Analytical processor performance modeling has received increased interest over the past few years. There are basically two approaches to constructing an analytical model: mechanistic modeling and empirical modeling. Mechanistic modeling builds up an analytical model starting from a basic understanding of the underlying system — white-box approach — whereas empirical modeling constructs an analytical model through statistical inference and machine learning from training data, e.g., regression modeling or neural networks — black-box approach. While an empirical model is typically easier to construct, it provides less insight than a mechanistic model. This paper bridges the gap between mechanistic and empirical modeling through hybrid mechanistic-empirical modeling (gray-box modeling). Starting from a generic, parameterized performance model that is inspired by mechanistic modeling, regression modeling infers the unknown parameters, alike empirical modeling. Mechanisticempirical models combine the best of both worlds: they provide insight (like mechanistic models) while being easy to construct (like empirical models). We build mechanistic-empirical performance models for three commercial processor cores, the Intel Pentium 4, Core 2 and Core i7, using SPEC CPU2000 and CPU2006, and report average prediction errors between 9 % and 13%. In addition, we demonstrate that the mechanistic-empirical model is more robust and less subject to overfitting than purely empirical models. A key feature of the proposed mechanistic-empirical model is that it enables constructing CPI stacks on real hardware, which provide insight in commercial processor performance and which offer opportunities for software and hardware optimization and analysis.
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