Comparison between Binary64 and Decimal64 Floating-Point Numbers

Comparison between Binary64 and Decimal64 Floating-Point Numbers

We introduce a software-oriented 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...

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Bibliographische Detailangaben
Hauptverfasser: Brisebarre, N., Mezzarobba, M., Muller, J.-M, Lauter, C.
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Accuracy
Approximation methods
Computer Arithmetic
Computer Science
Decimal Floating-Point
Digital arithmetic
Encoding
Floating-Point Arithmetic
Floating-Point Comparisons
Hardware
Other
Symbolic Computation
Testing
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Beschreibung
Zusammenfassung:We introduce a software-oriented 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.
ISSN:1063-6889
DOI:10.1109/ARITH.2013.23