Newbie questions

[Matthias Lang]

Matthias Lang writes:

 >  > Regarding your problem about determining the number of decimal
 >  > digits in a number, I just came to think of a simple enough
 >  > brute force O(log(N)) or rather O(NN) where NN is the
 >  > number of digits in the number:
 >  > 
 >  >     digits(N) when is_integer(N), N >= 0 -> digits(N, 1, 0).
 >  > 
 >  >     digits(N, M, D) when M > N -> D;
 >  >     digits(N, M, D) -> digits(N, M*10, D+1).
 > 
 > I haven't ever studied bignum implementation, neither for Erlang or in
 > general, but I don't think this solution is O(log N).
 > 
 > I would expect M*10 to be expensive, i.e. O(M). And I'm not too sure
 > about the cost of the "M > N" test.

Er, that's wrong too.

Bignum multiplication must be implemented as some sort of
shift-and-add. Which would make it O(log M), not O(M) as I said.

So I expect there to be log M multiplications, each costing log
M. That makes the whole thing O(log N * log N).

Matthias