Empirical program optimizers estimate the values of key optimization parameters by generating different program versions and running them on the actual hardware to determine which values give the best performance. In contrast, conventional compilers use models of programs and machines to choose these parameters. It is widely believed that empirical optimization is more effective than model-driven optimization, but few quantitative comparisons have been done to date. To make such a comparison, we replaced the empirical optimization engine in ATLAS (a system for generating dense numerical linear algebra libraries) with a model-based optimization engine that used detailed models to estimate values for optimization parameters, and then measured the relative performance of the two systems on three different hardware platforms. Our experiments show that although model-based optimization can be surprisingly effective, useful models may have to consider not only hardware parameters but also the ability of back-end compilers to exploit hardware resources.

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Cache-oblivious algorithms have been advanced as a way of circumventing some of the difficulties of optimizing applications to take advantage of the memory hierarchy of modern microprocessors. These algorithms are based on the divide-and-conquer paradigm -each division step creates sub-problems of smaller size, and when the working set of a sub-problem fits in some level of the memory hierarchy, the computations in that sub-problem can be executed without suffering capacity misses at that level. In this way, divideand-conquer algorithms adapt automatically to all levels of the memory hierarchy; in fact, for problems like matrix multiplication, matrix transpose, and FFT, these recursive algorithms are optimal to within constant factors for some theoretical models of the memory hierarchy.An important question is the following: how well do carefully tuned cache-oblivious programs perform compared to carefully tuned cache-conscious programs for the same problem? Is there a price for obliviousness, and if so, how much performance do we lose? Somewhat surprisingly, there are few studies in the literature that have addressed this question.This paper reports the results of such a study in the domain of dense linear algebra. Our main finding is that in this domain, even highly optimized cache-oblivious programs perform significantly worse than corresponding cacheconscious programs. We provide insights into why this is so, and suggest research directions for making cache-oblivious algorithms more competitive.

Abstract. As processor complexity increases compilers tend to deliver suboptimal performance. Library generators such as ATLAS, FFTW and SPIRAL overcome this issue by empirically searching in the space of possible program versions for the one that performs the best. Empirical search can also be applied by programmers, but because they lack a tool to automate the process, programmers need to manually re-write the application in terms of several parameters whose best value will be determined by the empirical search in the target machine. In this paper, we present the design of an annotation language, meant to be used either as an intermediate representation within library generators or directly by the programmer. This language that we call X represents parameterized programs in a compact and natural way. It provides an powerful optimization framework for high performance computing.

Empirical program optimizers estimate the values of key optimization parameters by generating different program versions and running them on the actual hardware to determine which values give the best performance. In contrast, conventional compilers use models of programs and machines to choose these parameters. It is widely believed that empirical optimization is more effective than model-driven optimization, but few quantitative comparisons have been done to date. To make such a comparison, we replaced the empirical optimization engine in ATLAS (a system for generating dense numerical linear algebra libraries) with a model-based optimization engine that used detailed models to estimate values for optimization parameters, and then measured the relative performance of the two systems on three different hardware platforms. Our experiments show that although model-based optimization can be surprisingly effective, useful models may have to consider not only hardware parameters but also the ability of back-end compilers to exploit hardware resources.