Prime factorization using square root approximation

An Approximation for the Inverse Square Root Function

Square form factorization

We present a detailed analysis of SQUFOF, Daniel Shanks’ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel.

Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

ÐThis paper deals with the computation of reciprocals, square roots, inverse square roots, and some elementary functions using small tables, small multipliers, and, for some functions, a final alargeo (almost full-length) multiplication. We propose a method, based on argument reduction and series expansion, that allows fast evaluation of these functions in high precision. The strength of this m...

Improving Goldschmidt Division, Square Root, and Square Root Reciprocal

ÐThe aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm, assuming 4-cycle pipelined multiplier, ...

Automatic Generation of Prime Factorization Algorithms Using Genetic Programming

This paper describes the application of the principles of genetic programming to the field of prime factorization. Any prime factorization algorithm is given one integer and must generate a complete list of primes such that, when multiplied together in varying degrees, produces the original integer. Constructing even a limited factoring algorithm in GP turns out to be extremely challenging and ...