Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic

David Defour (1) , Guillaume Hanrot (2) , Vincent Lefèvre (2) , Jean-Michel Muller (1) , Nathalie Revol (1) , Paul Zimmermann (2)

1 ST-CROLLES - STMicroelectronics [Crolles]
2 SPACES - Solving problems through algebraic computation and efficient software

Some aspects of what a standard for the implementation of the mathematical functions could be are presented. Firstly, the need for such a standard is motivated. Then the proposed standard is given. The question of roundings constitutes an important part of this paper: three levels are proposed, ranging from a level relatively easy to attain (with fixed maximal relative error) up to the best quality one, with correct rounding on the whole range of every function.We do not claim that we always suggest the right choices, or that we have thought about all relevant issues. The mere goal of this paper is to raise questions and to launch the discussion towards a standard.

Mots clés: IEEE 754 standard; nombre flottant; floating-point number; correct rounding; normalization; arrondi correct; normalisation; standard IEEE 754

Domaines: Autre [cs.OH]

David Defour, Guillaume Hanrot, Vincent Lefèvre, Jean-Michel Muller, Nathalie Revol, et al.. Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic. Numerical Algorithms, 2004, 37 (1-4), pp.367-375. ⟨inria-00099967⟩