A Division Algorithm Using Bisection Method in Residue Number System

Residue Number System (RNS) has computational advantages for large integer arithmetic. It provides the benefits of parallel, carry-free, and high-speed arithmetic in addition, subtraction, and multiplication. However, overflow detection, sign detection, magnitude detection, and division are time-consuming operations in RNS. The most interesting one of the above operations is division, and many related researches have been proposed to make it more efficient. Hiasat and Abdel-Aty-Zohdy proposed a high-speed division algorithm using the highest power comparison to speed up division in RNS. Their algorithm evaluates the quotient according to the highest powers of 2 in the dividend and the divisor. Nevertheless, the evaluated quotient is underestimated such that there are redundant execution rounds in their algorithm. Thus, Yang et al. proposed a division algorithm in RNS using parity checking technique in 2004. In this algorithm, the evaluated quotient is estimated precisely such that the actual quotient can be found quickly. However, computing the highest powers of 2 in the dividend and the divisor is time-consuming in RNS, and this computation must be performed in each execution round of Yang et al.’s algorithm. Consequently, we propose the bisection method in RNS to design a division algorithm in the paper. Our new algorithm uses the bisection method in RNS to find the quotient in a possible interval efficiently. Compared with Yang et al.’s algorithm, our algorithm has less execution rounds and greatly reduces the times of the highest-power computation in RNS.