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Other Possible Representations

   The digit representations mentioned in section 2.2.2 are by no means the only suitable ones. Section 1.2 lists the related work of a number of other authors, and a few of their representations are described here by way of comparison.

One interesting feature of the digit representations, including all the representations used in this work, is that they are incremental. An incremental representation is one in which extending the precision of a result can be performed without recomputing it from scratch. With the digit representations, we can extend the precision simply by computing more digits. Not all representations used for exact real arithmetic have this property.

Philipp Sünderhauf [27] observes that whilst incrementality would appear to be an intuitively useful property, this may not always be the case, even in situations where the incrementality is directly used. Some non-incremental representations report surprisingly high performance. Sünderhauf discusses this, and develops a ``hybrid'' representation from a non-incremental one which combines benefits of both incrementality and non-incrementality.


Martin Escardo