On Various Ways to Split a Floating-Point Number

Abstract

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.