Arbitrarily Parallelizable Code: A Model of Computation Evaluated on a Message-Passing Many-Core System

Abstract

The number of processing elements per solution is growing. From embedded devices now employing (often heterogeneous) multi-core processors, across many-core scientific computing platforms, to distributed systems comprising thousands of interconnected processors, parallel programming of one form or another is now the norm. Understanding how to efficiently parallelize code, however, is still an open problem, and the difficulties are exacerbated across heterogeneous processing, and especially at run time, when it is sometimes desirable to change the parallelization strategy to meet non-functional requirements (e.g., load balancing and power consumption). In this article, we investigate the use of a programming model based on series-parallel partial orders: computations are expressed as directed graphs that expose parallelization opportunities and necessary sequencing by construction. This programming model is suitable as an intermediate representation for higher-level languages. We then describe a model of computation for such a programming model that maps such graphs into a stack-based structure more amenable to hardware processing. We describe the formal small-step semantics for this model of computation and use this formal description to show that the model can be arbitrarily parallelized, at compile and runtime, with correct execution guaranteed by design. We empirically support this claim and evaluate parallelization benefits using a prototype open-source compiler, targeting a message-passing many-core simulation. We empirically verify the correctness of arbitrary parallelization, supporting the validity of our formal semantics, analyze the distribution of operations within cores to understand the implementation impact of the paradigm, and assess execution time improvements when five micro-benchmarks are automatically and randomly parallelized across 2 × 2 and 4 × 4 multi-core configurations, resulting in execution time decrease by up to 95% in the best case.