High Level Synthesis

This paper presents an integer linear programming (ILP) model for the scheduling problem in high level synthesis. In addition to time-constrained scheduling and resource-constrained scheduling, a new scheduling problem called feasible scheduling is constructed, which provides a paradigm for exploring the solution space. Extensive consideration is given to the following applications: scheduling with: chaining; multicycle operations by nonpipelined function units; multicycle operations by pipelined function units; functional pipelining; loop folding; mutually exclusive operations; scheduling under bus constraint; minimizing lifetimes of variables. The complexity of the number of variables in the formulation is O(s . n ) where s and n are the number of control steps and operations, respectively. Since we use the as soon as possible (ASAP), as late as possible (ALAP), and list scheduling techniques to reduce the solution space, the formulation becomes very efficient. A solution to a practical problem, such as the fifth-order filter, can be found optimally in a few seconds.