Scheduling loops with partial loop-carried dependencies

This paper deals with task scheduling, where each task is one particular iteration of a DO loop with partial loop-carried dependencies. Independent iterations of such loops can be scheduled in an order different from the one of classical serial execution, so as to increase program performance. The approach that we present is based both on the use of a directive added to the High Performance Fortran (HPF2) language, which specifies the dependencies between iterations, and on inspector/executor support, implemented in the C oLUMBO library, which builds the task graph and schedules tasks associated with iterations. We validate our approach by showing results achieved on an IBM SP2 for a sparse Cholesky factorization algorithm applied to real problems.