Primality test

miller-rabin.c

/* Primality test.
 *
 * Copyright (C) 2013 Chen-Pang He <jdh8＠ms63.hinet.net>
 * Don’t copy-paste the email.  It won’t work.
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
#include <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

uint32_t powmod (uint32_t base, uint32_t exp, uint32_t mod)
{
    uint32_t res = 1;
    base %= mod;
    while (exp) {
        if (exp % 2)
            res = res * (uint64_t)base % mod;
        exp /= 2;
        base = base * (uint64_t)base % mod;
    }
    return res;
}

/* Deterministic Miller-Rabin primality test */
int isPrime (uint32_t n)
{
    uint32_t d, r, s;
    
    switch (n) {
        case 0:
        case 1:
            return 0;
        case 2:
            return 1;
    }

    d = n - 1;
    s = 0;

    while (d % 2 == 0) {
        d /= 2;
        ++s;
    }
    for (r=0; r<s; ++r) {
        if (powmod(2, d, n) == 1 || powmod(2, d << r, n) == n - 1 ||
            powmod(7, d, n) == 1 || powmod(7, d << r, n) == n - 1 ||
            powmod(61, d, n) == 1 || powmod(61, d << r, n) == n - 1)
            return 1;
    }
    return 0;
}

int main (int argc, char *argv[])
{
    uint32_t n;

    if (argc != 2) {
        printf("Usage: %s num\n", argv[0]);
        puts("Test if num is prime.\n"
             "Warning: This program may crash if num overflows uint32_t.");
        return 1;
    }
    n = strtoul(argv[1], NULL, 10);

    if (isPrime(n))
        printf("%u is prime.\n", n);
    else
        printf("%u is composite.\n", n);
    return 0;
}