COMPUTATIONAL SIMILARITY (REPRINTED FROM CONCURRENCY PRACTICE AND EXPERIENCE VOL 7, PG 147-166, 1995)

This paper enunciates the principle of Computational Similarity, where by calculations with the same values for certain dimension less ratios are said to be ''computationally similar'' and as a consequence have the same optimum self-speedup and optimum number of processors. Based on a three-parameter description of the computer hardware, two dimensi onless ratios, which are only a function of the problem size and the h ardware parameters, completely determine the scaling. Contours of cons tant self-speedup can be drawn on a two-dimensional dimensionless Univ ersal Scaling Diagram (DUSD). This diagram is for a particular class o f timing expressions that can be shown to represent approximately the performance of a corresponding class of computer programs or benchmark s, but it applies to all computers describable by the three hardware p arameters and to all problem sizes. Thus the dimensionless ratios play a similar role in the study of computer performance as do the Reynold s and other dimensionless numbers in fluid dynamics. This dimensional analysis of computer performance is illustrated by the case of the FFT 1 benchmark from the Southampton ''Genesis'' distributed-memory Benchm arks.