Emulating round-to-nearest-ties-to-zero "augmented" floating-point operations using round-to-nearest-ties-to-even arithmetic

Sylvie Boldo (1, 2) , Christoph Q. Lauter (3) , Jean-Michel Muller (4, 5, 6)

1 LRI - Laboratoire de Recherche en Informatique
2 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
3 University of Alaska [Anchorage]
4 Université de Lyon
5 ARIC - Arithmetic and Computing
6 LIP - Laboratoire de l'Informatique du Parallélisme

The IEEE 754 Standards Committee for Floating-Point Arithmetic is recommending, in its draft standard, that new "augmente"' operations should be added in the next release of the standard. These operations use a new "rounding direction": round to nearest ties-to-zero. We show how they can be implemented using the currently available operations, using rounded-to-nearest ties-to-even.

Domaines: Autre [cs.OH]; Arithmétique des ordinateurs

Sylvie Boldo, Christoph Q. Lauter, Jean-Michel Muller. Emulating round-to-nearest-ties-to-zero "augmented" floating-point operations using round-to-nearest-ties-to-even arithmetic. 2019. ⟨hal-02137968v1⟩