Decompositions of graphs of functions and efficient iterations of lookup tables

TL;DR

This paper presents a method to implement functions as lookup tables that allows efficient computation of repeated applications with minimal dependence on the number of iterations or input, while only slightly increasing storage requirements.

Contribution

It introduces a novel approach to implement lookup table functions enabling fast repeated evaluations with minimal storage overhead.

Findings

Efficient evaluation of function powers f^m(x) independent of m and x

Implementation increases storage by a small constant factor

Applicable to functions represented as lookup tables

Abstract

We show that every function f implemented as a lookup table can be implemented such that the computational complexity of evaluating f^m(x) is small, independently of m and x. The implementation only increases the storage space by a small_constant_ factor.