Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
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A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software-routines, which enables the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example a table-lookup algorithm for calculating the function exp(x) - 1 that has been published by Tang \cite{tang92} is analyzed using these new tools. The result shows the high quality of the new approach.