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D. DasSarma, D.W. Matula, "Measuring the Accuracy of ROM Reciprocal Tables," IEEE Transactions on Computers, vol. 43, no. 8, pp. 932940, August, 1994.  
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@article{ 10.1109/12.295855, author = {D. DasSarma and D.W. Matula}, title = {Measuring the Accuracy of ROM Reciprocal Tables}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {8}, issn = {00189340}, year = {1994}, pages = {932940}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.295855}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Measuring the Accuracy of ROM Reciprocal Tables IS  8 SN  00189340 SP932 EP940 EPD  932940 A1  D. DasSarma, A1  D.W. Matula, PY  1994 KW  readonly storage; data handling; ROM; reciprocal tables; reciprocal table construction algorithm; worst case relative errors; extreme case test data; input values. VL  43 JA  IEEE Transactions on Computers ER   
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 kbitsin, mbitsout 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 kbitsin, kbitsout table with relative errors never any greater than 3/4 2/sup k/, and more generally with g guard bits that for (k+g)bitsout 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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