Booleans are the most basic values in computing. Machines, however, store Boolean values in larger compounds such as bytes or integers due to limitations in addressing memory locations. For individual values the relative waste of memory is huge, but the absolute waste is negligible. The latter radically changes if large numbers of Boolean values are processed in (multidimensional) arrays. Most programming languages, however, only provide sparse implementations of Boolean arrays. Thus, they waste large quantities of memory and, potentially, make poor use of cache hierarchies.
In the context of the functional data-parallel array programming language SAC we investigate dense implementations of Boolean arrays and compare their performance with traditional sparse implementations. A particular challenge arises in data-parallel execution on today's shared memory multi-core architectures: scheduling of loops over Boolean arrays is unaware of the non-standard addressing of dense Boolean arrays. We discuss our proposed solution and report on experiments analysing the impact of the runtime representation of Boolean arrays both on sequential performance as well as on scalability using up to 32 cores of a large ccNUMA multi-core system.
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