The term \( [N_{i-1}/q]r \) is always smaller or equal \( N_{i-1}(r/q) \) and with \( r < q \) we obtain always a number smaller than \( N_{i-1} \), which is smaller than \( M \). And since the number \( N_{i-1}\mathrm{MOD} (q) \) is between zero and \( q-1 \) then \( a(N_{i-1}\mathrm{MOD} (q)) < aq \). Combined with our definition of \( q=[M/a] \) ensures that this term is also smaller than \( M \) meaning that both terms fit into a 32-bit signed integer. None of these two terms can be negative, but their difference could. The algorithm below adds \( M \) if their difference is negative. Note that the program uses the bitwise \( \oplus \) operator to generate the starting point for each generation of a random number. The period of \( ran0 \) is \( \sim 2.1\times 10^{9} \). A special feature of this algorithm is that is should never be called with the initial seed set to \( 0 \).