[MrRage]

I always thought the fastest was the closed form formula: http://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_ex...

Unless looping and counting is that much faster than doing some floating point math?

[aarongolliver]

Only "faster" because you precompute digits of the golden ratio, and will quickly become inaccurate unless you compute more of them

[Bognar]

The closed form will become inaccurate at some point. However, there is a way to calculate Fibonacci accurately with O(log(n)) time (ignoring the time to multiply - otherwise O(M(n) log(n)) where M(n) is the time to multiply two numbers of n digits).