Runs a callback with error handling.

        .. versionchanged:: 6.0

           CancelledErrors are no longer logged.

def _run_callback(self, callback: Callable[[], Any]) -> None:
        """Runs a callback with error handling.

        .. versionchanged:: 6.0

           CancelledErrors are no longer logged.
        """
        try:
            ret = callback()
            if ret is not None:
                from tornado import gen

                # Functions that return Futures typically swallow all
                # exceptions and store them in the Future.  If a Future
                # makes it out to the IOLoop, ensure its exception (if any)
                # gets logged too.
                try:
                    ret = gen.convert_yielded(ret)
                except gen.BadYieldError:
                    # It's not unusual for add_callback to be used with
                    # methods returning a non-None and non-yieldable
                    # result, which should just be ignored.
                    pass
                else:
                    self.add_future(ret, self._discard_future_result)
        except asyncio.CancelledError:
            pass
        except Exception:
            app_log.error("Exception in callback %r", callback, exc_info=True)