def connect(
        self: _IOStreamType, address: tuple, server_hostname: str = None
    ) -> "Future[_IOStreamType]":
        """Connects the socket to a remote address without blocking.

        May only be called if the socket passed to the constructor was
        not previously connected.  The address parameter is in the
        same format as for `socket.connect <socket.socket.connect>` for
        the type of socket passed to the IOStream constructor,
        e.g. an ``(ip, port)`` tuple.  Hostnames are accepted here,
        but will be resolved synchronously and block the IOLoop.
        If you have a hostname instead of an IP address, the `.TCPClient`
        class is recommended instead of calling this method directly.
        `.TCPClient` will do asynchronous DNS resolution and handle
        both IPv4 and IPv6.

        If ``callback`` is specified, it will be called with no
        arguments when the connection is completed; if not this method
        returns a `.Future` (whose result after a successful
        connection will be the stream itself).

        In SSL mode, the ``server_hostname`` parameter will be used
        for certificate validation (unless disabled in the
        ``ssl_options``) and SNI (if supported; requires Python
        2.7.9+).

        Note that it is safe to call `IOStream.write
        <BaseIOStream.write>` while the connection is pending, in
        which case the data will be written as soon as the connection
        is ready.  Calling `IOStream` read methods before the socket is
        connected works on some platforms but is non-portable.

        .. versionchanged:: 4.0
            If no callback is given, returns a `.Future`.

        .. versionchanged:: 4.2
           SSL certificates are validated by default; pass
           ``ssl_options=dict(cert_reqs=ssl.CERT_NONE)`` or a
           suitably-configured `ssl.SSLContext` to the
           `SSLIOStream` constructor to disable.

        .. versionchanged:: 6.0

           The ``callback`` argument was removed. Use the returned
           `.Future` instead.

        """
        self._connecting = True
        future = Future()  # type: Future[_IOStreamType]
        self._connect_future = typing.cast("Future[IOStream]", future)
        try:
            self.socket.connect(address)
        except socket.error as e:
            # In non-blocking mode we expect connect() to raise an
            # exception with EINPROGRESS or EWOULDBLOCK.
            #
            # On freebsd, other errors such as ECONNREFUSED may be
            # returned immediately when attempting to connect to
            # localhost, so handle them the same way as an error
            # reported later in _handle_connect.
            if (
                errno_from_exception(e) not in _ERRNO_INPROGRESS
                and errno_from_exception(e) not in _ERRNO_WOULDBLOCK
            ):
                if future is None:
                    gen_log.warning(
                        "Connect error on fd %s: %s", self.socket.fileno(), e
                    )
                self.close(exc_info=e)
                return future
        self._add_io_state(self.io_loop.WRITE)
        return future