Imported gcc-4.4.3

[msp430-gcc.git] / gmp / mpz / millerrabin.c

diff --git a/gmp/mpz/millerrabin.c b/gmp/mpz/millerrabin.c
new file mode 100644 (file)
index 0000000..f717278
--- /dev/null
+++ b/gmp/mpz/millerrabin.c
@@ -0,0 +1,112 @@
+/* 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, 1997, 1998, 1999, 2000, 2001, 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 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.
+
+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.  If not, see http://www.gnu.org/licenses/.  */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+
+static int millerrabin __GMP_PROTO ((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;
+}