|
|
|
}
|
|
|
|
/* final block pattern copy */
|
|
|
|
memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
|
|
|
|
|
|
|
|
/*
|
|
|
|
* sieve for primes 17 and higher
|
|
|
|
*/
|
|
|
|
/* note highest useful factor and sieve spot */
|
|
|
|
if (stop-start > TABSIZE+TABSIZE) {
|
|
|
|
tab_lim = &table[TABSIZE]; /* sieve it all */
|
2002-10-09 19:38:55 +00:00
|
|
|
fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
|
1994-09-04 04:03:31 +00:00
|
|
|
} else {
|
|
|
|
tab_lim = &table[(stop-start)/2]; /* partial sieve */
|
2002-10-09 19:38:55 +00:00
|
|
|
fact_lim = sqrt(stop+1.0);
|
1994-09-04 04:03:31 +00:00
|
|
|
}
|
|
|
|
/* sieve for factors >= 17 */
|
|
|
|
factor = 17; /* 17 is first prime to use */
|
|
|
|
p = &prime[7]; /* 19 is next prime, pi(19)=7 */
|
|
|
|
do {
|
|
|
|
/* determine the factor's initial sieve point */
|
2002-10-09 19:38:55 +00:00
|
|
|
mod = start%factor;
|
|
|
|
if (mod & 0x1) {
|
|
|
|
q = &table[(factor-mod)/2];
|
1994-09-04 04:03:31 +00:00
|
|
|
} else {
|
2002-10-09 19:38:55 +00:00
|
|
|
q = &table[mod ? factor-(mod/2) : 0];
|
1994-09-04 04:03:31 +00:00
|
|
|
}
|
|
|
|
/* sive for our current factor */
|
|
|
|
for ( ; q < tab_lim; q += factor) {
|
|
|
|
*q = '\0'; /* sieve out a spot */
|
|
|
|
}
|
2002-10-09 19:38:55 +00:00
|
|
|
factor = *p++;
|
|
|
|
} while (factor <= fact_lim);
|
1994-09-04 04:03:31 +00:00
|
|
|
|
|
|
|
/*
|
|
|
|
* print generated primes
|
|
|
|
*/
|
|
|
|
for (q = table; q < tab_lim; ++q, start+=2) {
|
|
|
|
if (*q) {
|
2014-09-27 09:00:38 +00:00
|
|
|
if (start > SIEVEMAX) {
|
Correctly enumerate primes between 4295098369 and 3825123056546413050.
Prior to this commit, primes(6) relied solely on sieving with primes up
to 65537, with the effect that composite numbers which are the product
of two non-16-bit primes would be incorrectly identified as prime. For
example,
# primes 1099511627800 1099511627820
would output
1099511627803
1099511627807
1099511627813
when in fact only the first of those values is prime.
This commit adds strong pseudoprime tests to validate the candidates
which pass the initial sieving stage, using bases of 2, 3, 5, 7, 11,
13, 17, 19, and 23. Thanks to papers from C. Pomerance, J.L. Selfridge,
and S.S. Wagstaff, Jr.; G. Jaeschke; and Y. Jiang and Y. Deng, we know
that the smallest value which passes these tests is 3825123056546413051.
At present we do not know how many strong pseudoprime tests are required
to prove primality for values larger than 3825123056546413050, so we
force primes(6) to stop at that point.
Reviewed by: jmg
Relnotes: primes(6) now correctly enumerates primes up to
3825123056546413050
MFC after: 7 days
Sponsored by: EuroBSDCon devsummit
2014-09-26 09:40:48 +00:00
|
|
|
if (!isprime(start))
|
|
|
|
continue;
|
|
|
|
}
|
2014-09-27 09:00:38 +00:00
|
|
|
printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start);
|
1994-09-04 04:03:31 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2002-02-21 18:13:31 +00:00
|
|
|
static void
|
|
|
|
usage(void)
|
1994-09-04 04:03:31 +00:00
|
|
|
{
|
2002-10-09 19:38:55 +00:00
|
|
|
fprintf(stderr, "usage: primes [-h] [start [stop]]\n");
|
1994-09-04 04:03:31 +00:00
|
|
|
exit(1);
|
|
|
|
}
|