Instruction sequence expressions for the Karatsuba multiplication algorithm

Abstract

The Karatsuba multiplication algorithm is an algorithm for computing the product of two natural numbers represented in the binary number system. This means that the algorithm actually computes a function on bit strings. The restriction of this function to bit strings of any given length can be computed according to the Karatsuba multiplication algorithm by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe the instruction sequences concerned for the restrictions to bit strings of the different lengths by uniform terms from an algebraic theory.