The Foundations of Thread-level Parallelism in the SuperMatrix Runtime System∗

In this paper, we describe the interface and implementation of the SuperMatrix runtime system. SuperMatrix exploits parallelism from matrix computations by mapping a linear algebra algorithm to a directed acyclic graph (DAG). We give detailed descriptions of how to dynamically construct a DAG where tasks consisting of matrix operations represent the nodes and data dependencies between tasks represent the edges of the graph. We show the algorithm that, given a DAG as input, dispatches and schedules tasks to threads. Different scheduling heuristics and optimizations implemented as part of SuperMatrix are discussed, demonstrating the flexibility and portability that results from the separation of concerns. Using this flexible framework, we compare several scheduling algorithms, such as work stealing, that optimize for either load balancing or data locality, and we demonstrate that a relatively simple, single queue implementation provides exceptional performance while also allowing for the widest flexibility for further enhancements. Performance results from a sixteen core machine are provided.