Finding the number of digits of an integer

Question

What is the best method to find the number of digits of a positive integer?

I have found this 3 basic methods:

• conversion to string

Answer 1

This algorithm might be good also, assuming that:

• Number is integer and binary encoded (<< operation is cheap)

• We don't known number boundaries

  var num = 123456789L;
  var len = 0;
  var tmp = 1L;
  while(tmp < num)
  {
      len++;
      tmp = (tmp << 3) + (tmp << 1);
  }
  

This algorithm, should have speed comparable to for-loop (2) provided, but a bit faster due to (2 bit-shifts, add and subtract, instead of division).

As for Log10 algorithm, it will give you only approximate answer (that is close to real, but still), since analytic formula for computing Log function have infinite loop and can't be calculated precisely Wiki.