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) + SUM{|Ei|}) error bounds,
where p denotes the operation's precision and 
Ei 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.

CACM January, 1973

Richman, P. L.

variable-precision, exponential function,
error analysis, interval arithmetic

5.11

CA730106 JB January 24, 1978  4:32 PM

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