AN EFFICIENT ALGORITHM FOR TESTING THE QUALITY OF THE OUTPUT OF RANDOM NUMBER GENERATORS

This paper presents an efficient method and a computer program utilizing Walsh functions to test the quality of the output of a random number generator. The computer program is written in ZBasic and consists of six segments: (1) PMMLCG RANDOM NUMBER GENERATOR FUNCTION - This segment defines the portable Prime Modulus Multiplicative Linear Congruential Generator that is used as part of the Composite Sherif Dear (CSD) Random Number Generator, which is under study and testing in this paper; (2) INITIAL VARIABLE INPUT/HEADER OUTPUT - This segment requests user input for the experiment and prepares the output file with header information; (3) CSD RANDOM NUMBER GENERATOR SAMPLES - This segment generates multiple samples of the CSD Random Number Generator each with the desired sample size. The generated values are offset by 0.5; (4) DETERMINE THE WALSH TRANSFORM - This segment determines the Walsh Transform using a Manz Sequency Ordered In-Place Algorithm for the given sample; (5) DETERMINE THE KOLMOGOROV-SMIRNOV SAMPLE STATISTIC This segment computes the Kolmogorov-Smirnov sample statistic on the scaled Walsh Transform; (6) SAMPLING COMPLETE-SUMMARIZE RESULTS This segment summarizes the results for all samples and places the results into an output file. The Walsh functions based test shows that the output of the (CDS) random number generator satisfies the criteria of good random number generators.