article Combination Generators Share on Authors: W. H. Payne Computer Science Department, Washington State University, Pullman, WA Computer Science Department, Washington State University, Pullman, WAView Profile , F. M. Ives Mathematics and Computer Science Department, Western Washington State University, Bellingham, WA Mathematics and Computer Science Department, Western Washington State University, Bellingham, WAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 5Issue 2June 1979 pp 163–172https://doi.org/10.1145/355826.355830Online:01 June 1979Publication History 14citation2,503DownloadsMetricsTotal Citations14Total Downloads2,503Last 12 Months43Last 6 weeks8 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

article Free Access Share on Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm Author: W. H. Payne Computer Science Department, Washington State University, Pullman, WA Computer Science Department, Washington State University, Pullman, WAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 3Issue 4Dec. 1977 pp 346–358https://doi.org/10.1145/355759.355763Published:01 December 1977Publication History 18citation530DownloadsMetricsTotal Citations18Total Downloads530Last 12 Months18Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

The generalized feedback shift register pseudorandom number algorithm has several advantages over all other pseudorandom number generators. These advantages are: (1) it produces multidimensional pseudorandom numbers; (2) it has an arbitrarily long period independent of the word size of the computer on which it is implemented; (3) it is faster than other pseudorandom number generators; (4) the “same” floating-point pseudorandom number sequence is obtained on any machine, that is, the high order mantissa bits of each pseudorandom number agree on all machines— examples are given for IBM 360, Sperry-Rand-Univac 1108, Control Data 6000, and Hewlett-Packard 2100 series computers; (5) it can be coded in compiler languages (it is portable); (6) the algorithm is easily implemented in microcode and has been programmed for an Interdata computer.

Many cases arise in practice where a versatile hardwired pseudorandom number or pseudonoise generator would be extremely useful. General-purpose pseudonoise devices are not available today. We present a new sampling method, conditional bit sampling, which is suited for hardwired sampling devices because of its generality, simplicity, and accuracy. Random variables sampled from an arbitrary distribution are generated bit by bit from high- to low-order bits with the conditional bit algorithm. The result of a comparison of a uniform number to a conditional probability determines whether a bit in the sampled random number is set to one. The conditional probabilities are easily calculated for any probability distribution and must be arranged in special order. Simple Fortran programs make all necessary computations. Agreement between actual and theoretical performance of the conditional bit algorithm was excellent when sampling accuracy was evaluated for several examples of continuous and discrete densities. Sampling from empirically known, perhaps erratic-shaped, densities presents no problems. Only a small memory containing the conditional probabilities needs to be changed to alter the sampled distribution. The conditional bit algorithmic process always remains the same.

A hardwired device that produces a voltage with arbitrary amplitude distribution was constructed using a "conditional bit" algorithm to sample from an arbitrary voltage amplitude distribution. The sampling algorithm and hardware processor are independent of the distribution sampled. Only a small read-only memory ROM needs to be changed to alter the distribution sampled. It is possible to compute the accuracy of the sampled random variables from knowledge of the read-only memory contents. The sampling accuracy of the device may be arbitrarily increased by varying any of several design parameters. Our particular pseudonoise generator produced 200 000 random seven-bit variables/s. Contents of read-only memories for both a Gaussian and an arbitrary density were computed so that the maximum error was less than 2.73 percent. Both the sampling speed and accuracy of a conditional bit pseudonoise generator can be increased much in excess of our implementation.