Ways to do modulo multiplication with primitive types

Question

Is there a way to build e.g. (853467 * 21660421200929) % 100000000000007 without BigInteger libraries (note that each number fits into a 64 bit integer but the

Answer 1

You should use Russian Peasant multiplication. It uses repeated doubling to compute all the values (b*2^i)%m, and adds them in if the ith bit of a is set.

uint64_t mulmod(uint64_t a, uint64_t b, uint64_t m) {
    int64_t res = 0;
    while (a != 0) {
        if (a & 1) res = (res + b) % m;
        a >>= 1;
        b = (b << 1) % m;
    }
    return res;
}

It improves upon your algorithm because it takes O(log(a)) time, not O(a) time.

Caveats: unsigned, and works only if m is 63 bits or less.