[cabinpark]

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!

[brudgers]

Fibonacci numbers are so fun that Fibonacci Quarterly has been around for 52 years.

http://www.fq.math.ca/

[xtagon]

Just a guess, but it might be useful for fractal rendering. That's the only real application I can think of.

[eru]

The techniques developed are useful in other areas. Eg Double_Cast talks about fast matrix multiplication above---certainly a useful technique elsewhere.