Today I've written a little program that classifies and counts files based on the integer part of

`log2($file_size)`. So I would get these classes:

`0 <= SIZE < 1
1 <= SIZE < 2
2 <= SIZE < 4
4 <= SIZE < 8
and so on...
`

For that I would like to write this:

`$size_class = $size ? int( log($size) / log(2) ) : -1;
# red light on, possible error caused by floating point arithmetic
`

Now let's forget about the special case of

`$size == 0`. My input can only be positive integers (because these are file sizes), so I suppose the error coming from floating point arithmetic can bite me only in the case when

`$size` is a power of 2 (in the expression

`$size = 2**$x` the exponent is a natural number). Is this true?

But let's take it further. I've written a little test to check whether I will be bitten for all the powers of 2 that fits in my machine's floating point represantation:

`bash $ diff <( perl -E 'say int( log(2**$_) / log(2) ) for 1 .. 2**10'
+ ) <( seq 1 $(( 2**10 )) )
`

The output is this:

`1024c1024
< inf
---
> 1024
`

So there is not a single power of 2 (under 2**1024) that would be misclassified at least on my machine.

So my question is: Is there a theoretical explanation (for this restricted case of floating point aritmetic) why it can't be problematic or is it just by accident?

Please shed some light on this issue.

ps: Sorry, I know this is probably not Perl specific, but my question arose because there is no log2() function in Perl. (For example with a properly setup lookup table I could be able to do this classification with integer arithmetic only, but that would be a pain instead of this little snippet.)