Best way to find minimal difference between two values in a cyclic system?

Question

Take for example time:

If we take a 12-hour clock, we'd get the following results

What is the most efficient way to do that?

Assuming the values are doubles.

user_6741053 · Answer

Without using modulo operations. fabs is cheap.

double closest_dist_in_cycle(double a, double b, double cycle){
    double result = std::fabs(a - b);
    return std::min(result, cycle - result);
}

Reference:

user_7400903 · Answer

With mod being your cycle, and under the assumption that both input values are smaller than mod, you can use:

int x = std::min((mod + a - b) % mod, (mod - a + b) % mod);