Abstract
Remarkably fest methods for generating normal and exponential random variables have been developed for conventional computers-their average times are little more than that needed to generate the uniform variable used to produce the result. But for “supercomputers,” with vector and/or parallel operations, and particularly for massively parallel machines with hundreds or thousands of processors, average times are not the proper measure of the speed of a generating procedure. For them, the worst case applies: The next step in a simulation cannot begin until all of the processors have generated their particular normal (or exponential, gamma, Poisson, and such) variable. So, for such new or anticipated (SIMD) architectures we must consider efficient constant-time methods for generating the important random variables of Monte Carlo studies. We describe one here, for normal (Gaussian) random variables. It is, in effect, a very fast method for inverting the normal distribution function.
This is a preview of subscription content, access via your institution.
References
Black, S.C., and Kennedy, A.D. 1987. Gaussian random number generators on a Cyber-205. Computers in Physics, 1 (May/June), 59–68.
Marsaglia, G. 1961. Expressing a random variable in terms of uniform random variables. Annals Math Stat., 32: 894–898.
Marsaglia, G. 1962. Improving the polar method for generating normal random variables. Math Note D1-82-0203, Boeing Scientific Research Laboratories.
Marsaglia, G., and Tsang, W.-W. 1985. A fast, easily implemented method for sampling from decreasing or symmetric unimodal densities. SIAM J. Scientific and Statistical Computing, 5: 349–359.
Marsaglia, G., Ananthanarayanan, K., and Paul, N.J. 1976. Improvements on fast methods for generating normal random variables. Inf. Proc. Letters, 5: 123–456.
Petersen, W.P. 1988. Some vectorized random number generators for uniform, normal and Poisson distributions for CRAY X-MP. The J. Supercomputing, 1, 3 (Apr.), 327–335.
Tang, T.T.P. 1989. Table-driven implementations of the exponential function in IEEE floating-point arithmetic. ACM Trans. Math. Software, 18: 144–157.
Author information
Authors and Affiliations
Additional information
Research supported by the National Science Foundation, Grant DM880976.
Rights and permissions
About this article
Cite this article
Marsaglia, G. Normal (Gaussian) random variables for supercomputers. J Supercomput 5, 49–55 (1991). https://doi.org/10.1007/BF00155857
Issue Date:
DOI: https://doi.org/10.1007/BF00155857
Keywords
- Random variable generation
- Monte Carlo
- normal random variables
- Gaussian random variables
- supercomputers
- massively parallel systems
- exotic architectures