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## Section: New Results

### Design of Experiments

Performance engineering of scientific HPC applications requires to measure repeatedly the performance of applications or of computation kernels, which consume a large amount of time and resources. It is essential to design experiments so as to reduce this cost as much as possible. Our contribution along this axis is twofold: (1) the investigation sound exploration techniques and (2) the control of experiments to ensure the measurements are as representative as possible of real workload.

Writing, porting, and optimizing scientific applications makes autotuning techniques fundamental to lower the cost of leveraging the improvements on execution time and power consumption provided by the latest software and hardware platforms. Despite the need for economy, most autotuning techniques still require large budgets of costly experimental measurements to provide good results, while rarely providing exploitable knowledge after optimization. In [16], we investigate the use of Design of Experiments to propose a user-transparent autotuning technique that operates under tight budget constraints by significantly reducing the measurements needed to find good optimizations. Our approach enables users to make informed decisions on which optimizations to pursue and when to stop. We present an experimental evaluation of our approach and show it is capable of leveraging user decisions to find the best global configuration of a GPU Laplacian kernel using half of the measurement budget used by other common autotuning techniques. We show that our approach is also capable of finding speedups of up to $50×$, compared to gcc's -O3, for some kernels from the SPAPT benchmark suite, using up to $10×$ fewer measurements than random sampling. Although the results are very encouraging, our approach relies on assumptions on the geometry of the search space that are difficult to test in very large dimension. We are thus currently pursuing this line of research using non parametric approaches based on gaussian process regression, space filling designs and iteratively selecting configurations that yield the best expected improvement.

Our second contribution is related to the control of measurements. In [40], we relate a surprising observation on the performance of the highly optimized and regular DGEMM function on modern processors. The DGEMM function is a widely used implementation of the matrix product. While the asymptotic complexity of the algorithm only depends on the sizes of the matrices, we show that the performance is significantly impacted by the matrices content. Although it would be expected that special values like 1 or 0 may yield to specific behevior, we show that arbitrary constant values are no different and that random values incur a significant performance drop. Our experiments show that this may be due to bit flips in the CPU causing an energy consumption overhead. Such phenomenon reminds the importance of thoroughly randomizing every single parameter of experiments to avoid bias toward specific behavior.