usr/src/games/primes/primes.c

/*
 * 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.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *      This product includes software developed by the University of
 *      California, Berkeley and its contributors.
 * 4. Neither the name of the University nor the names of its contributors
 *    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
static char copyright[] =
"@(#) Copyright (c) 1989, 1993\n\
        The Regents of the University of California.  All rights reserved.\n";
#endif /* not lint */

#ifndef lint
static char sccsid[] = "@(#)primes.c    8.4 (Berkeley) 3/21/94";
#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:
 *      primes [start [stop]]
 *
 *      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
 */

#include <ctype.h>
#include <err.h>
#include <errno.h>
#include <limits.h>
#include <math.h>
#include <memory.h>
#include <stdio.h>
#include <stdlib.h>

#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
 * sieve, table[i] == 1 if and only iff 2*i-1 is prime.
 *
 * We make TABSIZE large to reduce the overhead of inner loop setup.
 */
char table[TABSIZE];     /* Eratosthenes sieve of odd numbers */

/*
 * prime[i] is the (i-1)th prime.
 *
 * We are able to sieve 2^32-1 because this byte table yields all primes
 * up to 65537 and 65537^2 > 2^32-1.
 */
extern ubig prime[];
extern ubig *pr_limit;          /* largest prime in the prime array */

/*
 * To avoid excessive sieves for small factors, we use the table below to
 * setup our sieve blocks.  Each element represents a odd number starting
 * with 1.  All non-zero elements are factors of 3, 5, 7, 11 and 13.
 */
extern char pattern[];
extern int pattern_size;        /* length of pattern array */

void    primes __P((ubig, ubig));
ubig    read_num_buf __P((void));
void    usage __P((void));

int
main(argc, argv)
        int argc;
        char *argv[];
{
        ubig start;             /* where to start generating */
        ubig stop;              /* don't generate at or above this value */
        int ch;
        char *p;

        while ((ch = getopt(argc, argv, "")) != EOF)
                switch (ch) {
                case '?':
                default:
                        usage();
                }
        argc -= optind;
        argv += optind;

        start = 0;
        stop = BIG;

        /*
         * Convert low and high args.  Strtoul(3) sets errno to
         * 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;
                start = strtoul(argv[0], &p, 10);
                if (errno)
                        err(1, "%s", argv[0]);
                if (*p != '\0')
                        errx(1, "%s: illegal numeric format.", argv[0]);

                errno = 0;
                stop = strtoul(argv[1], &p, 10);
                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;
                start = strtoul(argv[0], &p, 10);
                if (errno)
                        err(1, "%s", argv[0]);
                if (*p != '\0')
                        errx(1, "%s: illegal numeric format.", argv[0]);
                break;
        case 0:
                start = read_num_buf();
                break;
        default:
                usage();
        }

        if (start > stop)
                errx(1, "start value must be less than stop value.");
        primes(start, stop);
        exit(0);
}

/*
 * read_num_buf --
 *      This routine returns a number n, where 0 <= n && n <= BIG.
 */
ubig
read_num_buf()
{
        ubig val;
        char *p, buf[100];              /* > max number of digits. */

        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;
                val = strtoul(buf, &p, 10);
                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
 */
void
primes(start, stop)
        ubig start;     /* where to start generating */
        ubig stop;      /* don't generate at or above this value */
{
        register char *q;               /* sieve spot */
        register ubig factor;           /* index and factor */
        register char *tab_lim;         /* the limit to sieve on the table */
        register ubig *p;               /* prime table pointer */
        register ubig fact_lim;         /* highest prime for current block */

        /*
         * 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) {
                                printf("%u\n", factor);
                        }
                }
                /* 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 */
                        fact_lim = (int)sqrt(
                                        (double)(start)+TABSIZE+TABSIZE+1.0);
                } else {
                        tab_lim = &table[(stop-start)/2]; /* partial sieve */
                        fact_lim = (int)sqrt((double)(stop)+1.0);
                }
                /* 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 */
                        q = (char *)(start%factor); /* temp storage for mod */
                        if ((int)q & 0x1) {
                                q = &table[(factor-(int)q)/2];
                        } else {
                                q = &table[q ? factor-((int)q/2) : 0];
                        }
                        /* sive for our current factor */
                        for ( ; q < tab_lim; q += factor) {
                                *q = '\0'; /* sieve out a spot */
                        }
                } while ((factor=(ubig)(*(p++))) <= fact_lim);

                /*
                 * print generated primes
                 */
                for (q = table; q < tab_lim; ++q, start+=2) {
                        if (*q) {
                                printf("%u\n", start);
                        }
                }
        }
}

void
usage()
{
        (void)fprintf(stderr, "usage: primes [start [stop]]\n");
        exit(1);
}