diff options
Diffstat (limited to 'libtommath/etc/mersenne.c')
-rw-r--r-- | libtommath/etc/mersenne.c | 140 |
1 files changed, 140 insertions, 0 deletions
diff --git a/libtommath/etc/mersenne.c b/libtommath/etc/mersenne.c new file mode 100644 index 0000000..28ac834 --- /dev/null +++ b/libtommath/etc/mersenne.c @@ -0,0 +1,140 @@ +/* Finds Mersenne primes using the Lucas-Lehmer test + * + * Tom St Denis, tomstdenis@gmail.com + */ +#include <time.h> +#include <tommath.h> + +int +is_mersenne (long s, int *pp) +{ + mp_int n, u; + int res, k; + + *pp = 0; + + if ((res = mp_init (&n)) != MP_OKAY) { + return res; + } + + if ((res = mp_init (&u)) != MP_OKAY) { + goto LBL_N; + } + + /* n = 2^s - 1 */ + if ((res = mp_2expt(&n, s)) != MP_OKAY) { + goto LBL_MU; + } + if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) { + goto LBL_MU; + } + + /* set u=4 */ + mp_set (&u, 4); + + /* for k=1 to s-2 do */ + for (k = 1; k <= s - 2; k++) { + /* u = u^2 - 2 mod n */ + if ((res = mp_sqr (&u, &u)) != MP_OKAY) { + goto LBL_MU; + } + if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) { + goto LBL_MU; + } + + /* make sure u is positive */ + while (u.sign == MP_NEG) { + if ((res = mp_add (&u, &n, &u)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* reduce */ + if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* if u == 0 then its prime */ + if (mp_iszero (&u) == 1) { + mp_prime_is_prime(&n, 8, pp); + if (*pp != 1) printf("FAILURE\n"); + } + + res = MP_OKAY; +LBL_MU:mp_clear (&u); +LBL_N:mp_clear (&n); + return res; +} + +/* square root of a long < 65536 */ +long +i_sqrt (long x) +{ + long x1, x2; + + x2 = 16; + do { + x1 = x2; + x2 = x1 - ((x1 * x1) - x) / (2 * x1); + } while (x1 != x2); + + if (x1 * x1 > x) { + --x1; + } + + return x1; +} + +/* is the long prime by brute force */ +int +isprime (long k) +{ + long y, z; + + y = i_sqrt (k); + for (z = 2; z <= y; z++) { + if ((k % z) == 0) + return 0; + } + return 1; +} + + +int +main (void) +{ + int pp; + long k; + clock_t tt; + + k = 3; + + for (;;) { + /* start time */ + tt = clock (); + + /* test if 2^k - 1 is prime */ + if (is_mersenne (k, &pp) != MP_OKAY) { + printf ("Whoa error\n"); + return -1; + } + + if (pp == 1) { + /* count time */ + tt = clock () - tt; + + /* display if prime */ + printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt); + } + + /* goto next odd exponent */ + k += 2; + + /* but make sure its prime */ + while (isprime (k) == 0) { + k += 2; + } + } + return 0; +} |