ASYNC Loop Constructs for Relaxed Synchronization

Conventional iterative solvers for partial differential equations impose strict data dependencies between each solution point and its neighbors. When implemented in OpenMP, they repeatedly execute barrier synchronization in each iterative step to ensure that data dependencies are strictly satisfied. We propose new parallel annotations to support an asynchronous computation model for iterative solvers. ASYNC DO annotates a loop whose iterations can be executed by multiple processors, as OpenMP parallel DO loops in Fortran (or parallel for loops in C), but it does not require barrier synchronization. ASYNC REDUCTION annotates a loop which performs parallel reduction operations but uses a relaxed tree barrier, instead of the conventional barrier, to synchronize the processors. When a number of ASYNC DO and ASYNC REDUCTION loops are embedded in an iterative loop annotated by ASYNC REGION, the iterative solver allows each data point to be updated using the value of its neighbors which may not be the most current, instead of forcing the processor to wait for the new value to arrive. We discuss how the compiler can transform an ASYNC REGION (with embedded ASYNC DO and ASYNC REDUCTION) into an OpenMP parallel section with relaxed synchronization. We present experimental results to show the benefit of using ASYNC loop constructs in 2D and 3D multigrid methods as well as an SOR-preconditioned conjugate gradient linear system solver.