LU, QR and Cholesky factorizations using vector capabilities of GPUs

TitleLU, QR and Cholesky factorizations using vector capabilities of GPUs
Publication TypeJournal Article
Year of Publication2008
AuthorsVolkov, V., & Demmel J.
JournalTechnical Report No. UCB/EECS-2008-49
Date Published05/2008
Abstract

We present performance results for dense linear algebra using the 8-series NVIDIA GPUs. Our matrix-matrix multiply routine (GEMM) runs 60% faster than the vendor implementation in CUBLAS 1.1 and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80–90% of the peak GEMM rate. Our parallel LU running on two GPUs achieves up to ~300 Gflop/s. These results are accomplished by challenging the accepted view of the GPU architecture and programming guidelines. We argue that modern GPUs should be viewed as multithreaded multicore vector units. We exploit blocking similarly to vector computers and heterogeneity of the system by computing both on GPU and CPU. This study includes detailed benchmarking of the GPU memory system that reveals sizes and latencies of caches and TLB. We present a couple of algorithmic optimizations aimed at increasing parallelism and regularity in the problem that provide us with slightly higher performance.

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