4.4BSD/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 8.1 (Berkeley) 5/31/93";
#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.
*
* Prints "ouch" if start or stop is bogus.
*
* validation check: there are 664579 primes between 0 and 10^7
*/
#include <stdio.h>
#include <math.h>
#include <memory.h>
#include <ctype.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 */
#define MAX_LINE 255 /* max line allowed on stdin */
char *read_num_buf(); /* read a number buffer */
void primes(); /* print the primes in range */
char *program; /* our name */
main(argc, argv)
int argc; /* arg count */
char *argv[]; /* args */
{
char buf[MAX_LINE+1]; /* input buffer */
char *ret; /* return result */
ubig start; /* where to start generating */
ubig stop; /* don't generate at or above this value */
/*
* parse args
*/
program = argv[0];
start = 0;
stop = BIG;
if (argc == 3) {
/* convert low and high args */
if (read_num_buf(NULL, argv[1]) == NULL) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
if (read_num_buf(NULL, argv[2]) == NULL) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
if (sscanf(argv[1], "%ld", &start) != 1) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
if (sscanf(argv[2], "%ld", &stop) != 1) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
} else if (argc == 2) {
/* convert low arg */
if (read_num_buf(NULL, argv[1]) == NULL) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
if (sscanf(argv[1], "%ld", &start) != 1) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
} else {
/* read input until we get a good line */
if (read_num_buf(stdin, buf) != NULL) {
/* convert the buffer */
if (sscanf(buf, "%ld", &start) != 1) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
} else {
exit(0);
}
}
if (start > stop) {
fprintf(stderr, "%s: ouch\n", program);
exit(1);
}
primes(start, stop);
exit(0);
}
/*
* read_num_buf - read a number buffer from a stream
*
* Read a number on a line of the form:
*
* ^[ \t]*\(+?[0-9][0-9]\)*.*$
*
* where ? is a 1-or-0 operator and the number is within \( \).
*
* If does not match the above pattern, it is ignored and a new
* line is read. If the number is too large or small, we will
* print ouch and read a new line.
*
* We have to be very careful on how we check the magnitude of the
* input. We can not use numeric checks because of the need to
* check values against maximum numeric values.
*
* This routine will return a line containing a ascii number between
* 0 and BIG, or it will return NULL.
*
* If the stream is NULL then buf will be processed as if were
* a single line stream.
*
* returns:
* char * pointer to leading digit or +
* NULL EOF or error
*/
char *
read_num_buf(input, buf)
FILE *input; /* input stream or NULL */
char *buf; /* input buffer */
{
static char limit[MAX_LINE+1]; /* ascii value of BIG */
static int limit_len; /* digit count of limit */
int len; /* digits in input (excluding +/-) */
char *s; /* line start marker */
char *d; /* first digit, skip +/- */
char *p; /* scan pointer */
char *z; /* zero scan pointer */
/* form the ascii value of SEMIBIG if needed */
if (!isascii(limit[0]) || !isdigit(limit[0])) {
sprintf(limit, "%ld", SEMIBIG);
limit_len = strlen(limit);
}
/*
* the search for a good line
*/
if (input != NULL && fgets(buf, MAX_LINE, input) == NULL) {
/* error or EOF */
return NULL;
}
do {
/* ignore leading whitespace */
for (s=buf; *s && s < buf+MAX_LINE; ++s) {
if (!isascii(*s) || !isspace(*s)) {
break;
}
}
/* object if - */
if (*s == '-') {
fprintf(stderr, "%s: ouch\n", program);
continue;
}
/* skip over any leading + */
if (*s == '+') {
d = s+1;
} else {
d = s;
}
/* note leading zeros */
for (z=d; *z && z < buf+MAX_LINE; ++z) {
if (*z != '0') {
break;
}
}
/* scan for the first non-digit/non-plus/non-minus */
for (p=d; *p && p < buf+MAX_LINE; ++p) {
if (!isascii(*p) || !isdigit(*p)) {
break;
}
}
/* ignore empty lines */
if (p == d) {
continue;
}
*p = '\0';
/* object if too many digits */
len = strlen(z);
len = (len<=0) ? 1 : len;
/* accept if digit count is below limit */
if (len < limit_len) {
/* we have good input */
return s;
/* reject very large numbers */
} else if (len > limit_len) {
fprintf(stderr, "%s: ouch\n", program);
continue;
/* carefully check against near limit numbers */
} else if (strcmp(z, limit) > 0) {
fprintf(stderr, "%s: ouch\n", program);
continue;
}
/* number is near limit, but is under it */
return s;
} while (input != NULL && fgets(buf, MAX_LINE, input) != NULL);
/* error or EOF */
return NULL;
}
/*
* 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. Thus we take case when
* the double is larger than the value SEMIBIG. *sigh*
*/
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);
}
}
}
}