Fig. 6.15. Variation with number of operations of execution time for 200 graphs (heuristic and ILP solutions)

6.6 Summary

This chapter has presented work addressing the problem of architectural synthesis for multiple word-length systems. It has been demonstrated that the traditional architectural synthesis problems of operation scheduling, resource allocation, and resource binding, can be significantly complicated by the presence of multiple word-length arithmetic.

An Integer Linear Programming (ILP) construction for the multiple wordlength architectural synthesis problem has been formulated. The ILP formulation provides solutions which are optimal with respect to the area-based cost function, but su ers from long run-times which scale up rapidly with relaxation of the latency constraint.

A heuristic solution has been developed based on intertwined scheduling, resource binding / word-length selection, and word-length refinement. This involves techniques for scheduling with incompletely defined word-length information, combining binding and word-length selection, and latency-based word-length refinement based on critical path analysis.

The results from an implementation of both the ILP and the heuristic approach show that significant improvements to system area can be made

148 6 Scheduling and Resource Binding

by allowing non-critical operations to share large word-length resources. The heuristic solution has been shown to be within 16% of the optimal area, over a range of minimum-latency problem sizes for which a three orders of magnitude speedup over an ILP solver has been achieved. For non-minimum-latency problems, the execution speedup is even greater.