Multilevel Approaches to Fine Tune Performance of Linear Algebra Libraries

摘要

We propose a multilevel methodology to improve the performance of parallel codes whose run time increases at a faster rate than the increase in workload. We have derived the conditions under which the proposed methodology improves performance for a simple parallel computing model. Formulas to predict the amount of performance improvement that is attainable are also derived for this simple computing model. The effectiveness of the proposed strategy is demonstrated by applying it to the highly optimized BLAS (Basic Linear Algebra Subprograms) routines cblas_dgemm, cblas_dtrmm and cblas_dsymm from the Intel MKL (Math Kernel Library) on the Intel KNL (Knights Landing) platform. We are able to reduce the run time of MKL cblas_dgemm by 20%, cblas_dtrmm by 15%, and cblas_dsymm by 50% on double-precision matrices of size 16Kx16K. Further, our performance prediction formulas are demonstrated to be accurate on this platform.