How do I make private functions in a Perl module

sub my_private_function {
...
};

package TestPrivate;

require 5.004;

use strict;
use warnings;
use Carp;
use vars qw($VERSION @ISA @EXPORT @EXPORT_OK);

require Exporter;

@ISA = qw(Exporter AutoLoader);

our @EXPORT_OK = qw( public_function );
our @EXPORT    = qw( );

$VERSION = '0.01';

sub new {
    my ( $class, %args ) = @_;
    my $self = {};
    bless( $self, $class );
    $self->private_function("THIS SHOULD BE PRIVATE");
    $self->{public_variable} = "This is public";
    return $self;
}

sub public_function {
    my $self     = shift;
    my $new_text = shift;
    $self->{public_variable} = $new_text;
    print "Public Variable: $self->{public_variable}n";
    print "Internal Variable: $self->{internal_variable}n";
}

sub private_function {
    my $self     = shift;
    my $new_text = shift;
    $self->{internal_variable} = $new_text;
}

#!/usr/bin/perl
use strict;
use TestPrivate 'public_function';
my $foo = new TestPrivate();
$foo->public_function("Changed public variable");
$foo->private_function("I changed your private variable");
$foo->public_function("Changed public variable again");
$foo->{internal_variable} = "Yep, I changed your private variable again!";
$foo->public_function("Changed public variable the last time");

Public Variable: Changed public variable
Internal Variable: THIS SHOULD BE PRIVATE
Public Variable: Changed public variable again
Internal Variable: I changed your private variable
Public Variable: Changed public variable the last time
Internal Variable: Yep, I changed your private variable again!

caller eq __PACKAGE__ or die;

my $priv_func1 = sub { my $self = shift; say 'func1'; };

sub public_sub {
    my $self = shift;

    $priv_func1->( $self );
}

my $priv_func1 = sub {
    my $self = shift; say 'func1';
};

sub public_sub {
    my $self = shift;

    $self->$priv_func1(@_);
}

package My;

sub new {
  return bless { }, shift;
}

sub private_func {
  my ($s, %args) = @_;
  die "Error: Private method called"
    unless (caller)[0]->isa( ref($s) );

  warn "OK: Private method called by " . (caller)[0];
}

sub public_func {
  my ($s, %args) = @_;

  $s->private_func();
}

package main;

my $obj = My->new();

# This will succeed:
$obj->public_func( );

# This will fail:
$obj->private_func( );