Newbie questions

[Nick Linker]

Good day.

I was playing with Erlang for calculation over large numbers and 
discovered some issues:
1. math:log fails with "badarg" for big integers.
2. It is impossible to know how many digits in an integer _efficiently_ 
(i.e. with O(1) or O(log(n)), where n - number of digits). 
length(number_to_list(N)) appears to have O(n).
3. Let me define the following function:
    fib(0) -> 0;
    fib(1) -> 1;
    fib(N) -> fib(N-1) + fib(N-2).
I have failed to convert this function _without_ put/get to be able to 
compute even fib(100) within reasonable period of time (I guess I did it 
wrong so that tail recursion was not here). Is there a way to compute 
fib(N), N>=100 without side effects?

Thank you in advance,
Best regards,
Linker Nick.