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arXiv · 1211.3056

GPU-accelerated generation of correctly-rounded elementary functions

Pierre Fortin·Mourad Gouicem·Stef Graillat
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Abstract

The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such computations, namely Lefe'vre algorithm on Graphics Processing Units (GPUs) which are massively parallel architectures with a partial SIMD execution (Single Instruction Multiple Data). We first propose an analysis of the Lef\`evre hard-to-round argument search using the concept of continued fractions. We then propose a new parallel search algorithm much more efficient on GPU thanks to its more regular control flow. We also present an efficient hybrid CPU-GPU deployment of the generation of the polynomial approximations required in Lef\`evre algorithm. In the end, we manage to obtain overall speedups up to 53.4x on one GPU over a sequential CPU execution, and up to 7.1x over a multi-core CPU, which enable a much faster solving of the Table Maker's Dilemma for the double precision format.

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Pierre Fortin, Mourad Gouicem, Stef Graillat. 2012-11-13. GPU-accelerated generation of correctly-rounded elementary functions. https://arxiv.org/abs/1211.3056

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