Like what ctilmes suggested, but with a twist:

# Create a HASH which stores a mapping between function names
# and the associated function references (\&). Add any other
# functions to the quoted-word listing
my %commands = map { $_ => \&$_ } qw[
     set
     add
     mul
];

# ...

while (<STDIN>)
{
     my ($command, $param) = split(" ", $_);

     # Check that the function exists before calling it, could have a
     # bad $command being passed. Perhaps add a warning in an
     # else block?
     if ($command{$command}})
     {
          $register = $command{$command}->($register, $param);
     }
}
[download]

It might look a bit weird at first, but the map call works on a single listing that doesn't have duplication. I've also used the $ref->() style of calling which doesn't use an ampersand, but is functionally the same as &$ref().