Pipelining: just another transformation

A simple formulation of pipelining: 'Pipelining with N stages is equivalent to retiming where the number of delays on all inputs or all outputs, but not both, is increased by N' is used as the basis for a convenient and efficient treatment of pipelining in design of application specific computers. Classification of pipelining according to the optimization goal (throughput and resource utilization) and the latency is introduced. For polynomial complexity pipelining classes, optimal algorithms are presented. For other classes both proof of NP-completeness and efficient probabilistic algorithms are presented. Both theoretical and experimental properties of pipelining are discussed. In particular, a relationship with other transformations is explored. Due to close relationship between software pipelining and pipelining presented, all results can be easily modified for use in compilers for general purpose computers. Also, as a side result, the exact bound (solution) for iteration bound is derived.<>