JUCS - Journal of Universal Computer Science 12(5): 499-511, doi: 10.3217/jucs-012-05-0499
Reversible Karatsuba's Algorithm
expand article infoLuis 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
Open Access
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.
reversible computing, reversible circuit, arithmetic operations, multiplier