Software-defined floating-point number formats and their application to graph processing

Abstract

This paper proposes software-defined floating-point number formats for graph processing workloads, which can improve performance in irregular workloads by reducing cache misses. Efficient arithmetic on software-defined number formats is challenging, even when based on conversion to wider, hardware-supported formats. We derive efficient conversion schemes that are tuned to the IA64 and AVX512 instruction sets. We demonstrate that: (i) reduced-precision number formats can be applied to graph processing without loss of accuracy; (ii) conversion of floating-point values is possible with minimal instructions; (iii) conversions are most efficient when utilizing vectorized instruction sets, specifically on IA64 processors. Experiments on twelve real-world graph data sets demonstrate that our techniques result in speedups up to 89% for PageRank and Accelerated PageRank, and up to 35% for Single-Source Shortest Paths. The same techniques help to accelerate the integer-based maximal independent set problem by up to 262%. CCS Concepts• Computing methodologies → Vector / streaming algorithms; • Computer systems organization → Processors and memory architectures; • Mathematics of computing → Numerical analysis; • Software and its engineering → Domain specific languages.