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/*
* sieve.c
*
* Finds prime numbers using the Sieve of Eratosthenes
*
* This implementation uses a bitmap to represent all odd integers in a
* given range. We iterate over this bitmap, crossing off the
* multiples of each prime we find. At the end, all the remaining set
* bits correspond to prime integers.
*
* Here, we make two passes -- once we have generated a sieve-ful of
* primes, we copy them out, reset the sieve using the highest
* generated prime from the first pass as a base. Then we cross out
* all the multiples of all the primes we found the first time through,
* and re-sieve. In this way, we get double use of the memory we
* allocated for the sieve the first time though. Since we also
* implicitly ignore multiples of 2, this amounts to 4 times the
* values.
*
* This could (and probably will) be generalized to re-use the sieve a
* few more times.
*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is the MPI Arbitrary Precision Integer Arithmetic library.
*
* The Initial Developer of the Original Code is
* Michael J. Fromberger.
* Portions created by the Initial Developer are Copyright (C) 1998
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
*
* Alternatively, the contents of this file may be used under the terms of
* either the GNU General Public License Version 2 or later (the "GPL"), or
* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
* in which case the provisions of the GPL or the LGPL are applicable instead
* of those above. If you wish to allow use of your version of this file only
* under the terms of either the GPL or the LGPL, and not to allow others to
* use your version of this file under the terms of the MPL, indicate your
* decision by deleting the provisions above and replace them with the notice
* and other provisions required by the GPL or the LGPL. If you do not delete
* the provisions above, a recipient may use your version of this file under
* the terms of any one of the MPL, the GPL or the LGPL.
*
* ***** END LICENSE BLOCK ***** */
/* $Id: sieve.c,v 1.3 2004/04/27 23:04:37 gerv%gerv.net Exp $ */
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
typedef unsigned char byte;
typedef struct {
int size;
byte *bits;
long base;
int next;
int nbits;
} sieve;
void sieve_init(sieve *sp, long base, int nbits);
void sieve_grow(sieve *sp, int nbits);
long sieve_next(sieve *sp);
void sieve_reset(sieve *sp, long base);
void sieve_cross(sieve *sp, long val);
void sieve_clear(sieve *sp);
#define S_ISSET(S, B) (((S)->bits[(B)/CHAR_BIT]>>((B)%CHAR_BIT))&1)
#define S_SET(S, B) ((S)->bits[(B)/CHAR_BIT]|=(1<<((B)%CHAR_BIT)))
#define S_CLR(S, B) ((S)->bits[(B)/CHAR_BIT]&=~(1<<((B)%CHAR_BIT)))
#define S_VAL(S, B) ((S)->base+(2*(B)))
#define S_BIT(S, V) (((V)-((S)->base))/2)
int main(int argc, char *argv[])
{
sieve s;
long pr, *p;
int c, ix, cur = 0;
if(argc < 2) {
fprintf(stderr, "Usage: %s <width>\n", argv[0]);
return 1;
}
c = atoi(argv[1]);
if(c < 0) c = -c;
fprintf(stderr, "%s: sieving to %d positions\n", argv[0], c);
sieve_init(&s, 3, c);
c = 0;
while((pr = sieve_next(&s)) > 0) {
++c;
}
p = calloc(c, sizeof(long));
if(!p) {
fprintf(stderr, "%s: out of memory after first half\n", argv[0]);
sieve_clear(&s);
exit(1);
}
fprintf(stderr, "%s: half done ... \n", argv[0]);
for(ix = 0; ix < s.nbits; ix++) {
if(S_ISSET(&s, ix)) {
p[cur] = S_VAL(&s, ix);
printf("%ld\n", p[cur]);
++cur;
}
}
sieve_reset(&s, p[cur - 1]);
fprintf(stderr, "%s: crossing off %d found primes ... \n", argv[0], cur);
for(ix = 0; ix < cur; ix++) {
sieve_cross(&s, p[ix]);
if(!(ix % 1000))
fputc('.', stderr);
}
fputc('\n', stderr);
free(p);
fprintf(stderr, "%s: sieving again from %ld ... \n", argv[0], p[cur - 1]);
c = 0;
while((pr = sieve_next(&s)) > 0) {
++c;
}
fprintf(stderr, "%s: done!\n", argv[0]);
for(ix = 0; ix < s.nbits; ix++) {
if(S_ISSET(&s, ix)) {
printf("%ld\n", S_VAL(&s, ix));
}
}
sieve_clear(&s);
return 0;
}
void sieve_init(sieve *sp, long base, int nbits)
{
sp->size = (nbits / CHAR_BIT);
if(nbits % CHAR_BIT)
++sp->size;
sp->bits = calloc(sp->size, sizeof(byte));
memset(sp->bits, UCHAR_MAX, sp->size);
if(!(base & 1))
++base;
sp->base = base;
sp->next = 0;
sp->nbits = sp->size * CHAR_BIT;
}
void sieve_grow(sieve *sp, int nbits)
{
int ns = (nbits / CHAR_BIT);
if(nbits % CHAR_BIT)
++ns;
if(ns > sp->size) {
byte *tmp;
int ix;
tmp = calloc(ns, sizeof(byte));
if(tmp == NULL) {
fprintf(stderr, "Error: out of memory in sieve_grow\n");
return;
}
memcpy(tmp, sp->bits, sp->size);
for(ix = sp->size; ix < ns; ix++) {
tmp[ix] = UCHAR_MAX;
}
free(sp->bits);
sp->bits = tmp;
sp->size = ns;
sp->nbits = sp->size * CHAR_BIT;
}
}
long sieve_next(sieve *sp)
{
long out;
int ix = 0;
long val;
if(sp->next > sp->nbits)
return -1;
out = S_VAL(sp, sp->next);
#ifdef DEBUG
fprintf(stderr, "Sieving %ld\n", out);
#endif
/* Sieve out all multiples of the current prime */
val = out;
while(ix < sp->nbits) {
val += out;
ix = S_BIT(sp, val);
if((val & 1) && ix < sp->nbits) { /* && S_ISSET(sp, ix)) { */
S_CLR(sp, ix);
#ifdef DEBUG
fprintf(stderr, "Crossing out %ld (bit %d)\n", val, ix);
#endif
}
}
/* Scan ahead to the next prime */
++sp->next;
while(sp->next < sp->nbits && !S_ISSET(sp, sp->next))
++sp->next;
return out;
}
void sieve_cross(sieve *sp, long val)
{
int ix = 0;
long cur = val;
while(cur < sp->base)
cur += val;
ix = S_BIT(sp, cur);
while(ix < sp->nbits) {
if(cur & 1)
S_CLR(sp, ix);
cur += val;
ix = S_BIT(sp, cur);
}
}
void sieve_reset(sieve *sp, long base)
{
memset(sp->bits, UCHAR_MAX, sp->size);
sp->base = base;
sp->next = 0;
}
void sieve_clear(sieve *sp)
{
if(sp->bits)
free(sp->bits);
sp->bits = NULL;
}
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