Efficient multiple-precision integer division algorithm

Design and implementation of division algorithm is one of the most complicated problems in multi-precision arithmetic. Huang et al. [1] proposed an efficient multi-precision integer division algorithm, and experimentally showed that it is about three times faster than the most popular algorithms proposed by Knuth [2] and Smith [3]. This paper reports a bug in the algorithm of Huang et al. [1], and suggests the necessary corrections. The theoretical correctness proof of the proposed algorithm is also given. The resulting algorithm remains as fast as that of [1].

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Hong Shen,et al.  An Efficient Multiple-Precision Division Algorithm , 2005, Sixth International Conference on Parallel and Distributed Computing Applications and Technologies (PDCAT'05).

[3]  David M. Smith,et al.  A multiple-precision division algorithm , 1996, Math. Comput..

[4]  Kazuya Kato,et al.  Number Theory 1 , 1999 .

[5]  M. Rabin.  Probabilistic algorithm for testing primality , 1980 .

[6]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .