Is search really necessary to generate high-performance BLAS?

A key step in program optimization is the estimation of optimal values for parameters such as tile sizes and loop unrolling factors. Traditional compilers use simple analytical models to compute these values. In contrast, library generators like ATLAS use global search over the space of parameter values by generating programs with many different combinations of parameter values, and running them on the actual hardware to determine which values give the best performance. It is widely believed that traditional model-driven optimization cannot compete with search-based empirical optimization because tractable analytical models cannot capture all the complexities of modern high-performance architectures, but few quantitative comparisons have been done to date. To make such a comparison, we replaced the global search engine in ATLAS with a model-driven optimization engine and measured the relative performance of the code produced by the two systems on a variety of architectures. Since both systems use the same code generator, any differences in the performance of the code produced by the two systems can come only from differences in optimization parameter values. Our experiments show that model-driven optimization can be surprisingly effective and can generate code with performance comparable to that of code generated by ATLAS using global search.