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Comparison between binary and decimal floating-point numbers

Nicolas Brisebarre 1 Christoph Lauter 2 Marc Mezzarobba 3, 2 Jean-Michel Muller 1
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01021928
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Submitted on : Thursday, June 25, 2015 - 11:30:08 AM
Last modification on : Tuesday, November 19, 2019 - 2:45:48 AM
Long-term archiving on: : Wednesday, September 16, 2015 - 12:16:08 AM

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

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