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Measuring the accuracy of ROM reciprocal tables

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2 Author(s)
Das Sarma, D. ; Dept. of Comput. Sci. & Eng., Southern Methodist Univ., Dallas, TX, USA ; Matula, D.W.

It is proved that a conventional ROM reciprocal table construction algorithm generates tables that minimize the relative error. The worst case relative errors realized for such optimally computed k-bits-in, m-bits-out ROM reciprocal tables are then determined for all table sizes 3 ⩽ k, m ⩽ 12. It is then proved that the table construction algorithm always generates a k-bits-in, k-bits-out table with relative errors never any greater than 3(2-k)/4 for any k, and, more generally with g guard bits, that for (k + g)-bits-out the relative error is never any greater than 2-(k+1)(1 + 1/(2g+1)). To provide for determining test data without prior construction of a full ROM reciprocal table, a procedure that requires generation and searching of only a small portion of such a table to determine regions containing input data yielding the worst case relative errors is described

Published in:

Computer Arithmetic, 1993. Proceedings., 11th Symposium on

Date of Conference:

29 Jun-2 Jul 1993