1. A computer system that employs a plurality of threads of execution to perform a parallel-execution operation in which the threads identify tasks dynamically and in which the computer system: A) provides a global status word that includes a separate status-word field associated with each of the threads; and B) so operates the threads that each thread: i) executes a task-finding routine to find tasks previously identified dynamically and performs tasks thereby found, with the status-word field associated with that thread containing an activity-representing value, until the task-finding routine finds no more tasks; ii) when the task-finding routine finds no more tasks, sets the contents of the status-word field associated with that thread to an inactivity-indicating value; iii) while the status-word field associated with any other thread contains an activity-indicating value, searches for a task and, if it finds one, sets the status-word field to the activity-indicating value before attempting to execute a task; and iv) if none of the status-word fields contains an activity-indicating value, terminates its performance of the parallel-execution operation.