From e49cd0a23afd05df67120f36eab1648fea68cc1c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Niels=20M=C3=B6ller?= <nisse@lysator.liu.se>
Date: Thu, 28 Aug 2008 10:51:21 +0200
Subject: [PATCH] (main): Rewrote block-wise sieving to use less memory. New
options -s and -v.
Rev: nettle/examples/eratosthenes.c:1.9
---
examples/eratosthenes.c | 221 ++++++++++++++++++++++++++--------------
1 file changed, 145 insertions(+), 76 deletions(-)
diff --git a/examples/eratosthenes.c b/examples/eratosthenes.c
index 97abe191..287aaa35 100644
--- a/examples/eratosthenes.c
+++ b/examples/eratosthenes.c
@@ -28,6 +28,7 @@
# include "config.h"
#endif
+#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
@@ -53,7 +54,9 @@ usage(void)
fprintf(stderr, "Usage: erathostenes [OPTIONS] [LIMIT]\n\n"
"Options:\n"
" -? Display this message.\n"
- " -b SIZE Block size.\n");
+ " -b SIZE Block size.\n"
+ " -v Verbose output.\n"
+ " -s No output.\n");
}
static unsigned
@@ -83,16 +86,24 @@ static unsigned long *
vector_alloc(unsigned long size)
{
unsigned long end = (size + BITS_PER_LONG - 1) / BITS_PER_LONG;
- unsigned long i;
unsigned long *vector = malloc (end * sizeof(long));
if (!vector)
- return NULL;
+ {
+ fprintf(stderr, "Insufficient memory.\n");
+ exit(EXIT_FAILURE);
+ }
+ return vector;
+}
+
+static void
+vector_init(unsigned long *vector, unsigned long size)
+{
+ unsigned long end = (size + BITS_PER_LONG - 1) / BITS_PER_LONG;
+ unsigned long i;
for (i = 0; i < end; i++)
vector[i] = ~0;
-
- return vector;
}
static void
@@ -183,39 +194,78 @@ vector_find_next (const unsigned long *vector, unsigned long bit, unsigned long
will be spent converting the output to decimal). */
#define OUTPUT(n) printf("%lu\n", (n))
+static long
+atosize(const char *s)
+{
+ char *end;
+ long value = strtol(s, &end, 10);
+
+ if (value <= 0)
+ return 0;
+
+ /* FIXME: Doesn't check for overflow. */
+ switch(*end)
+ {
+ default:
+ return 0;
+ case '\0':
+ break;
+ case 'k': case 'K':
+ value <<= 10;
+ break;
+ case 'M':
+ value <<= 20;
+ break;
+ }
+ return value;
+}
+
int
main (int argc, char **argv)
{
- unsigned long *vector;
/* Generate all primes p <= limit */
unsigned long limit;
- unsigned long size;
+ unsigned long root;
+
+ unsigned long limit_nbits;
+
+ /* Represents numbers up to sqrt(limit) */
+ unsigned long sieve_nbits;
+ unsigned long *sieve;
+ /* Block for the rest of the sieving. Size should match the cache,
+ the default value corresponds to 64 KB. */
+ unsigned long block_nbits = 64L << 13;
+ unsigned long block_start_bit;
+ unsigned long *block;
+
unsigned long bit;
- unsigned long sieve_limit;
- unsigned long block_size;
- unsigned long block;
-
+ int silent = 0;
+ int verbose = 0;
int c;
- block_size = 0;
-
- while ( (c = getopt(argc, argv, "?b:")) != -1)
+ while ( (c = getopt(argc, argv, "?svb:")) != -1)
switch (c)
{
case '?':
usage();
return EXIT_FAILURE;
case 'b':
- {
- long arg = atol(optarg);
- if (arg <= 10)
- {
- usage();
- return EXIT_FAILURE;
- }
- block_size = (arg - 3) / 2;
- break;
- }
+ block_nbits = CHAR_BIT * atosize(optarg);
+ if (!block_nbits)
+ {
+ usage();
+ return EXIT_FAILURE;
+ }
+ break;
+
+ case 's':
+ silent = 1;
+ break;
+
+ case 'v':
+ verbose++;
+ break;
+
default:
abort();
}
@@ -237,83 +287,102 @@ main (int argc, char **argv)
return EXIT_FAILURE;
}
- size = (limit - 1) / 2;
-
- if (!block_size || block_size > size)
- block_size = size;
+ root = isqrt(limit);
+ /* Round down to odd */
+ root = (root - 1) | 1;
+ /* Represents odd numbers from 3 up. */
+ sieve_nbits = (root - 1) / 2;
+ sieve = vector_alloc(sieve_nbits );
+ vector_init(sieve, sieve_nbits);
- /* FIXME: Allocates a bit for all odd numbers up to limit. Could
- save a lot of memory by allocating space only for numbers up to
- the square root, plus one additional block. */
- vector = vector_alloc(size);
- if (!vector)
- {
- fprintf(stderr, "Insufficient memory.\n");
- return EXIT_FAILURE;
- }
-
- OUTPUT(2UL);
-
- bit = 0;
+ if (verbose)
+ fprintf(stderr, "Initial sieve using %lu bits.\n", sieve_nbits);
+
+ if (!silent)
+ printf("2\n");
if (limit == 2)
return EXIT_SUCCESS;
- sieve_limit = (isqrt(2*block_size + 1) - 1) / 2;
-
- while (bit < sieve_limit)
+ for (bit = 0;
+ bit < sieve_nbits;
+ bit = vector_find_next(sieve, bit + 1, sieve_nbits))
{
unsigned long n = 3 + 2 * bit;
-
- OUTPUT(n);
-
/* First bit to clear corresponds to n^2, which is bit
- (n^2 - 3) / 2 = n * bit + 3 (bit + 1)
- */
- vector_clear_bits (vector, n, n*bit + 3*(bit + 1), block_size);
+ (n^2 - 3) / 2 = (n + 3) * bit + 3
+ */
+ unsigned long n2_bit = (n+3)*bit + 3;
+
+ if (!silent)
+ printf("%lu\n", n);
- bit = vector_find_next (vector, bit + 1, block_size);
+ vector_clear_bits (sieve, n, n2_bit, sieve_nbits);
}
- /* No more marking, just output the remaining primes. */
- for (; bit < block_size ;
- bit = vector_find_next (vector, bit + 1, block_size))
+ limit_nbits = (limit - 1) / 2;
- OUTPUT(3 + 2 * bit);
+ if (sieve_nbits + block_nbits > limit_nbits)
+ block_nbits = limit_nbits - sieve_nbits;
- for (block = block_size; block < size; block += block_size)
+ if (verbose)
+ {
+ double storage = block_nbits / 8.0;
+ unsigned shift = 0;
+ const char prefix[] = " KMG";
+
+ while (storage > 1024 && shift < 3)
+ {
+ storage /= 1024;
+ shift++;
+ }
+ fprintf(stderr, "Blockwise sieving using blocks of %lu bits (%.3g %cByte)\n",
+ block_nbits, storage, prefix[shift]);
+ }
+
+ block = vector_alloc(block_nbits);
+
+ for (block_start_bit = bit; block_start_bit < limit_nbits; block_start_bit += block_nbits)
{
unsigned long block_start;
- unsigned long block_end;
+
+ if (block_start_bit + block_nbits > limit_nbits)
+ block_nbits = limit_nbits - block_start_bit;
- if (block + block_size > size)
- /* For the final block */
- block_size = size - block;
+ vector_init(block, block_nbits);
- block_start = 2*block + 3;
- block_end = 2*(block + block_size) + 3;
+ block_start = 3 + 2*block_start_bit;
- sieve_limit = (isqrt(block_end) - 1) / 2;
- for (bit = 0; bit < sieve_limit ;)
- {
+ if (verbose > 1)
+ fprintf(stderr, "Next block, n = %lu\n", block_start);
+
+ /* Sieve */
+ for (bit = 0; bit < sieve_nbits;
+ bit = vector_find_next(sieve, bit + 1, sieve_nbits))
+ {
unsigned long n = 3 + 2 * bit;
+ unsigned long sieve_start_bit = (n + 3) * bit + 3;
- unsigned long start = n*bit + 3*(bit + 1);
- if (start < block)
+ if (sieve_start_bit < block_start_bit)
{
- unsigned long k = (block + 1) / n;
- start = bit + k*n;
+ unsigned long k = (block_start + n - 1) / (2*n);
+ sieve_start_bit = n * k + bit;
+
+ assert(sieve_start_bit < block_start_bit + n);
}
- vector_clear_bits (vector, n, start, block + block_size);
+ assert(sieve_start_bit >= block_start_bit);
- bit = vector_find_next (vector, bit + 1, block + block_size);
+ vector_clear_bits(block, n, sieve_start_bit - block_start_bit, block_nbits);
+ }
+ for (bit = vector_find_next(block, 0, block_nbits);
+ bit < block_nbits;
+ bit = vector_find_next(block, bit + 1, block_nbits))
+ {
+ unsigned long n = block_start + 2 * bit;
+ if (!silent)
+ printf("%lu\n", n);
}
- for (bit = vector_find_next (vector, block, block + block_size);
- bit < block + block_size;
- bit = vector_find_next (vector, bit + 1, block + block_size))
- OUTPUT(3 + 2 * bit);
}
-
return EXIT_SUCCESS;
}
--
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