1. A method of processing data communications events in a parallel active messaging interface (‘PAMI’) of a parallel computer, the parallel computer comprising a plurality of compute nodes that execute a parallel application, the PAMI comprising data communications endpoints, each endpoint comprising a specification of data communications parameters for a thread of execution on a compute node, including specifications of a client, a context, and a task, the compute nodes and the endpoints coupled for data communications through the PAMI and through data communications resources, the method comprising: determining by an advance function, the advance function comprising a member method of a context, the advance function executing in a thread of execution on a compute node, that there are no actionable data communications events pending for the context, placing by the advance function the thread into a wait state, waiting for a subsequent data communications event for the context; responsive to occurrence of a subsequent data communications event for the context, awakening by the thread from the wait state; and processing by the advance function the subsequent data communications event now pending for the context.