--- /dev/null
+/* mpz_probab_prime_p --
+ An implementation of the probabilistic primality test found in Knuth's
+ Seminumerical Algorithms book. If the function mpz_probab_prime_p()
+ returns 0 then n is not prime. If it returns 1, then n is 'probably'
+ prime. If it returns 2, n is surely prime. The probability of a false
+ positive is (1/4)**reps, where reps is the number of internal passes of the
+ probabilistic algorithm. Knuth indicates that 25 passes are reasonable.
+
+Copyright (C) 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000 Free Software
+Foundation, Inc. Miller-Rabin code contributed by John Amanatides.
+
+This file is part of the GNU MP Library.
+
+The GNU MP 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 GNU MP 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 GNU MP Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+static int isprime _PROTO ((unsigned long int t));
+static int mpz_millerrabin _PROTO ((mpz_srcptr n, int reps));
+
+int
+#if __STDC__
+mpz_probab_prime_p (mpz_srcptr n, int reps)
+#else
+mpz_probab_prime_p (n, reps)
+ mpz_srcptr n;
+ int reps;
+#endif
+{
+ mp_limb_t r;
+
+ /* Handle small and negative n. */
+ if (mpz_cmp_ui (n, 1000000L) <= 0)
+ {
+ int is_prime;
+ if (mpz_sgn (n) < 0)
+ {
+ /* Negative number. Negate and call ourselves. */
+ mpz_t n2;
+ mpz_init (n2);
+ mpz_neg (n2, n);
+ is_prime = mpz_probab_prime_p (n2, reps);
+ mpz_clear (n2);
+ return is_prime;
+ }
+ is_prime = isprime (mpz_get_ui (n));
+ return is_prime ? 2 : 0;
+ }
+
+ /* If n is now even, it is not a prime. */
+ if ((mpz_get_ui (n) & 1) == 0)
+ return 0;
+
+ /* Check if n has small factors. */
+ if (UDIV_TIME > (2 * UMUL_TIME + 6))
+ r = mpn_preinv_mod_1 (PTR(n), SIZ(n), (mp_limb_t) PP, (mp_limb_t) PP_INVERTED);
+ else
+ r = mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) PP);
+ if (r % 3 == 0 || r % 5 == 0 || r % 7 == 0 || r % 11 == 0 || r % 13 == 0
+ || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0
+#if BITS_PER_MP_LIMB == 64
+ || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0
+ || r % 47 == 0 || r % 53 == 0
+#endif
+ )
+ {
+ return 0;
+ }
+
+ /* Do more dividing. We collect small primes, using umul_ppmm, until we
+ overflow a single limb. We divide our number by the small primes product,
+ and look for factors in the remainder. */
+ {
+ unsigned long int ln2;
+ unsigned long int q;
+ mp_limb_t p1, p0, p;
+ unsigned int primes[15];
+ int nprimes;
+
+ nprimes = 0;
+ p = 1;
+ ln2 = mpz_sizeinbase (n, 2) / 30; ln2 = ln2 * ln2;
+ for (q = BITS_PER_MP_LIMB == 64 ? 59 : 31; q < ln2; q += 2)
+ {
+ if (isprime (q))
+ {
+ umul_ppmm (p1, p0, p, q);
+ if (p1 != 0)
+ {
+ r = mpn_mod_1 (PTR(n), SIZ(n), p);
+ while (--nprimes >= 0)
+ if (r % primes[nprimes] == 0)
+ {
+ if (mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) primes[nprimes]) != 0)
+ abort ();
+ return 0;
+ }
+ p = q;
+ nprimes = 0;
+ }
+ else
+ {
+ p = p0;
+ }
+ primes[nprimes++] = q;
+ }
+ }
+ }
+
+ /* Perform a number of Miller-Rabin tests. */
+ return mpz_millerrabin (n, reps);
+}
+
+static int
+#if __STDC__
+isprime (unsigned long int t)
+#else
+isprime (t)
+ unsigned long int t;
+#endif
+{
+ unsigned long int q, r, d;
+
+ if (t < 3 || (t & 1) == 0)
+ return t == 2;
+
+ for (d = 3, r = 1; r != 0; d += 2)
+ {
+ q = t / d;
+ r = t - q * d;
+ if (q < d)
+ return 1;
+ }
+ return 0;
+}
+
+static int millerrabin _PROTO ((mpz_srcptr n, mpz_srcptr nm1,
+ mpz_ptr x, mpz_ptr y,
+ mpz_srcptr q, unsigned long int k));
+
+static int
+#if __STDC__
+mpz_millerrabin (mpz_srcptr n, int reps)
+#else
+mpz_millerrabin (n, reps)
+ mpz_srcptr n;
+ int reps;
+#endif
+{
+ int r;
+ mpz_t nm1, x, y, q;
+ unsigned long int k;
+ gmp_randstate_t rstate;
+ int is_prime;
+ TMP_DECL (marker);
+ TMP_MARK (marker);
+
+ MPZ_TMP_INIT (nm1, SIZ (n) + 1);
+ mpz_sub_ui (nm1, n, 1L);
+
+ MPZ_TMP_INIT (x, SIZ (n));
+ MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */
+
+ /* Perform a Fermat test. */
+ mpz_set_ui (x, 210L);
+ mpz_powm (y, x, nm1, n);
+ if (mpz_cmp_ui (y, 1L) != 0)
+ {
+ TMP_FREE (marker);
+ return 0;
+ }
+
+ MPZ_TMP_INIT (q, SIZ (n));
+
+ /* Find q and k, where q is odd and n = 1 + 2**k * q. */
+ k = mpz_scan1 (nm1, 0L);
+ mpz_tdiv_q_2exp (q, nm1, k);
+
+ gmp_randinit (rstate, GMP_RAND_ALG_DEFAULT, 32L);
+
+ is_prime = 1;
+ for (r = 0; r < reps && is_prime; r++)
+ {
+ do
+ mpz_urandomb (x, rstate, mpz_sizeinbase (n, 2) - 1);
+ while (mpz_cmp_ui (x, 1L) <= 0);
+
+ is_prime = millerrabin (n, nm1, x, y, q, k);
+ }
+
+ gmp_randclear (rstate);
+
+ TMP_FREE (marker);
+ return is_prime;
+}
+
+static int
+#if __STDC__
+millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
+ mpz_srcptr q, unsigned long int k)
+#else
+millerrabin (n, nm1, x, y, q, k)
+ mpz_srcptr n;
+ mpz_srcptr nm1;
+ mpz_ptr x;
+ mpz_ptr y;
+ mpz_srcptr q;
+ unsigned long int k;
+#endif
+{
+ unsigned long int i;
+
+ mpz_powm (y, x, q, n);
+
+ if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0)
+ return 1;
+
+ for (i = 1; i < k; i++)
+ {
+ mpz_powm_ui (y, y, 2L, n);
+ if (mpz_cmp (y, nm1) == 0)
+ return 1;
+ if (mpz_cmp_ui (y, 1L) == 0)
+ return 0;
+ }
+ return 0;
+}
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