Uniformity of random numbers taken modulo N

Question

One common way of choosing a random number in [0, n) is to take the result of rand() modulo n: rand() % n. However, even if the r

Answer 1

There are two problems with using remainder (% is not a "modulo" operator in C) to a uniform random number over a reduced range. First is that there is a slight bias toward smaller numbers (mentioned above) and second that typical PRNGs tend to be less random in the low order bits. I seem to recall that from Knuth (The Art of Computer Programming, Vol II, Seminumerical Algorithms) along with the claim that (after translating from MIX to C) rand()%2 is a poor source of random single bits. It's better to pick (rand() > RAND_MAX/2) (or test a high-order bit, if RAND_MAX is nearly a power of 2.)

The remainder should be good enough casual use on small intervals. Avoid it for simulations. Actually, avoid rand() altogether for large simulations or "Monte Carlo" computations. Implementations tend to have a period on the order of 2^32 or less. It's not hard to exceed 4 billion trials on a 2+ GHz processor.