std::mersenne_twister_engine and random number generation

Question

What is the distribution (uniform, poisson, normal, etc.) that is generated if I did the below? The output appears to indicate a uniform distribution. But then, why do we ne

Answer 1

std::mt19937_64 generates a pseudo-random mutually independent sequence of long long / unsigned long long numbers. It is supposed to be uniform but I don't know the exact details of the engine, though, it is one of the best discovered engines thus far.

By taking % n you get an approximation to pseudo-random uniform distribution over integers [0, ... ,n] - but it is inherently inaccurate. Certain numbers have slightly higher chance to occur while others have slightly lower chance depending on n. E.g., since 2^64 = 18446744073709551616 so with n=10000 first 1616 values have a slightly higher chance to occur than the last 10000-1616 values. std::uniform_distribution takes care of the inaccuracy by taking a new random number in very rare cases: say, if the number is above 18446744073709550000 for n=10000 take a new number - it would work. Though, concrete details are up to implementation.