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Ingy döt Net
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#ifndef _MILLER_RABIN_H_
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#define _MILLER_RABIN_H
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#include <gmp.h>
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bool miller_rabin_test(mpz_t n, int j);
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#endif
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#include <stdbool.h>
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#include <gmp.h>
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#include "primedecompose.h"
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#define MAX_DECOMPOSE 100
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bool miller_rabin_test(mpz_t n, int j)
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{
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bool res;
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mpz_t f[MAX_DECOMPOSE];
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mpz_t s, d, a, x, r;
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mpz_t n_1, n_3;
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gmp_randstate_t rs;
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int l=0, k;
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res = false;
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gmp_randinit_default(rs);
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mpz_init(s); mpz_init(d);
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mpz_init(a); mpz_init(x); mpz_init(r);
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mpz_init(n_1); mpz_init(n_3);
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if ( mpz_cmp_si(n, 3) <= 0 ) { // let us consider 1, 2, 3 as prime
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gmp_randclear(rs);
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return true;
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}
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if ( mpz_odd_p(n) != 0 ) {
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mpz_sub_ui(n_1, n, 1); // n-1
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mpz_sub_ui(n_3, n, 3); // n-3
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l = decompose(n_1, f);
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mpz_set_ui(s, 0);
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mpz_set_ui(d, 1);
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for(k=0; k < l; k++) {
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if ( mpz_cmp_ui(f[k], 2) == 0 )
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mpz_add_ui(s, s, 1);
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else
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mpz_mul(d, d, f[k]);
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} // 2^s * d = n-1
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while(j-- > 0) {
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mpz_urandomm(a, rs, n_3); // random from 0 to n-4
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mpz_add_ui(a, a, 2); // random from 2 to n-2
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mpz_powm(x, a, d, n);
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if ( mpz_cmp_ui(x, 1) == 0 ) continue;
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mpz_set_ui(r, 0);
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while( mpz_cmp(r, s) < 0 ) {
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if ( mpz_cmp(x, n_1) == 0 ) break;
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mpz_powm_ui(x, x, 2, n);
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mpz_add_ui(r, r, 1);
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}
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if ( mpz_cmp(x, n_1) == 0 ) continue;
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goto flush; // woops
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}
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res = true;
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}
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flush:
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for(k=0; k < l; k++) mpz_clear(f[k]);
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mpz_clear(s); mpz_clear(d);
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mpz_clear(a); mpz_clear(x); mpz_clear(r);
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mpz_clear(n_1); mpz_clear(n_3);
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gmp_randclear(rs);
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return res;
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}
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#include <gmp.h>
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#include "miller-rabin.h"
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#define PREC 10
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#define TOP 4000
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int main()
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{
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mpz_t num;
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mpz_init(num);
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mpz_set_ui(num, 1);
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while ( mpz_cmp_ui(num, TOP) < 0 ) {
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if ( miller_rabin_test(num, PREC) ) {
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gmp_printf("%Zd maybe prime\n", num);
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} /*else {
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gmp_printf("%Zd not prime\n", num);
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}*/ // remove the comment iff you're interested in
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// sure non-prime.
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mpz_add_ui(num, num, 1);
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}
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mpz_clear(num);
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return EXIT_SUCCESS;
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}
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// calcul a^n%mod
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size_t power(size_t a, size_t n, size_t mod)
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{
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size_t power = a;
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size_t result = 1;
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while (n)
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{
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if (n & 1)
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result = (result * power) % mod;
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power = (power * power) % mod;
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n >>= 1;
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}
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return result;
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}
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// n−1 = 2^s * d with d odd by factoring powers of 2 from n−1
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bool witness(size_t n, size_t s, size_t d, size_t a)
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{
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size_t x = power(a, d, n);
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size_t y;
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while (s) {
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y = (x * x) % n;
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if (y == 1 && x != 1 && x != n-1)
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return false;
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x = y;
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--s;
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}
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if (y != 1)
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return false;
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return true;
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}
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/*
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* if n < 1,373,653, it is enough to test a = 2 and 3;
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* if n < 9,080,191, it is enough to test a = 31 and 73;
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* if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
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* if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
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* if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
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* if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
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* if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.
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*/
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bool is_prime_mr(size_t n)
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{
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if (((!(n & 1)) && n != 2 ) || (n < 2) || (n % 3 == 0 && n != 3))
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return false;
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if (n <= 3)
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return true;
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size_t d = n / 2;
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size_t s = 1;
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while (!(d & 1)) {
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d /= 2;
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++s;
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}
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if (n < 1373653)
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return witness(n, s, d, 2) && witness(n, s, d, 3);
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if (n < 9080191)
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return witness(n, s, d, 31) && witness(n, s, d, 73);
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if (n < 4759123141)
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return witness(n, s, d, 2) && witness(n, s, d, 7) && witness(n, s, d, 61);
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if (n < 1122004669633)
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return witness(n, s, d, 2) && witness(n, s, d, 13) && witness(n, s, d, 23) && witness(n, s, d, 1662803);
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if (n < 2152302898747)
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return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11);
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if (n < 3474749660383)
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return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13);
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return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13) && witness(n, s, d, 17);
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}
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typedef unsigned long long int ulong;
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ulong mul_mod(ulong a, ulong b, const ulong mod) {
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ulong res = 0, c; // return (a * b) % mod, avoiding overflow errors while doing modular multiplication.
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for (b %= mod; a; a & 1 ? b >= mod - res ? res -= mod : 0, res += b : 0, a >>= 1, (c = b) >= mod - b ? c -= mod : 0, b += c);
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return res % mod;
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}
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ulong pow_mod(ulong n, ulong exp, const ulong mod) {
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ulong res = 1; // return (n ^ exp) % mod
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for (n %= mod; exp; exp & 1 ? res = mul_mod(res, n, mod) : 0, n = mul_mod(n, n, mod), exp >>= 1);
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return res;
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}
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int is_prime(ulong N) {
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// Perform a Miller-Rabin test, it should be a deterministic version.
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const ulong n_primes = 9, primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23};
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for (ulong i = 0; i < n_primes; ++i)
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if (N % primes[i] == 0) return N == primes[i];
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if (N < primes[n_primes - 1]) return 0;
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int res = 1, s = 0;
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ulong t;
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for (t = N - 1; ~t & 1; t >>= 1, ++s);
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for (ulong i = 0; i < n_primes && res; ++i) {
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ulong B = pow_mod(primes[i], t, N);
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if (B != 1) {
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for (int b = s; b-- && (res = B + 1 != N);)
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B = mul_mod(B, B, N);
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res = !res;
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}
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}
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return res;
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}
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int main(void){
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return is_prime(8193145868754512737);
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}
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