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On-the-Fly Rounding (Computing Arithmetic)
December 1992 (vol. 41 no. 12)
pp. 1497-1503

In implementations of operations based on digit-recurrence algorithms such as division, left-to-right multiplication and square root, the result is obtained in digit-serial form, from most significant digit to least significant. To reduce the complexity of the result-digit selection and allow the use of redundant addition, the result-digit has values from a signed-digit set. As a consequence, the result has to be converted to conventional representation, which can be done on-the-fly as the digits are produced, without the use of a carry-propagate adder. The authors describe three ways to modify this conversion process so that the result is rounded. The resulting operation is fast because no carry-propagate addition is needed. The schemes described apply also to online arithmetic operations.

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Index Terms:
digit rounding; computing arithmetic; digit-recurrence algorithms; digit-serial form; most significant digit; least significant; redundant addition; result-digit; signed-digit set; online arithmetic; digital arithmetic; number theory.
M.D. Ercegovac, T. Lang, "On-the-Fly Rounding (Computing Arithmetic)," IEEE Transactions on Computers, vol. 41, no. 12, pp. 1497-1503, Dec. 1992, doi:10.1109/12.214659
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