Scaling LAPACK panel operations using parallel cache assignment

Abstract

In LAPACK many matrix operations are cast as block algorithms which iteratively process a panel using an unblocked algorithm and then update a remainder matrix using the high performance Level 3 BLAS. The Level 3 BLAS have excellent scaling, but panel processing tends to be bus bound, and thus scales with bus speed rather than the number of processors ( p ). Amdahl's law therefore ensures that as p grows, the panel computation will become the dominant cost of these LAPACK routines. Our contribution is a novel parallel cache assignment approach to the panel factorization which we show scales well with p . We apply this general approach to the QR, QL, RQ, LQ and LU panel factorizations. We show results for two commodity platforms: an 8-core Intel platform and a 32-core AMD platform. For both platforms and all twenty implementations (five factorizations each of which is available in 4 types), we present results that demonstrate that our approach yields significant speedup over the existing state of the art.