Comparison between binary and decimal floating-point numbers

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

1 ARIC - Arithmetic and Computing
2 PEQUAN - Performance et Qualité des Algorithmes Numériques

We introduce an algorithm to compare a binary floating-point (FP) number and a decimal FP number, assuming the "binary encoding" of the decimal formats is used, and with a special emphasis on the basic interchange formats specified by the IEEE 754-2008 standard for FP arithmetic. It is a two-step algorithm: a first pass, based on the exponents only, quickly eliminates most cases, then, when the first pass does not suffice, a more accurate second pass is performed. We provide an implementation of several variants of our algorithm, and compare them.

Domaines: Arithmétique des ordinateurs; Calcul formel [cs.SC]

Nicolas Brisebarre, Christoph Lauter, Marc Mezzarobba, Jean-Michel Muller. Comparison between binary and decimal floating-point numbers. IEEE Transactions on Computers, 2016, 65 (7), pp.2032-2044. ⟨10.1109/TC.2015.2479602⟩. ⟨hal-01021928v2⟩