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2011

Performing Arithmetic Operations on Round-to-Nearest Representations

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Performing Arithmetic Operations on Round-to-Nearest Representations
—During any composite computation, there is a constant need for rounding intermediate results before they can participate in further processing. Recently, a class of number representations denoted RN-Codings were introduced, allowing an unbiased roundingto-nearest to take place by a simple truncation, with the property that problems with double-roundings are avoided. In this paper, we first investigate a particular encoding of the binary representation. This encoding is generalized to any radix and digit set; however, radix complement representations for even values of the radix turn out to be particularly feasible. The encoding is essentially an ordinary radix complement representation with an appended round-bit, but still allowing rounding-to-nearest by truncation, and thus avoiding problems with double-roundings. Conversions from radix complement to these round-to-nearest representations can be performed in constant time, whereas conversion the other way, in general, takes at leas...
Peter Kornerup, Jean-Michel Muller, Adrien Panhale
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where TC
Authors Peter Kornerup, Jean-Michel Muller, Adrien Panhaleux
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