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121 lines
3.1 KiB
C
121 lines
3.1 KiB
C
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/* mpz_nextprime(p,t) - compute the next prime > t and store that in p.
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Copyright 1999, 2000, 2001, 2008, 2009 Free Software Foundation, Inc.
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Contributed to the GNU project by Niels M<EFBFBD>ller and Torbjorn Granlund.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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static const unsigned char primegap[] =
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{
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2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,
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2,10,2,6,6,4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,10,6,6,6,2,6,4,2,10,14,4,2,
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4,14,6,10,2,4,6,8,6,6,4,6,8,4,8,10,2,10,2,6,4,6,8,4,2,4,12,8,4,8,4,6,
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12,2,18,6,10,6,6,2,6,10,6,6,2,6,6,4,2,12,10,2,4,6,6,2,12,4,6,8,10,8,10,8,
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6,6,4,8,6,4,8,4,14,10,12,2,10,2,4,2,10,14,4,2,4,14,4,2,4,20,4,8,10,8,4,6,
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6,14,4,6,6,8,6,12
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};
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#define NUMBER_OF_PRIMES 167
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void
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mpz_nextprime (mpz_ptr p, mpz_srcptr n)
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{
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unsigned short *moduli;
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unsigned long difference;
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int i;
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unsigned prime_limit;
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unsigned long prime;
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int cnt;
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mp_size_t pn;
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mp_bitcnt_t nbits;
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unsigned incr;
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TMP_SDECL;
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/* First handle tiny numbers */
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if (mpz_cmp_ui (n, 2) < 0)
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{
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mpz_set_ui (p, 2);
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return;
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}
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mpz_add_ui (p, n, 1);
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mpz_setbit (p, 0);
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if (mpz_cmp_ui (p, 7) <= 0)
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return;
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pn = SIZ(p);
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count_leading_zeros (cnt, PTR(p)[pn - 1]);
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nbits = pn * GMP_NUMB_BITS - (cnt - GMP_NAIL_BITS);
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if (nbits / 2 >= NUMBER_OF_PRIMES)
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prime_limit = NUMBER_OF_PRIMES - 1;
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else
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prime_limit = nbits / 2;
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TMP_SMARK;
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/* Compute residues modulo small odd primes */
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moduli = TMP_SALLOC_TYPE (prime_limit * sizeof moduli[0], unsigned short);
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for (;;)
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{
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/* FIXME: Compute lazily? */
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prime = 3;
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for (i = 0; i < prime_limit; i++)
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{
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moduli[i] = mpz_fdiv_ui (p, prime);
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prime += primegap[i];
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}
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#define INCR_LIMIT 0x10000 /* deep science */
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for (difference = incr = 0; incr < INCR_LIMIT; difference += 2)
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{
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/* First check residues */
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prime = 3;
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for (i = 0; i < prime_limit; i++)
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{
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unsigned r;
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/* FIXME: Reduce moduli + incr and store back, to allow for
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division-free reductions. Alternatively, table primes[]'s
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inverses (mod 2^16). */
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r = (moduli[i] + incr) % prime;
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prime += primegap[i];
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if (r == 0)
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goto next;
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}
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mpz_add_ui (p, p, difference);
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difference = 0;
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/* Miller-Rabin test */
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if (mpz_millerrabin (p, 25))
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goto done;
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next:;
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incr += 2;
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}
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mpz_add_ui (p, p, difference);
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difference = 0;
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}
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done:
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TMP_SFREE;
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}
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