Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci
Discrete Mathematics
2010-11-02 v1 Data Structures and Algorithms
Combinatorics
Abstract
Two very fast and simple O(lg n) algorithms for individual Fibonacci numbers are given and compared to competing algorithms. A simple O(lg n) recursion is derived that can also be applied to Lucas. A formula is given to estimate the largest n, where F_n does not overflow the implementation's data type. The danger of timing runs on input that is too large for the computer representation leads to false research results.
Keywords
Cite
@article{arxiv.1011.0148,
title = {Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci},
author = {L. F. Johnson},
journal= {arXiv preprint arXiv:1011.0148},
year = {2010}
}
Comments
11 pages, 1 table This paper illustrates the importance of considering storage size when running experiments and that the results of expermential comparsion of algorithms in a well known paper are at best unreliable because of register overflow. The two presented algorithms are concise but readable