primality_test

miller_rabin.c

#include <stdio.h>
#include <stdlib.h>

#include <sys/time.h>
void rand_init()
{
	unsigned ticks;
	struct timeval tv;
	gettimeofday(&tv, NULL);
	ticks = tv.tv_sec + tv.tv_usec;
	srand(ticks);
}

int pow_mod(int base, int power, int modulo)
{
	int result = 1;
	while (power > 0) {
		if ((power & 1) == 1) {
			result *= base;
			result %= modulo;
		}
		power >>= 1;
		base *= base;
		base %= modulo;
	}
	return result;
}

int mul_reminder(int even, int *k)
{
	int cnt = 0, r = even;
	while (r % 2 == 0) {
		r = r / 2;
		cnt ++;
	}
	*k = cnt;
	return r;
}

int miller_rabin(int a, int n)
{
	int j, k;
	int r = mul_reminder(n - 1, &k);
	int z = pow_mod(a, r, n);

	//printf("choose random base: %d (r=%d, k=%d) \n", a, r, k);
	if (z == 1 || z == n - 1)
		return 1; /* likely a prime */

	/* repeat k - 1 times */
	for (j = 0; j < k - 1; j++) {
		z = pow_mod(z, 2, n);
		if (z == 1)
			return 0; /* not prime witout -1 prior to 1 */
		else if (z == n - 1)
			return 1; /* likely a prime */
	}

	return 0; /* not prime because no -1 prior to a^{2^k·r} */
}

int primality_test(int n)
{
	/* conner cases for very small n */
	switch (n) {
	case 0:
	case 1:
		return 0;
	case 2:
	case 3:
		return 1;
	default:
		/* pass */;
	}

	/* make sure n is odd */
	if (n % 2 == 0)
		return 0;

	/* pick a random base value in [2, n - 2] */
	int base = 2 + rand() % (n - 3);
	return miller_rabin(base, n);
}

int test_primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997};

int true_primality(int n)
{
	int i;
	for (i = 0; i < sizeof(test_primes) / sizeof(int); i++)
		if (test_primes[i] == n)
			return 1;
	return 0;
}

int main()
{
	int n;
	rand_init();

	for (n = 0; n <= 997; n++) {
		if (true_primality(n)) {
			if (!primality_test(n))
				printf("judge wrong: %d (which is prime)\n", n);
		} else {
			if (primality_test(n))
				printf("guess wrong: %d (which is not prime)\n", n);
		}
	}
	return 0;
}