Resource constrained algebraic transformation for loop pipelining

Loop pipelining can be applied to a cyclic data-flow graph to reduce the iteration bound, which is the maximum computation-time-to-delay ratio among all the cycles in the data flow graph. Algebraic transformations can reduce the iteration bound substantially. However, resource constrained algebraic transformations for loop pipelining remains a hard problem because of the inherent nature of loop pipelining. In this paper, we propose a new method based on distribution graphs to solve this problem. A novel algorithm for algebraic transformation with resource constraints is provided, which works for non-pipelined schedules as well. Experimental results show that our algorithm is promising.