Adds an `.IOLoop` event handler to accept new connections on ``sock``.

    When a connection is accepted, ``callback(connection, address)`` will
    be run (``connection`` is a socket object, and ``address`` is the
    address of the other end of the connection).  Note that this signature
    is different from the ``callback(fd, events)`` signature used for
    `.IOLoop` handlers.

    A callable is returned which, when called, will remove the `.IOLoop`
    event handler and stop processing further incoming connections.

    .. versionchanged:: 5.0
       The ``io_loop`` argument (deprecated since version 4.1) has been removed.

    .. versionchanged:: 5.0
       A callable is returned (``None`` was returned before).

def add_accept_handler(
    sock: socket.socket, callback: Callable[[socket.socket, Any], None]
) -> Callable[[], None]:
    """Adds an `.IOLoop` event handler to accept new connections on ``sock``.

    When a connection is accepted, ``callback(connection, address)`` will
    be run (``connection`` is a socket object, and ``address`` is the
    address of the other end of the connection).  Note that this signature
    is different from the ``callback(fd, events)`` signature used for
    `.IOLoop` handlers.

    A callable is returned which, when called, will remove the `.IOLoop`
    event handler and stop processing further incoming connections.

    .. versionchanged:: 5.0
       The ``io_loop`` argument (deprecated since version 4.1) has been removed.

    .. versionchanged:: 5.0
       A callable is returned (``None`` was returned before).
    """
    io_loop = IOLoop.current()
    removed = [False]

    def accept_handler(fd: socket.socket, events: int) -> None:
        # More connections may come in while we're handling callbacks;
        # to prevent starvation of other tasks we must limit the number
        # of connections we accept at a time.  Ideally we would accept
        # up to the number of connections that were waiting when we
        # entered this method, but this information is not available
        # (and rearranging this method to call accept() as many times
        # as possible before running any callbacks would have adverse
        # effects on load balancing in multiprocess configurations).
        # Instead, we use the (default) listen backlog as a rough
        # heuristic for the number of connections we can reasonably
        # accept at once.
        for i in range(_DEFAULT_BACKLOG):
            if removed[0]:
                # The socket was probably closed
                return
            try:
                connection, address = sock.accept()
            except socket.error as e:
                # _ERRNO_WOULDBLOCK indicate we have accepted every
                # connection that is available.
                if errno_from_exception(e) in _ERRNO_WOULDBLOCK:
                    return
                # ECONNABORTED indicates that there was a connection
                # but it was closed while still in the accept queue.
                # (observed on FreeBSD).
                if errno_from_exception(e) == errno.ECONNABORTED:
                    continue
                raise
            set_close_exec(connection.fileno())
            callback(connection, address)

    def remove_handler() -> None:
        io_loop.remove_handler(sock)
        removed[0] = True

    io_loop.add_handler(sock, accept_handler, IOLoop.READ)
    return remove_handler