Uniform Random Number Generators

This paper discusses the testing of methods for generating uniform mlml)crs in a computer--the commonly used multiplicative and mixed congruential generators as well ks two new methods. Tests proposed here are more stringent than those usually applied, because ~he usual tests for randomness have passed severa:l of the commonly used procedures which subsequently gave poor results in actual Monte Carlo calculations. The princi-pal difl!eulty seems to be that certain simple functions of n-tuples of uniform random mlmbers do not have the distribution that probability theory predicts.