333 lines
8.9 KiB
C
333 lines
8.9 KiB
C
/*
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* Copyright (c) 1989, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* This code is derived from software contributed to Berkeley by
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* Landon Curt Noll.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char copyright[] =
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"@(#) Copyright (c) 1989, 1993\n\
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The Regents of the University of California. All rights reserved.\n";
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#endif /* not lint */
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#ifndef lint
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static char sccsid[] = "@(#)primes.c 8.4 (Berkeley) 3/21/94";
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#endif /* not lint */
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/*
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* primes - generate a table of primes between two values
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*
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* By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
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*
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* chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
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*
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* usage:
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* primes [start [stop]]
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*
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* Print primes >= start and < stop. If stop is omitted,
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* the value 4294967295 (2^32-1) is assumed. If start is
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* omitted, start is read from standard input.
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*
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* validation check: there are 664579 primes between 0 and 10^7
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*/
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#include <ctype.h>
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#include <err.h>
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#include <errno.h>
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#include <limits.h>
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#include <math.h>
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#include <memory.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include "primes.h"
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/*
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* Eratosthenes sieve table
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*
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* We only sieve the odd numbers. The base of our sieve windows are always
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* odd. If the base of table is 1, table[i] represents 2*i-1. After the
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* sieve, table[i] == 1 if and only iff 2*i-1 is prime.
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*
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* We make TABSIZE large to reduce the overhead of inner loop setup.
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*/
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char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
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/*
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* prime[i] is the (i-1)th prime.
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*
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* We are able to sieve 2^32-1 because this byte table yields all primes
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* up to 65537 and 65537^2 > 2^32-1.
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*/
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extern ubig prime[];
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extern ubig *pr_limit; /* largest prime in the prime array */
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/*
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* To avoid excessive sieves for small factors, we use the table below to
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* setup our sieve blocks. Each element represents a odd number starting
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* with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13.
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*/
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extern char pattern[];
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extern int pattern_size; /* length of pattern array */
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void primes __P((ubig, ubig));
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ubig read_num_buf __P((void));
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void usage __P((void));
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int
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main(argc, argv)
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int argc;
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char *argv[];
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{
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ubig start; /* where to start generating */
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ubig stop; /* don't generate at or above this value */
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int ch;
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char *p;
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while ((ch = getopt(argc, argv, "")) != EOF)
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switch (ch) {
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case '?':
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default:
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usage();
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}
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argc -= optind;
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argv += optind;
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start = 0;
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stop = BIG;
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/*
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* Convert low and high args. Strtoul(3) sets errno to
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* ERANGE if the number is too large, but, if there's
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* a leading minus sign it returns the negation of the
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* result of the conversion, which we'd rather disallow.
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*/
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switch (argc) {
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case 2:
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/* Start and stop supplied on the command line. */
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if (argv[0][0] == '-' || argv[1][0] == '-')
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errx(1, "negative numbers aren't permitted.");
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errno = 0;
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start = strtoul(argv[0], &p, 10);
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if (errno)
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err(1, "%s", argv[0]);
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if (*p != '\0')
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errx(1, "%s: illegal numeric format.", argv[0]);
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errno = 0;
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stop = strtoul(argv[1], &p, 10);
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if (errno)
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err(1, "%s", argv[1]);
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if (*p != '\0')
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errx(1, "%s: illegal numeric format.", argv[1]);
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break;
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case 1:
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/* Start on the command line. */
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if (argv[0][0] == '-')
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errx(1, "negative numbers aren't permitted.");
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errno = 0;
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start = strtoul(argv[0], &p, 10);
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if (errno)
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err(1, "%s", argv[0]);
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if (*p != '\0')
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errx(1, "%s: illegal numeric format.", argv[0]);
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break;
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case 0:
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start = read_num_buf();
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break;
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default:
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usage();
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}
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if (start > stop)
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errx(1, "start value must be less than stop value.");
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primes(start, stop);
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exit(0);
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}
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/*
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* read_num_buf --
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* This routine returns a number n, where 0 <= n && n <= BIG.
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*/
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ubig
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read_num_buf()
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{
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ubig val;
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char *p, buf[100]; /* > max number of digits. */
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for (;;) {
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if (fgets(buf, sizeof(buf), stdin) == NULL) {
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if (ferror(stdin))
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err(1, "stdin");
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exit(0);
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}
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for (p = buf; isblank(*p); ++p);
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if (*p == '\n' || *p == '\0')
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continue;
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if (*p == '-')
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errx(1, "negative numbers aren't permitted.");
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errno = 0;
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val = strtoul(buf, &p, 10);
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if (errno)
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err(1, "%s", buf);
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if (*p != '\n')
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errx(1, "%s: illegal numeric format.", buf);
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return (val);
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}
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}
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/*
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* primes - sieve and print primes from start up to and but not including stop
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*/
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void
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primes(start, stop)
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ubig start; /* where to start generating */
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ubig stop; /* don't generate at or above this value */
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{
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register char *q; /* sieve spot */
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register ubig factor; /* index and factor */
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register char *tab_lim; /* the limit to sieve on the table */
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register ubig *p; /* prime table pointer */
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register ubig fact_lim; /* highest prime for current block */
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/*
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* A number of systems can not convert double values into unsigned
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* longs when the values are larger than the largest signed value.
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* We don't have this problem, so we can go all the way to BIG.
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*/
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if (start < 3) {
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start = (ubig)2;
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}
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if (stop < 3) {
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stop = (ubig)2;
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}
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if (stop <= start) {
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return;
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}
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/*
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* be sure that the values are odd, or 2
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*/
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if (start != 2 && (start&0x1) == 0) {
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++start;
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}
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if (stop != 2 && (stop&0x1) == 0) {
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++stop;
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}
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/*
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* quick list of primes <= pr_limit
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*/
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if (start <= *pr_limit) {
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/* skip primes up to the start value */
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for (p = &prime[0], factor = prime[0];
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factor < stop && p <= pr_limit; factor = *(++p)) {
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if (factor >= start) {
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printf("%u\n", factor);
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}
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}
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/* return early if we are done */
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if (p <= pr_limit) {
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return;
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}
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start = *pr_limit+2;
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}
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/*
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* we shall sieve a bytemap window, note primes and move the window
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* upward until we pass the stop point
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*/
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while (start < stop) {
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/*
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* factor out 3, 5, 7, 11 and 13
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*/
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/* initial pattern copy */
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factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
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memcpy(table, &pattern[factor], pattern_size-factor);
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/* main block pattern copies */
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for (fact_lim=pattern_size-factor;
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fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
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memcpy(&table[fact_lim], pattern, pattern_size);
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}
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/* final block pattern copy */
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memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
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/*
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* sieve for primes 17 and higher
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*/
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/* note highest useful factor and sieve spot */
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if (stop-start > TABSIZE+TABSIZE) {
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tab_lim = &table[TABSIZE]; /* sieve it all */
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fact_lim = (int)sqrt(
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(double)(start)+TABSIZE+TABSIZE+1.0);
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} else {
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tab_lim = &table[(stop-start)/2]; /* partial sieve */
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fact_lim = (int)sqrt((double)(stop)+1.0);
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}
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/* sieve for factors >= 17 */
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factor = 17; /* 17 is first prime to use */
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p = &prime[7]; /* 19 is next prime, pi(19)=7 */
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do {
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/* determine the factor's initial sieve point */
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q = (char *)(start%factor); /* temp storage for mod */
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if ((int)q & 0x1) {
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q = &table[(factor-(int)q)/2];
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} else {
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q = &table[q ? factor-((int)q/2) : 0];
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}
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/* sive for our current factor */
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for ( ; q < tab_lim; q += factor) {
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*q = '\0'; /* sieve out a spot */
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}
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} while ((factor=(ubig)(*(p++))) <= fact_lim);
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/*
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* print generated primes
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*/
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for (q = table; q < tab_lim; ++q, start+=2) {
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if (*q) {
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printf("%u\n", start);
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}
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}
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}
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}
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void
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usage()
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{
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(void)fprintf(stderr, "usage: primes [start [stop]]\n");
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exit(1);
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}
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