### Some New Results in Pseudo-Random Number GenerationSome New Results in Pseudo-Random Number Generation

Access Restriction
Subscribed

 Author Van Gelder, A. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1967 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia (M&M).The main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by M&M, none gave satisfactory results.The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of $\textit{n}-tuples$ of consecutively generated numbers. In any Monte Carlo or simulation problem where $\textit{n}$ supposedly independent random numbers are required at each step, this behavior is likely to be important.Finally, since the tests presented here differ in certain details from those of M&M, some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly. main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia (M&M).The main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by M&M, none gave satisfactory results.The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of $\textit{n}-tuples$ of consecutively generated numbers. In any Monte Carlo or simulation problem where $\textit{n}$ supposedly independent random numbers are required at each step, this behavior is likely to be important.Finally, since the tests presented here differ in certain details from those of M&M, some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly. none gave satisfactory results.The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of $\textit{n}-tuples$ of consecutively generated numbers. In any Monte Carlo or simulation problem where $\textit{n}$ supposedly independent random numbers are required at each step, this behavior is likely to be important.Finally, since the tests presented here differ in certain details from those of Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia (M&M).The main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by M&M, none gave satisfactory results.The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of $\textit{n}-tuples$ of consecutively generated numbers. In any Monte Carlo or simulation problem where $\textit{n}$ supposedly independent random numbers are required at each step, this behavior is likely to be important.Finally, since the tests presented here differ in certain details from those of M&M, some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly. some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1967-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 14 Issue Number 4 Page Count 8 Starting Page 785 Ending Page 792

#### Open content in new tab

Source: ACM Digital Library