while (<FILE>) {
    $count += () = /\Q$constant\E/g;
}
print "$constant occurs $count times\n";
##</code><code>##

use File::Slurp;
my $constant = '$_';
$_ = read_file('filename.pl');
$count = () = /\Q$constant\E/g;
print "$constant occurs $count times\n";