Retiming of DSP programs for optimum vectorization

Vectorization of digital signal processing programs given in form of data-flow graphs (DFG) is treated. It is shown that for cyclic unit-rate graphs an inherent upper bound on the linear vectorization factor exists. Using the retiming transformation of the original graph this bound can be raised up to a transformation-independent bound which is in general not tight. The authors give a sufficient condition for efficient linear vectorization (vectorization approaching the bound) and propose a corresponding algorithm. As a side result, a useful theorem for retiming of strongly connected graphs is given.