Performance on SIMD architectures of auto-tuned programs for matrix multiplication

The amount of numerical computations in scientific programs is ever increasing. Hence in recent years, a growing interest has emerged in dynamically adapting the precision of floating-point computations to balance performance and accuracy. We focus here on iterative routines. For that purpose, a tool was recently introduced, which enables such precision adaptation at the iteration level, leveraging multiple-precision computations and delta-debugging techniques, in order to produce a set of possible adaptations. The study presented in this article extends the exploration initiated by the aforementioned tool. For doing this, we developed a new tool to apply these adaptations to the input C program, allowing next to examine the performance characteristics of the output program. Leveraging SIMD microarchitectures, we investigate the potential for enhancing the performances delivered by this approach on the execution of precision-adapted iterative routines. By benchmarking against non-optimized versions, we assess the speedup achieved across a spectrum of the matrix multiplication program, and we illustrate how our framework of precision adaptation allows for achieving significant speedups on matrix multiplication, varying according to the accuracy threshold.