Enhancing Parallelism by Removing Cyclic Data Dependencies

The parallel execution of loop iterations often is inhibited by recurrence relations on scalar variables. Examples are the use of induction variables and recursive functions. Due to the cyclic dependence between the iterations, these loops have to be executed sequentially. A method is presented to convert a family of coupled linear recurrence relations into explicit functions of a loop index. When the cyclic dependency is the only factor preventing a parallel execution, the conversion eeectively removes the dependency and allows the loop to be executed in parallel. The technique is based on constructing and solving a set of coupled linear diierence equations at compile-time. The method is general for an arbitrary number of coupled scalar variables and can be implemented by a straightforward algorithm. Results show that the parallelism of several sequential EISPACK do-loops is signiicantly enhanced by the converting them into do-all loops.