145 lines
2.3 KiB
C
145 lines
2.3 KiB
C
/* Finds Mersenne primes using the Lucas-Lehmer test
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*
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* Tom St Denis, tomstdenis@gmail.com
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*/
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#include <time.h>
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#include <tommath.h>
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int
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is_mersenne (long s, int *pp)
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{
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mp_int n, u;
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int res, k;
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*pp = 0;
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if ((res = mp_init (&n)) != MP_OKAY) {
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return res;
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}
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if ((res = mp_init (&u)) != MP_OKAY) {
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goto LBL_N;
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}
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/* n = 2^s - 1 */
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if ((res = mp_2expt(&n, s)) != MP_OKAY) {
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goto LBL_MU;
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}
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if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
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goto LBL_MU;
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}
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/* set u=4 */
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mp_set (&u, 4);
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/* for k=1 to s-2 do */
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for (k = 1; k <= s - 2; k++) {
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/* u = u^2 - 2 mod n */
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if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
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goto LBL_MU;
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}
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if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
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goto LBL_MU;
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}
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/* make sure u is positive */
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while (u.sign == MP_NEG) {
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if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
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goto LBL_MU;
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}
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}
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/* reduce */
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if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
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goto LBL_MU;
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}
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}
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/* if u == 0 then its prime */
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if (mp_iszero (&u) == 1) {
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mp_prime_is_prime(&n, 8, pp);
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if (*pp != 1) printf("FAILURE\n");
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}
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res = MP_OKAY;
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LBL_MU:mp_clear (&u);
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LBL_N:mp_clear (&n);
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return res;
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}
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/* square root of a long < 65536 */
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long
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i_sqrt (long x)
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{
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long x1, x2;
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x2 = 16;
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do {
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x1 = x2;
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x2 = x1 - ((x1 * x1) - x) / (2 * x1);
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} while (x1 != x2);
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if (x1 * x1 > x) {
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--x1;
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}
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return x1;
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}
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/* is the long prime by brute force */
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int
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isprime (long k)
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{
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long y, z;
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y = i_sqrt (k);
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for (z = 2; z <= y; z++) {
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if ((k % z) == 0)
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return 0;
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}
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return 1;
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}
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int
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main (void)
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{
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int pp;
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long k;
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clock_t tt;
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k = 3;
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for (;;) {
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/* start time */
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tt = clock ();
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/* test if 2^k - 1 is prime */
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if (is_mersenne (k, &pp) != MP_OKAY) {
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printf ("Whoa error\n");
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return -1;
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}
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if (pp == 1) {
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/* count time */
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tt = clock () - tt;
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/* display if prime */
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printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
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}
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/* goto next odd exponent */
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k += 2;
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/* but make sure its prime */
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while (isprime (k) == 0) {
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k += 2;
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}
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}
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return 0;
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}
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/* $Source: /cvs/libtom/libtommath/etc/mersenne.c,v $ */
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/* $Revision: 1.3 $ */
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/* $Date: 2006/03/31 14:18:47 $ */
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