412 lines
11 KiB
C
412 lines
11 KiB
C
/*
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* Copyright (c) 1989 The Regents of the University of California.
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* 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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char copyright[] =
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"@(#) Copyright (c) 1989 The Regents of the University of California.\n\
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All rights reserved.\n";
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#endif /* not lint */
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#ifndef lint
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/*static char sccsid[] = "from: @(#)primes.c 5.4 (Berkeley) 6/1/90";*/
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static char rcsid[] = "$Id: primes.c,v 1.2 1993/08/01 18:53:04 mycroft Exp $";
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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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* Prints "ouch" if start or stop is bogus.
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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 <stdio.h>
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#include <math.h>
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#include <memory.h>
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#include <ctype.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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#define MAX_LINE 255 /* max line allowed on stdin */
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char *read_num_buf(); /* read a number buffer */
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void primes(); /* print the primes in range */
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char *program; /* our name */
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main(argc, argv)
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int argc; /* arg count */
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char *argv[]; /* args */
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{
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char buf[MAX_LINE+1]; /* input buffer */
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char *ret; /* return result */
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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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* parse args
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*/
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program = argv[0];
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start = 0;
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stop = BIG;
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if (argc == 3) {
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/* convert low and high args */
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if (read_num_buf(NULL, argv[1]) == NULL) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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if (read_num_buf(NULL, argv[2]) == NULL) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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if (sscanf(argv[1], "%ld", &start) != 1) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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if (sscanf(argv[2], "%ld", &stop) != 1) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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} else if (argc == 2) {
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/* convert low arg */
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if (read_num_buf(NULL, argv[1]) == NULL) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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if (sscanf(argv[1], "%ld", &start) != 1) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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} else {
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/* read input until we get a good line */
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if (read_num_buf(stdin, buf) != NULL) {
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/* convert the buffer */
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if (sscanf(buf, "%ld", &start) != 1) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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} else {
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exit(0);
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}
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}
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if (start > stop) {
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fprintf(stderr, "%s: ouch\n", program);
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exit(1);
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}
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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 - read a number buffer from a stream
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*
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* Read a number on a line of the form:
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*
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* ^[ \t]*\(+?[0-9][0-9]\)*.*$
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*
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* where ? is a 1-or-0 operator and the number is within \( \).
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*
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* If does not match the above pattern, it is ignored and a new
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* line is read. If the number is too large or small, we will
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* print ouch and read a new line.
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*
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* We have to be very careful on how we check the magnitude of the
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* input. We can not use numeric checks because of the need to
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* check values against maximum numeric values.
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*
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* This routine will return a line containing a ascii number between
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* 0 and BIG, or it will return NULL.
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*
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* If the stream is NULL then buf will be processed as if were
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* a single line stream.
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*
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* returns:
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* char * pointer to leading digit or +
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* NULL EOF or error
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*/
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char *
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read_num_buf(input, buf)
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FILE *input; /* input stream or NULL */
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char *buf; /* input buffer */
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{
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static char limit[MAX_LINE+1]; /* ascii value of BIG */
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static int limit_len; /* digit count of limit */
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int len; /* digits in input (excluding +/-) */
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char *s; /* line start marker */
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char *d; /* first digit, skip +/- */
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char *p; /* scan pointer */
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char *z; /* zero scan pointer */
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/* form the ascii value of SEMIBIG if needed */
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if (!isascii(limit[0]) || !isdigit(limit[0])) {
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sprintf(limit, "%ld", SEMIBIG);
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limit_len = strlen(limit);
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}
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/*
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* the search for a good line
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*/
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if (input != NULL && fgets(buf, MAX_LINE, input) == NULL) {
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/* error or EOF */
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return NULL;
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}
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do {
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/* ignore leading whitespace */
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for (s=buf; *s && s < buf+MAX_LINE; ++s) {
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if (!isascii(*s) || !isspace(*s)) {
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break;
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}
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}
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/* object if - */
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if (*s == '-') {
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fprintf(stderr, "%s: ouch\n", program);
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continue;
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}
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/* skip over any leading + */
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if (*s == '+') {
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d = s+1;
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} else {
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d = s;
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}
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/* note leading zeros */
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for (z=d; *z && z < buf+MAX_LINE; ++z) {
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if (*z != '0') {
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break;
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}
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}
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/* scan for the first non-digit/non-plus/non-minus */
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for (p=d; *p && p < buf+MAX_LINE; ++p) {
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if (!isascii(*p) || !isdigit(*p)) {
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break;
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}
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}
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/* ignore empty lines */
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if (p == d) {
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continue;
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}
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*p = '\0';
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/* object if too many digits */
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len = strlen(z);
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len = (len<=0) ? 1 : len;
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/* accept if digit count is below limit */
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if (len < limit_len) {
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/* we have good input */
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return s;
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/* reject very large numbers */
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} else if (len > limit_len) {
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fprintf(stderr, "%s: ouch\n", program);
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continue;
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/* carefully check against near limit numbers */
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} else if (strcmp(z, limit) > 0) {
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fprintf(stderr, "%s: ouch\n", program);
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continue;
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}
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/* number is near limit, but is under it */
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return s;
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} while (input != NULL && fgets(buf, MAX_LINE, input) != NULL);
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/* error or EOF */
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return NULL;
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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
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* into unsigned longs when the values are larger than
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* the largest signed value. Thus we take case when
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* the double is larger than the value SEMIBIG. *sigh*
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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;
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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;
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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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