UNIFORM RANDOM NUMBER GENERATORS FOR SUPERCOMPUTERS

RICHARD P. BRENT

Abstract

We consider the requirements for uniform pseudo-random number generators on modern vector and parallel supercomputers, consider the pros and cons of various classes of methods, and outline what is currently available. We propose a class of random number generators which have good statistical properties and can be implemented efficiently on vector processors and parallel machines. A good method for initialization of these generators is described, and an implementation on a Fujitsu VP 2200/10 vector processor is discussed.

Comments

Only the Abstract is given here. The full paper appeared as [1]. Related theory is given in [2]. For work on normally distributed random numbers, see [3].

References

1. R. P. Brent, “Uniform random number generators for supercomputers” Proc. Fifth Australian Supercomputer Conference, Melbourne, December 1992, 95–104. rpb132.

2. R. P. Brent, “On the periods of generalized Fibonacci recurrences”, Mathematics of Computation, to appear. Available as Report TR-CS-92-03, Computer Sciences Laboratory, ANU, March 1992; and Report CMA-MR8-92/SMS-31-92, Centre for Mathematics and its Applications, April 1992, 11 pp. rpb133.

3. R. P. Brent, Fast Normal Random Number Generators for Vector Processors, Technical Report TR-CS-93-04, Computer Sciences Laboratory, Australian National University, March 1993, 7 pp. rpb141.

Computer Sciences Laboratory, Australian National University, Canberra, ACT 0200 E-mail address: rpb@cslab.anu.edu.au

1991 Mathematics Subject Classification. Primary 65C10; Secondary 65Y05, 65Y10. Key words and phrases. Random numbers, vector processor, uniform distribution, parallel computa-

tion, pipelining, linear recurrence, generalized Fibonacci generator, additive generator.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1992, 5ASC Organising Committee. Comments \begin{matrix}c \\ ◯ \end{matrix} 1993, R. P. Brent. rpb132a typeset using AMS-L^{A}TEX