Author:

Abstract:

False dependences are caused by the reuse of memory to store different data. These false dependences severely constrain the schedule of statement instances, effectively serializing successive accesses to the same memory location. Several array expansion techniques have been proposed to eliminate some or all of these false dependences, enabling more reorderings of statement instances during loop nest transformations. However, array expansion is only relevant when complemented with a storage mapping optimization step, typically taking advantage of the fixed schedule set in earlier phases of the compilation, folding successive values into a compact set of contracted arrays. Furthermore, array expansion can result in memory footprint and locality damages that may not be recoverable through storage mapping optimization when intermediate transformation steps have abused the freedom offered by the removal of false dependences. Array expansion and storage mapping optimization are also complex procedures not found in most compilers, and the latter is moreover performed using suboptimal heuristics (particularly in the multi-array case). Finally, array expansion may not remove all false dependences when considering data-dependent control and access patterns. For all these reasons, it is desirable to explore alternatives to array expansion as a means to avoid the spurious serialization effect of false dependences. This serialization is unnecessary in general, as semantics preservation in presence of memory reuse only requires the absence of interference among live-ranges, an unordered constraint compatible with the their commutation. We present a technique to deal with memory reuse without serializing successive uses of memory, but also without increasing memory requirements or preventing important loop transformations such as loop distribution. The technique is generic, fine-grained (instancewise) and extends two recently proposed, more restrictive approaches. It has been systematically tested in PPCG and shown to be essential to the parallelizing compilation of a variety of loop nests, including large pencil programs with many scalar variables.