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.)
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
 a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

For: 

Use: 
 &   & 
 <   < 
 >   > 
 [   [ 
 ]   ] 
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.