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 Fn 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.
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