On multiplying large periodic integers. I

More On Squaring and Multiplying Large Integers

t = vzge(b,w,a)

A quantum architecture for multiplying signed integers

Multiplying huge integers using Fourier transforms

Multiplying huge integers of n digits can be done in time O(n log(n)) using Fast Fourier Transforms (FFT), instead of the O(n) time complexity normally required. In this paper we present this technique from the viewpoint of polynomial multiplication, explaining a recursive divide-and-conquer approach to FFT multiplication. We have compared both methods of multiplication quantitatively and prese...

Periodic Sets of Integers

On the circuit complexity of the standard and the Karatsuba methods of multiplying integers

The goal of the present paper is to obtain accurate estimates for the complexity of two practical multiplication methods: standard (school) and Karatsuba [1]. Here, complexity is the minimal possible number of gates in a logic circuit implementing the required function over the basis {AND,OR,XOR,NAND,NOR,XNOR}. One can find upper estimates for the said methods e.g. in [2]. The standard method h...