A study of 128-bit multipliers for congruential pseudorandom number generators Original Research Article

A study was conducted of multipliers for 128-bit congruential pseudorandom number generators. Extensive analysis and testing resulted in the identification of over 2000 good multipliers of the form A=5k mod 2128, where k is a prime number. The integer lattice structure from any single multiplier is so fine that it is not visible when REAL*8 values are returned in up to four dimensions, or REAL*4 values in seven dimensions. The multipliers are designed to be used in sets, and are suitable for use in massively-parallel computation.