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

I can suggest an improvement for your algorithm.

You actually calculate a * b iteratively by adding each time b, doing modulo after each iteration. It's better to add each time b * x, whereas x is determined so that b * x won't overflow.

int64_t mulmod(int64_t a, int64_t b, int64_t m)
{
    a %= m;
    b %= m;

    int64_t x = 1;
    int64_t bx = b;

    while (x < a)
    {
        int64_t bb = bx * 2;
        if (bb <= bx)
            break; // overflow

        x *= 2;
        bx = bb;
    }

    int64_t ans = 0;

    for (; x < a; a -= x)
        ans = (ans + bx) % m;

    return (ans + a*b) % m;
}