Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
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You're replying to a comment by John Fremlin.
I looked at this a while ago because I was annoyed about stupid implementations of Fibonacci. I quickly noticed that the value of Fn quickly overflows fixed precision datatypes so as you point out you can't use fixed precision arithmetic and have to take account the non-trivial complexity of your operations.
I looks at the real complexity for Binet's formula and implement the better identity used by GMP
F2k = (Fk+1)^2 − (Fk−1)^2
Glimpses of Lisp: Fibonacci and the Netflix prize
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Peter Krumins' blog about programming, hacking, software reuse, software ideas, computer security, browserling, google and technology.
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