Optimization for performance and energy for batched matrix computations on GPUs

Azzam Haidar, Tingxing Dong, Piotr Luszczek, Stanimire Tomov, Jack Dongarra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

As modern hardware keeps evolving, an increasingly effective approach to develop energy efficient and high-performance solvers is to design them to work on many small size in-dependent problems. Many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs. We describe the development of the main one-sided factorizations that work for a set of small dense matrices in parallel, and we illustrate our techniques on the LU and Cholesky factorizations. We refer to this mode of operation as a batched factorization. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-only execution. The goal of avoiding multicore CPU use, e.g., as in the hybrid CPU-GPU algorithms, is to exclusively benefit from the GPU's significantly higher energy efficiency, as well as from the removal of the costly CPU-to-GPU communications. Furthermore, we do not use a single symmetric multiprocessor (on the GPU) to factorize a single problem at a time. We illustrate how our performance analysis and the use of profiling and tracing tools guided the development and optimization of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library (when using two sockets of Intel Sandy Bridge CPUs). Compared to a batched LU factorization featured in the CUBLAS library for GPUs, we achieved up to 2:5 speedup on the K40 GPU.

Original languageEnglish
Title of host publicationACM International Conference Proceeding Series
EditorsXiang Gong
PublisherAssociation for Computing Machinery
Pages59-69
Number of pages11
ISBN (Electronic)9781450334075
DOIs
StatePublished - Feb 7 2015
Event8th Annual Workshop on General Purpose Processing using Graphics Processing Unit, GPGPU 2015 - San Francisco, United States
Duration: Feb 7 2015 → …

Publication series

NameACM International Conference Proceeding Series
Volume2015-February

Conference

Conference8th Annual Workshop on General Purpose Processing using Graphics Processing Unit, GPGPU 2015
Country/TerritoryUnited States
CitySan Francisco
Period02/7/15 → …

Funding

Keywords

  • Batched factorization
  • Hardware accelerators
  • Numerical linear algebra
  • Numerical software libraries
  • One-sided factorization algorithms

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