Uniform Random Number Generators
M. Donald MacLaren, George Marsaglia · Journal of the ACM · 1965
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.TwO alternative generating methods are described, one of them using a table of uniform numbers, the other one combining two congruential generators.Both of these methods passed the tests, whereas the conventional multiplieative and mixed congruential methods did not.