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A Priori Worst Case Error Bounds for Floating-Point Computations
July 1998 (vol. 47 no. 7)
pp. 750-756

Abstract—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 enable 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 [16] is analyzed using these new tools. The result shows the high quality of the new approach.

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Index Terms:
Rigorous error bounds, table-lookup algorithms, elementary function algorithms, automation of error analysis.
Citation:
Walter Krämer, "A Priori Worst Case Error Bounds for Floating-Point Computations," IEEE Transactions on Computers, vol. 47, no. 7, pp. 750-756, July 1998, doi:10.1109/12.709374
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