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B-adic Number Stream

Valérie Ménissier-Morain [20] uses a representation of reals as streams of integers. A real r is represented by a stream of integers $(c_n)_{n \in \mathbb{N}}$ with the property that | r-cnB-n| < B-n.

r = \lim_{n \rightarrow \infty} \left(\frac{c_n}{B^{-n}}\right)\end{displaymath}

This representation is not incremental. If we evaluate a result, and subsequently require the same result to a higher precision, we must examine a later element in the stream. This is computed from scratch, unlike the dyadic digit representation used in this work in which later digits simply refine earlier results. Despite its non-incremental nature, this representation reportedly performs well in practice.

Martin Escardo