Compound cubic congruential pseudorandom numbers (Q1365542)

This paper is concerned with a simple compound cubic congruential method for uniform pseudorandom number generation. The compound cubic congruential method is given in the following form: \(y_{n+1}^{(i)}\equiv a_ib_i^{-2}(y_n^{(i)}-c_i)^3+b_i+c_i\pmod{p_i},\;x_n^{(i)}=y_n^{(i)}/p_i,\;x_n\equiv x_n^{(1)}+\cdots+x_n^{(r)}\pmod 1,\;n\geq 0\) with a suitable integer \(p_i\) satisfying \(p_i\equiv 5\pmod 6,\;(i=1,\cdots,r)\) and integers \(a_i,b_i\) and \(c_i\) chosen in \(\{0,1,\cdots,p_i-1\}\), or in a corresponding integrated way. Following some auxiliary results, a theorem on an upper bound for the discrepancy, a measure of independence property of successive compound cubic congruential pseudorandom numbers, is established and discussed. Then a concrete example of a compound cubic congruential pseudorandom number generator is presented.