Towards a High-Performance Tensor Algebra Package for Accelerators

Marc Baboulin (1, 2) , Veselin Dobrev (3) , Jack Dongarra (4) , Christopher Earl (3) , Joel Falcou (1, 2) , Azzam Haidar (4) , Ian Karlin (3) , Tzanio Kolev (3) , Ian Masliah (1, 2) , Stanimire Tomov (4)

1 LRI - Laboratoire de Recherche en Informatique
2 POSTALE - Performance Optimization by Software Transformation and Algorithms & Librairies Enhancement
3 LLNL - Lawrence Livermore National Laboratory
4 ICL - Innovative Computing Laboratory [Knoxville]

Numerous important applications, e.g., high-order FEM simulations, can be expressed through tensors. Examples are computation of FE matrices and SpMV products expressed as generalized tensor contractions. Contractions by the first index can often be represented as tensor index reordering plus gemm, which is a key factor to achieve high-performance. We present ongoing work on the design of a high-performance package in MAGMA for Tensor algebra that includes techniques to organize tensor contractions, data storage, and parametrization related to batched execution of large number of small tensor contractions. We apply auto-tuning and code generation techniques to provide an architecture-aware, user-friendly interface.

Domaines: Analyse numérique [cs.NA]; Calcul parallèle, distribué et partagé [cs.DC]

Marc Baboulin, Veselin Dobrev, Jack Dongarra, Christopher Earl, Joel Falcou, et al.. Towards a High-Performance Tensor Algebra Package for Accelerators. Smoky Mountains Computational Sciences and Engineering Conference (SMC 2015), Aug 2015, Gatlinburg, United States. , 2015. ⟨hal-01231234⟩