Great link and I like the mention of the fact there is actually an analytical formula for the Fibonacci number as well that allows computing it in constant time. Unfortunately, machine precision issues make it nearly impossible to accurately calculate anything large enough to be worth the speedup you get as there is no practical way to store enough of the digits in square root of 5, so you need a symbolic algebra implementation that can compute an exact answer and reduce it to a natural number.

Why symbolic algebra vs infinite precision floating point which is comparatively much cheaper computationally (& memory wise too?)?