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Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci (1011.0148v1)
Published 31 Oct 2010 in cs.DM, cs.DS, and math.CO
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.