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82 lines
1.9 KiB
82 lines
1.9 KiB
// Check whether a mersenne number is prime,
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// using the Lucas-Lehmer test.
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// [Donald Ervin Knuth: The Art of Computer Programming, Vol. II:
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// Seminumerical Algorithms, second edition. Section 4.5.4, p. 391.]
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// We work with integers.
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#include <cln/integer.h>
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using namespace std;
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using namespace cln;
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// Checks whether 2^q-1 is prime, q an odd prime.
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bool mersenne_prime_p (int q)
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{
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cl_I m = ((cl_I)1 << q) - 1;
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int i;
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cl_I L_i;
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for (i = 0, L_i = 4; i < q-2; i++)
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L_i = mod(L_i*L_i - 2, m);
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return (L_i==0);
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}
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// Same thing, but optimized.
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bool mersenne_prime_p_opt (int q)
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{
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cl_I m = ((cl_I)1 << q) - 1;
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int i;
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cl_I L_i;
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for (i = 0, L_i = 4; i < q-2; i++) {
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L_i = square(L_i) - 2;
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L_i = ldb(L_i,cl_byte(q,q)) + ldb(L_i,cl_byte(q,0));
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if (L_i >= m)
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L_i = L_i - m;
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}
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return (L_i==0);
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}
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// Now we work with modular integers.
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#include <cln/modinteger.h>
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// Same thing, but using modular integers.
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bool mersenne_prime_p_modint (int q)
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{
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cl_I m = ((cl_I)1 << q) - 1;
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cl_modint_ring R = find_modint_ring(m); // Z/mZ
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int i;
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cl_MI L_i;
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for (i = 0, L_i = R->canonhom(4); i < q-2; i++)
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L_i = R->minus(R->square(L_i),R->canonhom(2));
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return R->equal(L_i,R->zero());
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}
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#include <cln/io.h> // we do I/O
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#include <stdlib.h> // declares exit()
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#include <cln/timing.h>
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int main (int argc, char* argv[])
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{
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if (!(argc == 2)) {
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cerr << "Usage: lucaslehmer exponent" << endl;
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exit(1);
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}
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int q = atoi(argv[1]);
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if (!(q >= 2 && ((q % 2)==1))) {
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cerr << "Usage: lucaslehmer q with q odd prime" << endl;
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exit(1);
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}
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bool isprime;
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{ CL_TIMING; isprime = mersenne_prime_p(q); }
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{ CL_TIMING; isprime = mersenne_prime_p_opt(q); }
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{ CL_TIMING; isprime = mersenne_prime_p_modint(q); }
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cout << "2^" << q << "-1 is ";
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if (isprime)
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cout << "prime" << endl;
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else
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cout << "composite" << endl;
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}
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// Computing time on a i486, 33 MHz:
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// 1279: 2.02 s
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// 2281: 8.74 s
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// 44497: 14957 s
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