139 lines
2.3 KiB
C
139 lines
2.3 KiB
C
|
/* Finds Mersenne primes using the Lucas-Lehmer test
|
||
|
|
*
|
||
|
|
* Tom St Denis, tomstdenis@gmail.com
|
||
|
|
*/
|
||
|
|
#include <time.h>
|
||
|
|
#include <tommath.h>
|
||
|
|
|
||
|
|
static mp_err is_mersenne(long s, bool *pp)
|
||
|
|
{
|
||
|
|
mp_int n, u;
|
||
|
|
mp_err res;
|
||
|
|
int k;
|
||
|
|
|
||
|
|
*pp = false;
|
||
|
|
|
||
|
|
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, (int)s)) != MP_OKAY) {
|
||
|
|
goto LBL_MU;
|
||
|
|
}
|
||
|
|
if ((res = mp_sub_d(&n, 1uL, &n)) != MP_OKAY) {
|
||
|
|
goto LBL_MU;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* set u=4 */
|
||
|
|
mp_set(&u, 4uL);
|
||
|
|
|
||
|
|
/* 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, 2uL, &u)) != MP_OKAY) {
|
||
|
|
goto LBL_MU;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* make sure u is positive */
|
||
|
|
while (mp_isneg(&u)) {
|
||
|
|
if ((res = mp_add(&u, &n, &u)) != MP_OKAY) {
|
||
|
|
goto LBL_MU;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* reduce */
|
||
|
|
if ((res = mp_reduce_2k(&u, &n, 1uL)) != MP_OKAY) {
|
||
|
|
goto LBL_MU;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* if u == 0 then its prime */
|
||
|
|
if (mp_iszero(&u)) {
|
||
|
|
mp_prime_is_prime(&n, 8, pp);
|
||
|
|
if (!*pp) printf("FAILURE\n");
|
||
|
|
}
|
||
|
|
|
||
|
|
res = MP_OKAY;
|
||
|
|
LBL_MU:
|
||
|
|
mp_clear(&u);
|
||
|
|
LBL_N:
|
||
|
|
mp_clear(&n);
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* square root of a long < 65536 */
|
||
|
|
static 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 */
|
||
|
|
static 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)
|
||
|
|
{
|
||
|
|
bool 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) {
|
||
|
|
/* count time */
|
||
|
|
tt = clock() - tt;
|
||
|
|
|
||
|
|
/* display if prime */
|
||
|
|
printf("2^%-5ld - 1 is prime, test took %ld ticks\n", k, (long)tt);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* goto next odd exponent */
|
||
|
|
k += 2;
|
||
|
|
|
||
|
|
/* but make sure its prime */
|
||
|
|
while (isprime(k) == 0) {
|
||
|
|
k += 2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|