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

10/31/2010

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by   L. F. Johnson, et al.

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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.