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.