On various ways to split a floating-point number

Claude-Pierre Jeannerod (1) , Jean-Michel Muller (1, 2) , Paul Zimmermann (3)

1 ARIC - Arithmetic and Computing
2 CNRS - Centre National de la Recherche Scientifique
3 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms

We review several ways to split a floating-point number, that is, to decompose it into the exact sum of two floating-point numbers of smaller precision. All the methods considered here involve only a few IEEE floating-point operations, with rounding to nearest and including possibly the fused multiply-add (FMA). Applications range from the implementation of integer functions such as round and floor to the computation of suitable scaling factors aimed, for example, at avoiding spurious underflows and overflows when implementing functions such as the hypotenuse.

Domaines: Algorithme et structure de données [cs.DS]

Claude-Pierre Jeannerod, Jean-Michel Muller, Paul Zimmermann. On various ways to split a floating-point number. ARITH 2018 - 25th IEEE Symposium on Computer Arithmetic, Jun 2018, Amherst (MA), United States. pp.53-60, ⟨10.1109/ARITH.2018.8464793⟩. ⟨hal-01774587v2⟩