Abstract

In the approach described in this paper the performance of an application is described via a network of its building blocks. If each of the building blocks is assigned a value in the ‘performance algebra’, which turns out to be an ordered semigroup, the total performance can be obtained by applying a semigroup homomorphism. Data movement, arithmetic operations and delays (such as dispatching overhead) and their interactions can be algebraically modelled. The method can be applied to whole applications but also to operations close to the instruction level. Hockney's laws and Amdahl's law can be retrieved as well as the law of the harmonic mean. In addition, a number of inequalities for algebraic constructs are given and the relationship between a ‘machine independent’ and a ‘machine dependent’ application algebra is studied. We formulate an ‘abstract benchmarking problem’ and discuss a number of applications.

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