Speculative parallelization of partial reduction variables

Abstract

Reduction variables are an important class of cross-thread dependence that can be parallelized by exploiting the associativity and commutativity of their operation. In this paper, we define a class of shared variables called partial reduction variables (PRV). These variables either cannot be proven to be reductions or they violate the requirements of a reduction variable in some way. We describe an algorithm that allows the compiler to detect PRVs, and we also discuss the necessary requirements to parallelize detected PRVs. Based on these requirements, we propose an implementation in a TLS system to parallelize PRVs that works by a combination of techniques at compile time and in the hardware. The compiler transforms the variable under the assumption that the reduction-like behavior proven statically will hold true at runtime. However, if a thread reads or updates the shared variable as a result of an alias or unlikely control path, a lightweight hardware mechanism will detect the access and synchronize it to ensure correct execution. We implement our compiler analysis and transformation in GCC, and analyze its potential on the SPEC CPU 2000 benchmarks. We find that supporting PRVs provides up to 46% performance gain over a highly optimized TLS system and on average 10.7% performance improvement.

A framework for enhancing data reuse via associative reordering

“…Multidimensional retiming has been previously studied in the literature, mostly for the purpose of parallelism exposure [6,16,36,45] or to fix transformations for legality [30,41]. We take a different approach, seeking a characterization of different data reuse patterns and register pressure when applying arbitrary multidimensional retiming.…”

Discovery and exploitation of general reductions: A constraint based approach

“…The authors of [20] present an approach for the parallelization of a wide class of scalar reductions. They start from the observation that many reductions in real benchmark programs are not detected by current static analysis approaches.…”

“…Early work focused on well structured Fortran and paid little attention to automatic compiler-based detection. More recent work has attempted to find reductions in more complex C code with partial reduction variables [20]. This is based on update chains in the dependence graph and requires hardware speculation support, but is unable to detect histogram reductions.…”

Improving Transactional Memory Performance for Irregular Applications

“…A partial reduction occurs when some locations of A[] are read or written outside the reduction sentence. In this case, the reduction condition is fulfilled only in a portion of the reduction variable [4].…”