Fibonacci grows exponentially. The base is phi (the golden ratio), so it's not quite as fast as 2^n, but it's still pretty fast. only the smallest 94 or so Fibonacci numbers can be represented by an unsigned 64-bit integer, so a lookup table is probably your best option.
However, if you really did want to compute it, you could invert the closed form solution to get something like:
int fibIndex(long n) {
return Math.round(Math.log(n * Math.sqrt(5))/Math.log(PHI));
}
this may be of by one, and of course cannot distinguish between the double 1s early in the sequence.