Fine-grained floating-point precision analysis

Abstract

Floating-point computation is ubiquitous in high-performance scientific computing, but rounding error can compromise the results of extended calculations, especially at large scales. In this paper, we present new techniques that use binary instrumentation and modification to do fine-grained floating-point precision analysis, simulating any level of precision less than or equal to the precision of the original program. These techniques have an average of 40–70% lower overhead and provide more fine-grained insights into a program’s sensitivity than previous mixed-precision analyses. We also present a novel histogram-based visualization of a program’s floating-point precision sensitivity, as well as an incremental search technique that allows developers to incrementally trade off analysis time for detail, including the ability to restart analyses from where they left off. We present results from several case studies and experiments that show the efficacy of these techniques. Using our tool and its novel visualization, application developers can more quickly determine for specific data sets whether their application could be run using fewer double precision variables, saving both time and memory space.