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.)
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