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Measuring the Accuracy of ROM Reciprocal Tables
August 1994 (vol. 43 no. 8)
pp. 932-940

We prove that a convenient 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/spl les/k,m/spl les/12. We next prove the table construction algorithm always generates a k-bits-in, k-bits-out table with relative errors never any greater than 3/4 2/sup -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 extreme case test data and to compute the precision of a reciprocal table without prior construction of the full ROM reciprocal table, we describe a procedure that requires generation and inspection of only a small portion of such a table to identify input values guaranteed to include the worst case relative errors in the table.

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Index Terms:
read-only storage; data handling; ROM; reciprocal tables; reciprocal table construction algorithm; worst case relative errors; extreme case test data; input values.
D. DasSarma, D.W. Matula, "Measuring the Accuracy of ROM Reciprocal Tables," IEEE Transactions on Computers, vol. 43, no. 8, pp. 932-940, Aug. 1994, doi:10.1109/12.295855
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