Empirical Performance-Model Driven Data Layout Optimization

Empirical optimizers like ATLAS have been very effective in optimizing computational kernels in libraries. The best choice of parameters such as tile size and degree of loop unrolling is determined by executing different versions of the computation. In contrast, optimizing compilers use a model-driven approach to program transformation. While the model-driven approach of optimizing compilers is generally orders of magnitude faster than ATLAS-like library generators, its effectiveness can be limited by the accuracy of the performance models used. Very often, simplified abstractions such as reuse distance are used instead of more accurate metrics like cache miss cost, in order to make modeldriven compiler optimization feasible. In this paper, we describe an approach, in which a class of computations is modeled in terms of its constituent operations that are empirically measured. The empirical measurement of the constituent operations allows modeling of the overall execution time of the computation. The performance model with empirically determined cost components is used to perform data layout optimization in the context of the Tensor Contraction Engine, a compiler for a high-level domain-specific language for expressing computational models in quantum chemistry. This may be viewed as an example of the telescoping language approach to optimizing a sequence of library calls using semantic information about the performance properties of the library routines. The effectiveness of the approach is demonstrated through experimental measurements on some representative computations from quantum chemistry.