Lower bounds on the iteration time and the number of resources for functional pipelined data flow graphs

An algorithm is presented to determine two lower bounds in functional pipelined data path synthesis. Given an iteration time constraint and a task initiation latency, the algorithm computes a lower bound on the number of functional units required to execute the data flow graph (DFG) of a loop body, and given a resource constraint and a task initiation latency the algorithm computes a lower bound on the number of time steps required to execute the DFG. The lower bounds not only greatly reduce the size of the solution space, but also provide a means to measure the proximity of the final solution to an optimal one. The bounds are computed in polynomial time; therefore the algorithm is very effective, especially for large DFGs. Experiments indicate that the lower bound is very tight. For all of the test cases the difference between our solution and the optimal solution is not greater than one