Multiplicative linear congruential generators (MLCG) using 32-bit integers have a period of at most . This many random numbers can be generated in seconds on a modern workstation.

Period must be much greater than the number of random numbers used in the simulation, or else the results can be incorrect. Modest Ising model simulation, lattice, sweeps, uses random numbers.

Using 64-bit words, or combining two 32-bit MLCGs, can give periods # nanoseconds per year. These are adequate for largest simulations done today (Gigaflop-year). Other generators (lagged Fibonacci, etc.) have even longer periods. These or combined 64-bit MLCGs will be required for Teraflop-year simulations.

Random number generators will be the subject of a later lecture.

Paul Coddington, Northeast Parallel Architectures Center at Syracuse University, paulc@npac.syr.edu