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+/* mpz_millerrabin(n,reps) -- An implementation of the probabilistic primality
+ test found in Knuth's Seminumerical Algorithms book. If the function
+ mpz_millerrabin() returns 0 then n is not prime. If it returns 1, then n is
+ 'probably' 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.
+
+ THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
+ CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
+ FUTURE GNU MP RELEASES.
+
+Copyright 1991, 1993, 1994, 1996-2002, 2005 Free Software Foundation, Inc.
+
+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 either:
+
+ * the GNU Lesser General Public License as published by the Free
+ Software Foundation; either version 3 of the License, or (at your
+ option) any later version.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+
+static int millerrabin (mpz_srcptr, mpz_srcptr,
+ mpz_ptr, mpz_ptr,
+ mpz_srcptr, unsigned long int);
+
+int
+mpz_millerrabin (mpz_srcptr n, int reps)
+{
+ int r;
+ mpz_t nm1, nm3, x, y, q;
+ unsigned long int k;
+ gmp_randstate_t rstate;
+ int is_prime;
+ TMP_DECL;
+ TMP_MARK;
+
+ MPZ_TMP_INIT (nm1, SIZ (n) + 1);
+ mpz_sub_ui (nm1, n, 1L);
+
+ MPZ_TMP_INIT (x, SIZ (n) + 1);
+ 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;
+ 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);
+
+ /* n-3 */
+ MPZ_TMP_INIT (nm3, SIZ (n) + 1);
+ mpz_sub_ui (nm3, n, 3L);
+ ASSERT (mpz_cmp_ui (nm3, 1L) >= 0);
+
+ gmp_randinit_default (rstate);
+
+ is_prime = 1;
+ for (r = 0; r < reps && is_prime; r++)
+ {
+ /* 2 to n-2 inclusive, don't want 1, 0 or -1 */
+ mpz_urandomm (x, rstate, nm3);
+ mpz_add_ui (x, x, 2L);
+
+ is_prime = millerrabin (n, nm1, x, y, q, k);
+ }
+
+ gmp_randclear (rstate);
+
+ TMP_FREE;
+ return is_prime;
+}
+
+static int
+millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y,
+ mpz_srcptr q, unsigned long int k)
+{
+ 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;
+}