A Fast Division Algorithm in Residue Number System

• Main Authors: Jen-Ho Yang, 楊仁和
• Other Authors: Chien-Yuan Chen
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/75671053522418611820

碩士 === 義守大學 === 資訊工程學系 === 90 === Residue Number System (RNS) has computational advantages for very large integer arithmetic because of its properties of parallel, carry free, and high-speed arithmetic. However, overflow detection, sign detection, relative-magnitude detection, and division in RNS are very difficult problems. In 1995, Hiasat and Zohdy proposed a high-speed division algorithm for RNS. Their algorithm computes the temporal quotient according to the highest powers of 2 in the dividend and the divisor. After computing the temporal quotient, the algorithm finds the actual quotient to be the sum of all temporal quotients. However, the temporal quotient is underestimated. Thus, we improve Hiasat and Zohdy’s division algorithm in RNS by additionally dealing with the highest 2 bits of the dividend and the divisor. Moreover, we also consider the case of handling the highest i bits, where i>2. Unfortunately, the improvement is in vain because the temporal quotients are nearly the same when i>=2. According to the above description, we propose a fast division algorithm based on the highest 2 bits of the dividend and divisor in RNS. Comparing with Hiasat and Zohdy’s algorithm, our algorithm reduces the number of execution rounds by 25%.