GPU-accelerated generation of correctly-rounded elementary functions

Pierre Fortin (1) , Mourad Gouicem (2) , Stef Graillat (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
2 LIP6 - Laboratoire d'Informatique de Paris 6

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 Lefèvre 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 Lefèvre 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.

Mots clés: SIMD; control flow divergence; floating-point arithmetic; elementary function; correct rounding; Table Maker's Dilemma; Lefèvre algorithm; GPU computing

Domaines: Arithmétique des ordinateurs; Calcul parallèle, distribué et partagé [cs.DC]

Pierre Fortin, Mourad Gouicem, Stef Graillat. GPU-accelerated generation of correctly-rounded elementary functions. 2013. ⟨hal-00751446v1⟩