GPU-accelerated generation of correctly-rounded elementary functions

Pierre Fortin, Mourad Gouicem, Stef Graillat
UPMC Univ Paris 06 and CNRS UMR 7606, LIP6
UPMC University, 2013


   title={GPU-accelerated generation of correctly-rounded elementary functions},

   author={Fortin, Pierre and Gouicem, Mourad and Graillat, Stef},



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The IEEE 754-2008 standard recommends the correct rounding of 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 Lefevre algorithm, on Graphics Processing Units (GPU) which are massively parallel architectures with a partial SIMD execution (Single Instruction Multiple Data). We first propose an analysis of the Lefevre 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 polynomial approximations required in Lefevre 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.
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