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Measuring the accuracy of ROM reciprocal tables

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

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⩽k,m⩽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 ¾2-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

Published in:

Computers, IEEE Transactions on  (Volume:43 ,  Issue: 8 )

Date of Publication:

Aug 1994

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