Comparison between binary64 and decimal64 floating-point numbers

Nicolas Brisebarre (1, 2) , Marc Mezzarobba (1, 2) , Jean-Michel Muller (1, 2) , Christoph Lauter (3)

1 ARIC - Arithmetic and Computing
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 PEQUAN - Performance et Qualité des Algorithmes Numériques

We introduce an algorithm that allows one to quickly compare a binary64 floating-point (FP) number and a decimal64 FP number, assuming the "binary encoding" of the decimal formats specified by the IEEE 754-2008 standard for FP arithmetic is used. It is a two-step algorithm: a first pass, based on the exponents only, makes it possible to quickly eliminate most cases, then when the first pass does not suffice, a more accurate second pass is required. We provide an implementation of several variants of our algorithm, and compare them.

Keywords: Floating-Point Arithmetic; Decimal arithmetic; Comparisons

Domains: Computer Science [cs]; Other [cs.OH]; Computer Science [cs]; Symbolic Computation [cs.SC]; Computer Science [cs]; Computer Arithmetic

Nicolas Brisebarre, Marc Mezzarobba, Jean-Michel Muller, Christoph Lauter. Comparison between binary64 and decimal64 floating-point numbers. 21st IEEE Symposium on Computer Arithmetic, Apr 2013, Austin, TX, United States. pp.145-152, ⟨10.1109/ARITH.2013.23⟩. ⟨ensl-00737881v4⟩