Comparison between Binary and Decimal Floating-Point Numbers

Nicolas Brisebarre; Christoph Lauter; Marc Mezzarobba; Jean Michel Muller

doi:10.1109/TC.2015.2479602

Comparison between Binary and Decimal Floating-Point Numbers

Nicolas Brisebarre, Christoph Lauter, Marc Mezzarobba, Jean Michel Muller

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	7271015
Pages (from-to)	2032-2044
Number of pages	13
Journal	IEEE Transactions on Computers
Volume	65
Issue number	7
DOIs	https://doi.org/10.1109/TC.2015.2479602
Publication status	Published - 1 Jul 2016

Keywords

Floating-point arithmetic
binary arithmetic
comparisons
radix-10 arithmetic

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10.1109/TC.2015.2479602

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title = "Comparison between Binary and Decimal Floating-Point Numbers",

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.",

keywords = "Floating-point arithmetic, binary arithmetic, comparisons, radix-10 arithmetic",

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KW - binary arithmetic

KW - comparisons

KW - radix-10 arithmetic

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Comparison between Binary and Decimal Floating-Point Numbers

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Keywords

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