Fibonacci, tribonacci, …, hexanacci and parallel “error-free” machine arithmetic

Abstract

The paper proposes a new method of synthesis of machine arithmetic systems for “error-free” parallel computations. The difference of the proposed approach from calculations in traditional Residue Number Systems (RNS) for the direct sum of rings is the parallelization of calculations in finite reductions of non-quadratic global fields whose elements are represented in number systems generated by sequences of powers of roots of the characteristic polynomial for the n-Fibonacci sequence.

Keywords

• finite fields
• n-fibonacci and n-lucas numbers
• parallel machine arithmetic