Wordpress-allow login with email address

Wordpress allow login with email address

    function login_with_email_address($username)  
    {  
      $user = get_user_by_email($username);  
      if(!empty($user->user_login))  
          $username = $user->user_login;  
      return $username;  
    }  
    add_action('wp_authenticate','login_with_email_address');