ACCURATE ROUNDING SCHEME FOR THE NEWTON-RAPHSON METHOD USING REDUNDANT BINARY REPRESENTATION

This paper proposes a new algorithm of estimation and compensation of the error effect for rounding in the case of implementation of divisio n and square root using the Newton-Raphson method. First, we analyze t he error of the hardware system to confirm the condition of the implem entation with respect to this algorithm. Next, we describe in detail h ow to compensate the error by using this algorithm. Finally, we show t hat the hardware components for this algorithm, the direct rounding me chanism in the recode circuit and the sticky digit generating circuit, can be realized simply by improving the redundant binary representati on multiplier. The number of increasing cycles for this new algorithm is only one, and the rounding result using this algorithm satisfies IE EE Standard 754 rounding perfectly.