Optimal Distribution Assignment Placement

Dynamic data redistribution is a key technique for maintaining data locality and workload balance in data-parallel languages like HPF. On the other hand, redistributions can be very expensive and signiicantly degrade a program's performance. In this article, we present a novel and aggressive approach for avoiding unnecessary remappings by eliminating partially dead and partially redundant distribution changes. Basically, this approach evolves from extending and combining two algorithms for these optimizations achieving optimal results for sequential programs. Optimality, however, becomes more intricate by the combination. On the other hand, and in contrast to the sequential setting, the data-parallel one leads to a hierarchy of algorithms of varying power and eeciency tting a user's individual needs. The power and exibility of the new approach are demonstrated by illustrating examples. First practical experiences underline its importance and eeectivity. 1 Motivation The user-controlled distribution of data across the local memories of the processing nodes is a central feature of data-parallel languages like High Performance Fortran (HPF) 3], Fortran D 4], or Vienna Fortran 13]. A program's performance can critically depend on the distribution chosen. Dynamic data redistri-butions, e.g., in case of varying computational kernels or dynamically varying processor workloads, are thus a major means for improving the performance. On the other hand, remappings can be quite expensive as communication is required to migrate the array elements to their new owning processors. Unnecessary distribution changes can therefore signiicantly degrade a program's performance. Avoiding them is of key importance to gain eeciency. In this article we present a novel and aggressive approach for distribution assignment placement (DAP), which, in essence, works by eliminatingpartially dead and partially redundant distribution changes. Basically, this approach evolves from extending and combining two algorithms for partially dead and partially redundant assignment elimination achieving optimal results for sequential programs (cf. 7, 8]). Intuitively, the new algorithm computes beneecial insertion points for distribution assignments by means of code hoisting and sinking in-terleaved by eliminating redundant and dead code, which covers motion of invariant remappings out of loops as well. Besides the well-known second-order