Is this with or without the use of integer?

with:

$ cat test.pl
use 5.18.2;
use warnings;
use integer;

my $x = 2;
my $y = 2.00000000000000123;
say qq{$x $y};

if ($x == $y or $x == $y-1 or $x == $y+1) { say "in exact range"; }
if ($y-1 <= $x && $x <= $y+1)             { say "in <= range";    }
if (abs ($y-$x) <= 1)                     { say "in abs range";   }

$ perl -v | grep 5.2
This is perl 5, version 24, subversion 1 (v5.24.1) built for x86_64-li
+nux-thread-multi-ld

$ perl test.pl
2 2.00000000000000123
in exact range
in <= range
in abs range
[download]

Same on 5.28.0

2.0000000000000000123 (two more zeroes), yields

2 2.00000000000000001
in exact range
in <= range
in abs range
[download]


Enjoy, Have FUN! H.Merijn