Although fib grows exponentially, so it does the same for not so big numbers (a back-of-an-envelope calculation gives me that fib(91) doesn't fit in 63 bits).

Although fib grows exponentially, so it does the same for not so big numbers (a back-of-an-envelope calculation gives me that fib(91) doesn't fit in 63 bits). OTOH, if I had to calculate fib(X), and not fib(1..X), I'd use the exponential formula (relying on floating point) instead of the recurrence (which uses integer), so I guess the error would be detected at the conversion to integer.