1. A user-level read-copy update (RCU) method, comprising: establishing a user-level RCU subsystem that executes within threads of a user-level multithreaded application; said multithreaded application comprising one or more reader threads that read RCU-protected data elements in a shared memory; said multithreaded application comprising one or more updater threads that update said RCU-protected data elements in said shared memory; said reader threads and said updater threads being preemptible and comprising signal handlers that process signals; implementing a reader registration component in said RCU subsystem that registers said reader threads for RCU critical section processing, said reader registration component performing reader registration while said reader threads remain preemptible and with their signal handlers being operational; implementing a reader unregistration component in said RCU subsystem that unregisters said reader threads from RCU critical section processing, said reader unregistration component performing reader unregistration while said reader threads remain preemptible and their signal handlers are operational; and implementing a grace period detection component in said RCU subsystem that considers a registration status of said reader threads and determines when it is safe to perform RCU second-phase update processing to remove stale versions of updated data elements that are being referenced by said reader threads, or take other RCU second-phase update processing actions.