contrib/gmp/mpz/pprime_p.c

   1 /* mpz_probab_prime_p --
   2    An implementation of the probabilistic primality test found in Knuth's
   3    Seminumerical Algorithms book.  If the function mpz_probab_prime_p()
   4    returns 0 then n is not prime.  If it returns 1, then n is 'probably'
   5    prime.  If it returns 2, n is surely prime.  The probability of a false
   6    positive is (1/4)**reps, where reps is the number of internal passes of the
   7    probabilistic algorithm.  Knuth indicates that 25 passes are reasonable.
   8
   9 Copyright 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2005 Free
  10 Software Foundation, Inc.  Miller-Rabin code contributed by John Amanatides.
  11
  12 This file is part of the GNU MP Library.
  13
  14 The GNU MP Library is free software; you can redistribute it and/or modify
  15 it under the terms of the GNU Lesser General Public License as published by
  16 the Free Software Foundation; either version 3 of the License, or (at your
  17 option) any later version.
  18
  19 The GNU MP Library is distributed in the hope that it will be useful, but
  20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  21 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  22 License for more details.
  23
  24 You should have received a copy of the GNU Lesser General Public License
  25 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
  26
  27 #include "gmp.h"
  28 #include "gmp-impl.h"
  29 #include "longlong.h"
  30
  31 static int isprime __GMP_PROTO ((unsigned long int));
  32
  33
  34 /* MPN_MOD_OR_MODEXACT_1_ODD can be used instead of mpn_mod_1 for the trial
  35    division.  It gives a result which is not the actual remainder r but a
  36    value congruent to r*2^n mod d.  Since all the primes being tested are
  37    odd, r*2^n mod p will be 0 if and only if r mod p is 0.  */
  38
  39 int
  40 mpz_probab_prime_p (mpz_srcptr n, int reps)
  41 {
  42   mp_limb_t r;
  43   mpz_t n2;
  44
  45   /* Handle small and negative n.  */
  46   if (mpz_cmp_ui (n, 1000000L) <= 0)
  47     {
  48       int is_prime;
  49       if (mpz_cmpabs_ui (n, 1000000L) <= 0)
  50         {
  51           is_prime = isprime (mpz_get_ui (n));
  52           return is_prime ? 2 : 0;
  53         }
  54       /* Negative number.  Negate and fall out.  */
  55       PTR(n2) = PTR(n);
  56       SIZ(n2) = -SIZ(n);
  57       n = n2;
  58     }
  59
  60   /* If n is now even, it is not a prime.  */
  61   if ((mpz_get_ui (n) & 1) == 0)
  62     return 0;
  63
  64 #if defined (PP)
  65   /* Check if n has small factors.  */
  66 #if defined (PP_INVERTED)
  67   r = MPN_MOD_OR_PREINV_MOD_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP,
  68                                (mp_limb_t) PP_INVERTED);
  69 #else
  70   r = mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP);
  71 #endif
  72   if (r % 3 == 0
  73 #if GMP_LIMB_BITS >= 4
  74       || r % 5 == 0
  75 #endif
  76 #if GMP_LIMB_BITS >= 8
  77       || r % 7 == 0
  78 #endif
  79 #if GMP_LIMB_BITS >= 16
  80       || r % 11 == 0 || r % 13 == 0
  81 #endif
  82 #if GMP_LIMB_BITS >= 32
  83       || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0
  84 #endif
  85 #if GMP_LIMB_BITS >= 64
  86       || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0
  87       || r % 47 == 0 || r % 53 == 0
  88 #endif
  89       )
  90     {
  91       return 0;
  92     }
  93 #endif /* PP */
  94
  95   /* Do more dividing.  We collect small primes, using umul_ppmm, until we
  96      overflow a single limb.  We divide our number by the small primes product,
  97      and look for factors in the remainder.  */
  98   {
  99     unsigned long int ln2;
 100     unsigned long int q;
 101     mp_limb_t p1, p0, p;
 102     unsigned int primes[15];
 103     int nprimes;
 104
 105     nprimes = 0;
 106     p = 1;
 107     ln2 = mpz_sizeinbase (n, 2);        /* FIXME: tune this limit */
 108     for (q = PP_FIRST_OMITTED; q < ln2; q += 2)
 109       {
 110         if (isprime (q))
 111           {
 112             umul_ppmm (p1, p0, p, q);
 113             if (p1 != 0)
 114               {
 115                 r = MPN_MOD_OR_MODEXACT_1_ODD (PTR(n), (mp_size_t) SIZ(n), p);
 116                 while (--nprimes >= 0)
 117                   if (r % primes[nprimes] == 0)
 118                     {
 119                       ASSERT_ALWAYS (mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) primes[nprimes]) == 0);
 120                       return 0;
 121                     }
 122                 p = q;
 123                 nprimes = 0;
 124               }
 125             else
 126               {
 127                 p = p0;
 128               }
 129             primes[nprimes++] = q;
 130           }
 131       }
 132   }
 133
 134   /* Perform a number of Miller-Rabin tests.  */
 135   return mpz_millerrabin (n, reps);
 136 }
 137
 138 static int
 139 isprime (unsigned long int t)
 140 {
 141   unsigned long int q, r, d;
 142
 143   if (t < 3 || (t & 1) == 0)
 144     return t == 2;
 145
 146   for (d = 3, r = 1; r != 0; d += 2)
 147     {
 148       q = t / d;
 149       r = t - q * d;
 150       if (q < d)
 151         return 1;
 152     }
 153   return 0;
 154 }