Computer performance analysis and the Pi Theorem

  • Authors:

  • Robert W. Numrich

  • Affiliations:

  • Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, USA

  • Venue:
  • Computer Science - Research and Development
  • Year:
  • 2014

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Abstract

This paper applies the Pi Theorem of dimensional analysis to a representative set of examples from computer performance analysis. It is a survey paper that takes a different look at problems involving latency, bandwidth, cache-miss ratios, and the efficiency of parallel numerical algorithms. The Pi Theorem is the fundamental tool of dimensional analysis, and it applies to problems in computer performance analysis just as well as it does to problems in other sciences. Applying it requires the definition of a system of measurement appropriate for computer performance analysis with a consistent set of units and dimensions. Then a straightforward recipe for each specific problem reduces the number of independent variables to a smaller number of dimensionless parameters. Two machines with the same values of these parameters are self-similar and behave the same way. Self-similarity relationships emphasize how machines are the same rather than how they are different. The Pi Theorem is simple to state and simple to prove, using purely algebraic methods, but the results that follow from it are often surprising and not simple at all. The results are often unexpected but they almost always reveal something new about the problem at hand.