Computational similarity

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Abstract
The paper enunciates the principle of computational similarity, whereby calculations with the same values for certain dimensionless ratios are said to be ‘computationally similar’ and as a consequence have the same optimum self‐speed‐up and optimum number of processors. Based on a three‐parameter description of the computer hardware, two dimensionless ratios, which are only a function of the problem size and the hardware parameters, completely determine the scaling. Contours of constant self‐speed‐up can be drawn on a two‐dimensional dimensionless universal scaling diagram (DUSD). This diagram is for a particular class of timing expressions that can be shown to represent approximately the performance of a corresponding class of computer programs or benchmarks, but it applies to all computers describable by the three hardware parameters and to all problem sizes. Thus the dimensionless ratios play a similar role in the study of computer performance, as do the Reynolds and other dimensionless numbers in fluid dynamics. This dimensional analysis of computer performance is illustrated by the case of the FFT1 benchmark from the Southampton ‘Genesis’ distributed‐memory benchmarks.