Benchmarking GPUs to tune dense linear algebra

TLDR

The study challenges conventional GPU architecture views, arguing that modern GPUs should be seen as multithreaded multicore vector units. They use blocking strategies like vector computers, leverage GPU–CPU heterogeneity, and apply algorithmic optimizations to boost parallelism and regularity. Benchmarking shows GEMM up to 60 % faster than vendor, LU/QR/Cholesky reaching 80–90 % of peak GEMM, parallel LU on two GPUs achieving ~540 Gflop/s, and detailed GPU memory profiling uncovers cache and TLB sizes and latencies.

Abstract

We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrix-matrix multiply routine (GEMM) runs up to 60% faster than the vendor's implementation 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 ~540 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.