Dense Matrix Computations on NUMA Architectures with Distance-Aware Work Stealing

Rabab Al-Omairy, Guillermo Miranda, Hatem Ltaief, Rosa M. Badia, Xavier Martorell, Jesus Labarta, David Keyes


We employ the dynamic runtime system OmpSs to decrease the overhead of data motion in the now ubiquitous non-uniform memory access (NUMA) high concurrency environment of multicore processors. The dense numerical linear algebra algorithms of Cholesky factorization and symmetric matrix inversion are employed as representative benchmarks. Work stealing occurs within an innovative NUMA-aware scheduling policy to reduce data movement between NUMA nodes. The overall approach achieves separation of concerns by abstracting the complexity of the hardware from the end users so that high productivity can be achieved. Performance results on a large NUMA system outperform the state-of-the-art existing implementations up to a two fold speedup for the Cholesky factorization, as well as the symmetric matrix inversion, while the OmpSs-enabled code maintains strong similarity to its original sequential version.

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