The input you're showing is too short for producing performance problems!

So what are the real dimensions?

For instance

• Size of input?
• Do you apply same "interval-files" to different "point-files"?
• How many point-files?
• Are your points always between 1 and 21?

Knowing these parameters help preprocessing costly parts.

Considering var names:

Names like input1, input2, hash1, hash2, key1, key2, p and o really don't improve readability!

Try descriptive names like $point, $start, $stop, %count and %active.

And please don't delete comments!

HTH!

update

I don't know if its much faster, but an approach reading all data into array and counting over slices will at least improve readablity:

  DB<159> use List::Util qw/sum/
 => 0

  DB<160> \@a
 => [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]

  DB<161> $start=4;$stop=11
 => 11

  DB<162> $count{"a"}{$start}{$stop}=sum @a[$start..$stop]
 => 3
[download]

I'm pretty sure this approach could be translated to counting single bits with vec or pack