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
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 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 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 : Comparisons Decimal arithmetic Floating-Point Arithmetic
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Conference papers
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00737881
Contributor : Marc Mezzarobba <>
Submitted on : Monday, February 11, 2013 - 2:23:46 PM
Last modification on : Thursday, March 21, 2019 - 2:39:19 PM
Long-term archiving on : Saturday, April 1, 2017 - 10:00:20 PM

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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⟩

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