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/* bignum-next-prime.c
*
*/
/* nettle, low-level cryptographics library
*
* Copyright (C) 2002 Niels Möller
*
* The nettle library is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* The nettle library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with the nettle library; see the file COPYING.LIB. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02111-1301, USA.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <limits.h>
/* Needed for alloca on freebsd */
#include <stdlib.h>
#include "bignum.h"
#include "nettle-internal.h"
/* From gmp.h */
/* Test for gcc >= maj.min, as per __GNUC_PREREQ in glibc */
#if defined (__GNUC__) && defined (__GNUC_MINOR__)
#define GNUC_PREREQ(maj, min) \
((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
#else
#define GNUC_PREREQ(maj, min) 0
#endif
#if GNUC_PREREQ (3,0)
# define UNLIKELY(cond) __builtin_expect ((cond) != 0, 0)
#else
# define UNLIKELY(cond) cond
#endif
/* From some benchmarking using the examples nextprime(200!) and
nextprime(240!), it seems that it pays off to use a prime list up
to around 5000--10000 primes. There are 6541 odd primes less than
2^16. */
static const uint16_t primes[] = {
/* Generated by
./examples/eratosthenes 65535 \
| awk '{ if (NR % 10 == 2) printf ("\n"); if (NR > 1) printf("%d, ", $1); }
END { printf("\n"); }' > prime-list.h
*/
#include "prime-list.h"
};
#define NUMBER_OF_PRIMES (sizeof(primes) / sizeof(primes[0]))
#ifdef mpz_millerrabin
# define PRIME_P mpz_millerrabin
#else
# define PRIME_P mpz_probab_prime_p
#endif
/* NOTE: The mpz_nextprime in current GMP is unoptimized. */
void
nettle_next_prime(mpz_t p, mpz_t n, unsigned count, unsigned prime_limit,
void *progress_ctx, nettle_progress_func *progress)
{
mpz_t tmp;
TMP_DECL(moduli, unsigned, NUMBER_OF_PRIMES);
unsigned difference;
if (prime_limit > NUMBER_OF_PRIMES)
prime_limit = NUMBER_OF_PRIMES;
/* First handle tiny numbers */
if (mpz_cmp_ui(n, 2) <= 0)
{
mpz_set_ui(p, 2);
return;
}
mpz_set(p, n);
mpz_setbit(p, 0);
if (mpz_cmp_ui(p, 8) < 0)
return;
mpz_init(tmp);
if (mpz_cmp_ui(p, primes[prime_limit-1]) <= 0)
/* Use only 3, 5 and 7 */
/* FIXME: Could do binary search in the table. */
prime_limit = 3;
/* Compute residues modulo small odd primes */
/* FIXME: Could be sped up by collecting limb-sized products of the
primes, to reduce the calls to mpz_fdiv_ui */
/* FIXME: Could also handle the first few primes separately; compute
the residue mod 15015 = 3 * 7 * 11 * 13, and tabulate the steps
between the 5760 odd numbers in this interval that have no factor
in common with 15015.
*/
TMP_ALLOC(moduli, prime_limit);
{
unsigned i;
for (i = 0; i < prime_limit; i++)
moduli[i] = mpz_fdiv_ui(p, primes[i]);
}
for (difference = 0; ; difference += 2)
{
int composite = 0;
unsigned i;
if (difference >= UINT_MAX - 10)
{ /* Should not happen, at least not very often... */
mpz_add_ui(p, p, difference);
difference = 0;
}
/* First check residues */
for (i = 0; i < prime_limit; i++)
{
if (moduli[i] == 0)
composite = 1;
moduli[i] += 2;
if (UNLIKELY(moduli[i] >= primes[i]))
moduli[i] -= primes[i];
}
if (composite)
continue;
mpz_add_ui(p, p, difference);
difference = 0;
if (progress)
progress(progress_ctx, '.');
/* Miller-Rabin test */
if (PRIME_P(p, count))
break;
#if 0
if (progress)
progress(progress_ctx, '*');
#endif
}
mpz_clear(tmp);
}
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