Fast, Sound and Precise Narrowing of the Exponential Function
نویسنده
چکیده
In this paper we present an algorithm for narrowing the constraint y = e x. The algorithm has been designed to be fast by using only IEEE multiplication. The main diiculty is to design algorithms which soundly, rapidly, and precisely compute upper and lower bounds on e x and ln(y). We prove that our algorithms are correct and produce upper and lower bounds which diier by at most 2 ULP. Experiments indicate that the bounds diier by 1 ULP 99.8% of the time. The method we describe is table-driven as is Gal's accurate tables method, but the table is easier to construct and hence this method may be applicable to wider classes of functions.
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