Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci

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.

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