Satisfying your dependencies with SuperMatrix

SuperMatrix out-of-order scheduling leverages high-level abstractions and straightforward data dependency analysis to provide a general-purpose mechanism for obtaining parallelism from a wide range of linear algebra operations. Viewing submatrices as the fundamental unit of data allows us to decompose operations into component tasks that operate upon these submatrices. Data dependencies between tasks are determined by observing the submatrix blocks read from and written to by each task. We employ the same dynamic out-of-order execution techniques traditionally exploited by modern superscalar micro-architectures to execute tasks in parallel according to data dependencies within linear algebra operations. This paper provides a general explanation of the SuperMatrix implementation followed by empirical evidence of its broad applicability through performance results of several standard linear algebra operations on a wide range of computer architectures.