Automatic error analysis for determining precision
Communications of the ACM
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
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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.