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Unum: Adaptive Floating-Point Arithmetic

Authors: Enric Morancho;

Unum: Adaptive Floating-Point Arithmetic

Abstract

Usually, arithmetic units represent numeric data-types employing fixed-length representations. For instance, hardware representations of real numbers usually employ fixed-length formats defined by the IEEE Standard 754 (32-bit single-precision, 64-bit double-precision, , floating-point numbers). Fixed-length representations allow simpler and faster arithmetic units than variable-length representations. However, fixed-length representations lack the ability to adapt both their accuracy and dynamic range to the application requirements. As some variable-length representations expose this adaptivity, they allow hardware implementations to exploit this adaptivity. Recently, Unum (universal number) representation has been proposed as an extension of floating-point representations. Unum is a variable-length representation that adapts the bitsize of the representation to the actual numbers being represented and, moreover, Unum associates and propagates accuracy information through arithmetic operations. In this work we compare Unum versus the floating-point representations defined by IEEE Standard 754. We show that Unum arithmetic improves IEEE 754 arithmetic: a) results obtained using Unum arithmetic are more reliable than IEEE 754's results because Unum does not hide accuracy issues, and b) Unum arithmetic units may implement energy-efficient techniques because Unum dynamically adapts the bitsize of the representation to the actual numbers being represented.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
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