The following code may do what you want:

use strict;
use warnings;

my @pairs =
    (
    [undef, undef], [0, undef], [0, 0], ['', undef], ['', ''], [1, und
+ef], [1, 1],
    [0, '0'], [0, 0], ['0', '0'], ['0e0', '0'], ['x', '0'], ['x', 0],
    );

 
for (@pairs)
    {
    my @pair = (@$_);
    print defined $pair[0] ? ">$pair[0]<" : 'undef';
    print ', ' . (defined $pair[1] ? ">$pair[1]<" : 'undef');
    print ': ' . (equals (@$_) ? "match\n" : "different\n");
    }

sub equals {
    my ($lhs, $rhs) = @_;
    
    #False if mix of defined and undef
    return 0 if defined $lhs != defined $rhs;
    
    # True if both undef
    return 1 if ! defined $lhs && ! defined $rhs;
    
    # False if different as numbers
    no warnings "numeric";
    return 0 if (0 + $lhs) != (0 + $rhs);
    
    # False if different as strings
    return 0 if ('' . $lhs) ne ('' . $rhs);
    
    return 1;
}
[download]

Prints:

undef, undef: match
>0<, undef: different
>0<, >0<: match
><, undef: different
><, ><: match
>1<, undef: different
>1<, >1<: match
>0<, >0<: match
>0<, >0<: match
>0<, >0<: match
>0e0<, >0<: different
>x<, >0<: different
>x<, >0<: different
[download]