Synchronization of pipelines

A recently formulated general timing model of synchronous operation is applied to the special case of latch-controlled pipelined circuits. The model accounts for multiphase synchronous clocking, correctly captures the behavior of label-sensitive latches, handles both short- and long-path delays, accommodates wave pipelining, and leads to a comprehensive set of timing constraints. Concurrency of pipeline circuits is defined as a function of the clock schedule and degree of wave pipelining. The authors then identify a special class of clock schedules, coincident multiphase clocks, which provide a lower bound on the value of the optimum cycle time. It is shown that the region of feasible solutions for single-phase clocking can be nonconvex or even disjoint, and a closed-form expression for the minimum cycle time of a restricted but practical form of single-phase clocking is derived. The authors compare these forms of clocking on three pipeline examples and highlight some of the issues in pipeline synchronization