SuperMatrix: A Multithreaded Runtime Scheduling System for Algorithms-by-Blocks Ernie Chan Field G. Van Zee Paolo Bientinesi Enrique S. Quintana-Ort´ı Robert van de Geijn Department of Computer Science Gregorio Quintana-Ort´ı Department of Computer Sciences Duke University Departamento de Ingenier´ıa y Ciencia de The University of Texas at Austin Durham, NC 27708 Computadores Austin, Texas 78712
[email protected] Universidad Jaume I {echan,field,rvdg}@cs.utexas.edu 12.071–Castellon,´ Spain {quintana,gquintan}@icc.uji.es Abstract which led to the adoption of out-of-order execution in many com- This paper describes SuperMatrix, a runtime system that paral- puter microarchitectures [32]. For the dense linear algebra opera- lelizes matrix operations for SMP and/or multi-core architectures. tions on which we will concentrate in this paper, many researchers We use this system to demonstrate how code described at a high in the early days of distributed-memory computing recognized that level of abstraction can achieve high performance on such archi- “compute-ahead” techniques could be used to improve parallelism. tectures while completely hiding the parallelism from the library However, the coding complexity required of such an effort proved programmer. The key insight entails viewing matrices hierarchi- too great for these techniques to gain wide acceptance. In fact, cally, consisting of blocks that serve as units of data where oper- compute-ahead optimizations are still absent from linear algebra ations over those blocks are treated as units of computation. The packages such as ScaLAPACK [12] and PLAPACK [34]. implementation transparently enqueues the required operations, in- Recently, there has been a flurry of interest in reviving the idea ternally tracking dependencies, and then executes the operations of compute-ahead [1, 25, 31].