Transforming linear algebra libraries: From abstraction to parallelism

We have built a body of evidence which shows that, given a mathematical specification of a dense linear algebra operation to be implemented, it is possible to mechanically derive families of algorithms and subsequently to mechanically translate these algorithms into high-performing code. In this paper, we add to this evidence by showing that the algorithms can be statically analyzed and translated into directed acyclic graphs (DAGs) of coarse-grained operations that are to be performed. DAGs naturally express parallelism, which we illustrate by representing the DAGs with the G graphical programming language used by LabVIEW. The LabVIEW compiler and runtime execution system then exploit parallelism from the resulting code. Respectable speedup on a sixteen core architecture is reported.