Good stuff! I love Fibonacci algorithms and if you dig deeper, there are even faster algorithms that exploit even more identities like the fast doubling and look-up tables.
It's a fun recreational mathematics thing, but unfortunately I've never come across a problem where I need to solve Fibonacci insanely quickly. However I still keep my hopes up!
The techniques developed are useful in other areas. Eg Double_Cast talks about fast matrix multiplication above---certainly a useful technique elsewhere.
It's a fun recreational mathematics thing, but unfortunately I've never come across a problem where I need to solve Fibonacci insanely quickly. However I still keep my hopes up!