JUCS - Journal of Universal Computer Science 12(5): 499-511, doi: 10.3217/jucs-012-05-0499
Reversible Karatsuba's Algorithm
Luis Antonio Brasil Kowada‡, Renato Portugal§, Celina Miraglia Herrera de Figueiredo‡ Universidade Federal do Rio de Janeiro - UFRJ, Rio de Janeiro, Brazil§ Laboratório Nacional de Computação Científica - LNCC, Petropolis, Brazil
Corresponding author: Luis Antonio Brasil Kowada ( kowada@cos.ufrj.br ) © Luis Antonio Brasil Kowada, Renato Portugal, Celina Miraglia Herrera de Figueiredo. This article is freely available under the J.UCS Open Content License. Citation:
Kowada LAB, Portugal R, Miraglia Herrera de Figueiredo C (2006) Reversible Karatsuba's Algorithm. JUCS - Journal of Universal Computer Science 12(5): 499-511. https://doi.org/10.3217/jucs-012-05-0499 |  |
Abstract
Karatsuba discovered the first algorithm that accomplishes multiprecision integer multiplication with complexity below that of the grade-school method. This algorithm is implemented nowadays in computer algebra systems using irreversible logic. In this paper we describe reversible circuits for the Karatsuba's algorithm and analyze their computational complexity. We discuss garbage disposal methods and compare with the well known Bennett's schemes. These circuits can be used in reversible computers which have the advantage of being very efficient in terms of energy consumption. The algorithm can also be used in quantum computers and is an improvement of previous circuits for the same purpose described in the literature.
Keywords
reversible computing, reversible circuit, arithmetic operations, multiplier