# Unrestricted Algorithms for Generating Elementary Functions

• F. W. J. Olver
Part of the Computing Supplementum book series (COMPUTING, volume 2)

## Abstract

An “unrestricted” algorithm for generating a mathematical function is a computational algorithm in which the user may demand any accuracy for arguments of any magnitude. Two interesting mathematical problems arise in the construction of such algorithms for the elementary functions. First, an efficient method is needed to determine realistic a priori error bounds that is applicable when the number of arithmetical Operations is unbounded. Secondly, the free parameters associated with the algorithm need to be optimized in order to minimize the total Computing time. The first problem is solved by application of a recently-developed logarithmic form of interval analysis. The second is solved by asymptotic methods.

## Keywords

Word Length Dual Form Relative Precision Conventional Definition Arbitrary Precision
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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