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Two very fast and simple O(lg n) algorithms for individual Fibonacci numbersare given and compared to competing algorithms. A simple O(lg n) recursion isderived that can also be applied to Lucas. A formula is given to estimate thelargest n, where F_n does not overflow the implementation's data type. Thedanger of timing runs on input that is too large for the computerrepresentation leads to false research results.

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