Comparison between Binary and Decimal Floating-Point Numbers

Nicolas Brisebarre

doi:10.1109/TC.2015.2479602

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Comparison between Binary and Decimal Floating-Point Numbers

2016-07-01

DOI：10.1109/TC.2015.2479602

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Abstract

En 中文

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

comparisons

radix-10 arithmetic

binary arithmetic