Towards solving the Table Maker's Dilemma on GPU

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

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

Since 1985, the IEEE 754 standard defines formats, rounding modes and basic operations for floating-point arithmetic. In 2008 the standard has been extended, and recommendations have been added about the rounding of some elementary functions such as trigonometric functions (cosine, sine, tangent and their inverses), exponentials, and logarithms. However to guarantee the exact rounding of these functions one has to approximate them with a sufficient precision. Finding this precision is known as the Table Maker's Dilemma. To determine this precision, it is necessary to find the hardest-to-round argument of these functions. Lefèvre et al. proposed in 1998 an algorithm which improves the exhaustive search by computing a lower bound on the distance between a line segment and a grid. We present in this paper an analysis of this algorithm in order to deploy it efficiently on GPU. We manage to obtain a speedup of 15.4 on a NVIDIA Fermi GPU over one single high-end CPU core.

Mots clés: Table Maker's Dilemma; Correct Rounding; Floating-point arithmetic; GPGPU

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

Pierre Fortin, Mourad Gouicem, Stef Graillat. Towards solving the Table Maker's Dilemma on GPU. 20th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, Feb 2012, Garching, Germany. pp.407 - 415, ⟨10.1109/PDP.2012.64⟩. ⟨hal-00642337⟩