WP custom login functions

/* Main redirection of the default login page */
function redirect_login_page() {
    $login_page  = home_url('/login/');
    $page_viewed = basename($_SERVER['REQUEST_URI']);

    if($page_viewed == "wp-login.php" && $_SERVER['REQUEST_METHOD'] == 'GET') {
        wp_redirect($login_page);
        exit;
    }
}
add_action('init','redirect_login_page');

/* Where to go if a login failed */
function custom_login_failed() {
    $login_page  = home_url('/login/');
    wp_redirect($login_page . '?login=failed');
    exit;
}
add_action('wp_login_failed', 'custom_login_failed');

/* Where to go if any of the fields were empty */
function verify_user_pass($user, $username, $password) {
    $login_page  = home_url('/login/');
    if($username == "" || $password == "") {
        wp_redirect($login_page . "?login=empty");
        exit;
    }
}
add_filter('authenticate', 'verify_user_pass', 1, 3);

/* What to do on logout */
function logout_redirect() {
    $login_page  = home_url('/login/');
    wp_redirect($login_page . "?login=false");
    exit;
}
add_action('wp_logout','logout_redirect');