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

Regarding the three methods you propose for "determining the number of digits necessary to represent a given number in a given base", I don't like any of them, actually; I prefer the method I give below instead.

Re your method #1 (strings): Anything involving converting back-and-forth between strings and numbers is usually very slow.

Re your method #2 (temp/=10): This is fatally flawed because it assumes that x/10 always means "x divided by 10". But in many programming languages (eg: C, C++), if "x" is an integer type, then "x/10" means "integer division", which isn't the same thing as floating-point division, and it introduces round-off errors at every iteration, and they accumulate in a recursive formula such as your solution #2 uses.

Re your method #3 (logs): it's buggy for large numbers (at least in C, and probably other languages as well), because floating-point data types tend not to be as precise as 64-bit integers.

Hence I dislike all 3 of those methods: #1 works but is slow, #2 is broken, and #3 is buggy for large numbers. Instead, I prefer this, which works for numbers from 0 up to about 18.44 quintillion:

unsigned NumberOfDigits (uint64_t Number, unsigned Base)
{
   unsigned Digits = 1;
   uint64_t Power  = 1;
   while ( Number / Power >=  Base )
   {
      ++Digits;
      Power *= Base;
   }
   return Digits;
}