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...

• Type: Journal
• Year: 2011
• Where: TC
• Authors: Peter Kornerup, Jean-Michel Muller, Adrien Panhaleux
• Keywords: Constant Time, Radix Complement, Radix Complement Representation, Software Engineering, TC 2011