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

• from 1 to 5 = 4
• from 5 to 1 = 4
• from 11 to 1 = 2
• from 1 to 11 = 2

What is the most efficient way to do that?

Assuming the values are doubles.

Answer 1

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:

How would fabs(double) be implemented on x86? Is it an expensive operation?

Answer 2

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);