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H. Kabuo, T. Taniguchi, A. Miyoshi, H. Yamashita, M. Urano, H. Edamatsu, S. Kuninobu, "Accurate Rounding Scheme for the NewtonRaphson Method Using Redundant Binary Representation," IEEE Transactions on Computers, vol. 43, no. 1, pp. 4351, January, 1994.  
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@article{ 10.1109/12.250608, author = {H. Kabuo and T. Taniguchi and A. Miyoshi and H. Yamashita and M. Urano and H. Edamatsu and S. Kuninobu}, title = {Accurate Rounding Scheme for the NewtonRaphson Method Using Redundant Binary Representation}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {1}, issn = {00189340}, year = {1994}, pages = {4351}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.250608}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Accurate Rounding Scheme for the NewtonRaphson Method Using Redundant Binary Representation IS  1 SN  00189340 SP43 EP51 EPD  4351 A1  H. Kabuo, A1  T. Taniguchi, A1  A. Miyoshi, A1  H. Yamashita, A1  M. Urano, A1  H. Edamatsu, A1  S. Kuninobu, PY  1994 KW  digital arithmetic; error analysis; rounding scheme; NewtonRaphson method; redundant binary representation; error effect; recode circuit; sticky digit generating circuit; redundant binary representation multiplier. VL  43 JA  IEEE Transactions on Computers ER   
Proposes a new algorithm of estimation and compensation of the error effect for rounding in the case of implementation of division and square root using the NewtonRaphson method. The authors analyze the error of the hardware system to confirm the condition of the implementation with respect to this algorithm. Next, they describe in detail how to compensate the error by using this algorithm. Finally, they show that the hardware components for this algorithm, the direct rounding mechanism in the recode circuit and the sticky digit generating circuit, can be realized simply by improving the redundant binary representation multiplier. The number of increasing cycles for this new algorithm is only one, and the rounding result using this algorithm satisfies IEEE Standard 754 rounding perfectly.
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