Research and Advances

Variable-precision exponentiation

A previous paper presented an efficient algorithm, called the Recomputation Algorithm, for evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision arithmetic operations. The Recomputation Algorithm can be applied to expressions involving any variable-precision operations having O(10-p + ∑ | &egr;i |) error bounds, where p denotes the operation's precision and &egr;i denotes the error in the operation's ith argument. This paper presents an efficient variable-precision exponential operation with an error bound of the above order. Other operations, such as log, sin, and cos, which have simple series expansions, can be handled similarly.

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Research and Advances

The choice of base

A digital computer is considered, whose memory words are composed of N r-state devices plus two sign bits (two state devices). The choice of base &bgr; for the internal representation of floating-point numbers on such a computer is discussed. It is shown that in a certain sense &bgr; = r is best.

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