eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-09-16
16:1
16:9
10.4230/LIPIcs.FUN.2021.16
article
Efficient Algorithm for Multiplication of Numbers in Zeckendorf Representation
Idziaszek, Tomasz
1
Independent Researcher, Poland
In the Zeckendorf representation an integer is expressed as a sum of Fibonacci numbers in which no two are consecutive. We show O(n log n) algorithm for multiplication of two n-digit numbers in Zeckendorf representation.
For this purpose we investigate a relationship between the numeral system using Zeckendorf representations and the golden ratio numeral system. We also show O(n) algorithms for converting numbers between these systems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol157-fun2021/LIPIcs.FUN.2021.16/LIPIcs.FUN.2021.16.pdf
Fibonacci numbers
Zeckendorf representation
multiplication algorithm
Fast Fourier Transform
golden ratio numeral system
Lucas numbers