source/libs/gmp/gmp-src/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, 1996-2002, 2005 Free Software Foundation, Inc.
  10
  11 This file is part of the GNU MP Library.
  12
  13 The GNU MP Library is free software; you can redistribute it and/or modify
  14 it under the terms of either:
  15
  16   * the GNU Lesser General Public License as published by the Free
  17     Software Foundation; either version 3 of the License, or (at your
  18     option) any later version.
  19
  20 or
  21
  22   * the GNU General Public License as published by the Free Software
  23     Foundation; either version 2 of the License, or (at your option) any
  24     later version.
  25
  26 or both in parallel, as here.
  27
  28 The GNU MP Library is distributed in the hope that it will be useful, but
  29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  30 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  31 for more details.
  32
  33 You should have received copies of the GNU General Public License and the
  34 GNU Lesser General Public License along with the GNU MP Library.  If not,
  35 see https://www.gnu.org/licenses/.  */
  36
  37 #include "gmp.h"
  38 #include "gmp-impl.h"
  39 #include "longlong.h"
  40
  41 static int isprime (unsigned long int);
  42
  43
  44 /* MPN_MOD_OR_MODEXACT_1_ODD can be used instead of mpn_mod_1 for the trial
  45    division.  It gives a result which is not the actual remainder r but a
  46    value congruent to r*2^n mod d.  Since all the primes being tested are
  47    odd, r*2^n mod p will be 0 if and only if r mod p is 0.  */
  48
  49 int
  50 mpz_probab_prime_p (mpz_srcptr n, int reps)
  51 {
  52   mp_limb_t r;
  53   mpz_t n2;
  54
  55   /* Handle small and negative n.  */
  56   if (mpz_cmp_ui (n, 1000000L) <= 0)
  57     {
  58       int is_prime;
  59       if (mpz_cmpabs_ui (n, 1000000L) <= 0)
  60         {
  61           is_prime = isprime (mpz_get_ui (n));
  62           return is_prime ? 2 : 0;
  63         }
  64       /* Negative number.  Negate and fall out.  */
  65       PTR(n2) = PTR(n);
  66       SIZ(n2) = -SIZ(n);
  67       n = n2;
  68     }
  69
  70   /* If n is now even, it is not a prime.  */
  71   if ((mpz_get_ui (n) & 1) == 0)
  72     return 0;
  73
  74 #if defined (PP)
  75   /* Check if n has small factors.  */
  76 #if defined (PP_INVERTED)
  77   r = MPN_MOD_OR_PREINV_MOD_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP,
  78                                (mp_limb_t) PP_INVERTED);
  79 #else
  80   r = mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP);
  81 #endif
  82   if (r % 3 == 0
  83 #if GMP_LIMB_BITS >= 4
  84       || r % 5 == 0
  85 #endif
  86 #if GMP_LIMB_BITS >= 8
  87       || r % 7 == 0
  88 #endif
  89 #if GMP_LIMB_BITS >= 16
  90       || r % 11 == 0 || r % 13 == 0
  91 #endif
  92 #if GMP_LIMB_BITS >= 32
  93       || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0
  94 #endif
  95 #if GMP_LIMB_BITS >= 64
  96       || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0
  97       || r % 47 == 0 || r % 53 == 0
  98 #endif
  99       )
 100     {
 101       return 0;
 102     }
 103 #endif /* PP */
 104
 105   /* Do more dividing.  We collect small primes, using umul_ppmm, until we
 106      overflow a single limb.  We divide our number by the small primes product,
 107      and look for factors in the remainder.  */
 108   {
 109     unsigned long int ln2;
 110     unsigned long int q;
 111     mp_limb_t p1, p0, p;
 112     unsigned int primes[15];
 113     int nprimes;
 114
 115     nprimes = 0;
 116     p = 1;
 117     ln2 = mpz_sizeinbase (n, 2);        /* FIXME: tune this limit */
 118     for (q = PP_FIRST_OMITTED; q < ln2; q += 2)
 119       {
 120         if (isprime (q))
 121           {
 122             umul_ppmm (p1, p0, p, q);
 123             if (p1 != 0)
 124               {
 125                 r = MPN_MOD_OR_MODEXACT_1_ODD (PTR(n), (mp_size_t) SIZ(n), p);
 126                 while (--nprimes >= 0)
 127                   if (r % primes[nprimes] == 0)
 128                     {
 129                       ASSERT_ALWAYS (mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) primes[nprimes]) == 0);
 130                       return 0;
 131                     }
 132                 p = q;
 133                 nprimes = 0;
 134               }
 135             else
 136               {
 137                 p = p0;
 138               }
 139             primes[nprimes++] = q;
 140           }
 141       }
 142   }
 143
 144   /* Perform a number of Miller-Rabin tests.  */
 145   return mpz_millerrabin (n, reps);
 146 }
 147
 148 static int
 149 isprime (unsigned long int t)
 150 {
 151   unsigned long int q, r, d;
 152
 153   if (t < 3 || (t & 1) == 0)
 154     return t == 2;
 155
 156   for (d = 3, r = 1; r != 0; d += 2)
 157     {
 158       q = t / d;
 159       r = t - q * d;
 160       if (q < d)
 161         return 1;
 162     }
 163   return 0;
 164 }