Empirically Tuning LAPACK’s Blocking Factor for Increased Performance

Abstract—LAPACK (Linear Algebra PACKage) is a statically cache-blocked library, where the blocking factor (NB) is deter-mined by the service routine ILAENV. Users are encouraged to tune NB to maximize performance on their platform/BLAS (the BLAS are LAPACK’s computational engine), but in practice very few users do so (both because it is hard, and because its importance is not widely understood). In this paper we (1) Discuss our empirical tuning framework for discovering good NB settings, (2) quantify the performance boost that tuning NB can achieve on several LAPACK routines across multiple architectures and BLAS implementations, (3) compare the best performance of LAPACK’s statically blocked routines against state of the art recursively blocked routines, and vendor-optimized LAPACK implementations, to see how much performance loss is mandated by LAPACK’s present static blocking strategy, and finally (4) use results to determine how best to block nonsquare matrices once good square blocking factors are discovered. I