Everything else is talking about bigints. If you were dealing with fixed-length integers, just use a lookup table. Also, you're wrong regarding floating-point

Everything else is talking about bigints. If you were dealing with fixed-length integers, just use a lookup table. Also, you're wrong regarding floating-point. On my machine, fib(101) is off from your approximation by ~2 million (!). Well before hitting the limits of a 64-bit float. It starts erroring at n=71, and only gets worse from there. Worse, the relative delta grows as n increases.