1. ECE 506 Reconfigurable Computing http://www.ece.arizona.edu/~ece506 Lecture 6 Clustering Ali Akoglu

2. Before Placement: Clustering °Intra-cluster connections: fast °Inter-cluster connections: slow Need to pack BLEs °Goals: Reduce stress on routing Take advantage of local fast interconnect Reduce inter-cluster wiring Minimize critical path (timing- driven) °How do we do this Take advantage of cluster architecture °Tradeoffs

3. Basic Clustering (Betz) °How many distinct inputs should be provided to a cluster of N 4-LUTs? °How many 4 LUTs should be included in a cluster to create the most area-efficient logic block?

4. VPACK

5. Basic Clustering (Betz) °Flow Iterate until all BLEs consumed Start new cluster by selecting a random BLE -select the currently unclustered BLE with the most used inputs, Add BLE with most shared inputs with current cluster to cluster -to minimize the number of inputs that must be routed to each cluster. Keep adding until either cluster full or input pins used up Hill climbing – if some cluster BLEs unused -Add another BLE even if cluster input count temporarily overflowed -If input count not eventually reduced select best choice from before hill climbing

6. Logic Utilization

7. Number of Inputs per Cluster Lots of opportunities for input sharing in large clusters (Betz – CICC’99) Reducing inputs reduces the size of the device and makes it faster. Most FPGA devices (Xilinx, Lucent) have 4 BLE per cluster with more inputs than actually needed.

8. TVPACK

9. Architecture Modeling Tri-state buffer and pass transistor distribution Cluster Size vs. Routing resources (Tile size) Transistor and Buffer Scaling based on segment length Flexibility of Switches (Fc=W for large cluster size is a waste?)

10. Logic Cluster Structure

11. Timing-Driven Clustering – T-VPACK °Optimization goals of VPack Pack each cluster to its capacity -Minimize number of clusters Minimize number of inputs per cluster -Reduce the number of external connections

12. Timing-Driven Clustering – T-VPACK °Optimization goal of T-VPack Minimize number of external connections on critical path Why? -External connections have higher delay and internal connections -Reducing number of external nets on critical path will reduce delay

13. Timing-Driven Clustering – T-VPACK °First stage Identify connections that are on the critical path °Second Stage Pack BLEs sequentially along the critical path Recompute criticality of remaining BLEs

14. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4

15. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 Arrival Times

16. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 3 3 1 Arrival Times

17. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7 7 Arrival Times

18. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7 7 13 15 14 Arrival Times

19. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7 7 13 15 14 18 22 18 Arrival Times

20. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7 7 13 15 14 22/22 18/22 arrival time/required time

21. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7 / 15 7 13 14/ 18 22/22 18/22 15 / 15 arrival time/required time

22. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7/ 13 13 14 / 18 22/22 18/22 15 / 15 7 / 15 arrival time/required time

23. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 9 7/ 13 13 / 15 14 / 18 22/22 18/22 15 / 15 7 / 15 arrival time/required time

24. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 3 1 7 / 9 9 / 9 7/ 13 13 / 15 14 / 18 22/22 18/22 15 / 15 7 / 15 arrival time/required time

25. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 0 0 1 / 5 3 / 3 1 / 9 7 / 9 9 / 9 7/ 13 13 / 15 14 / 18 22/22 18/22 15 / 15 7 / 15 arrival time/required time

26. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 / 4 0 / 0 0 / 8 1 / 5 3 / 3 1 / 9 7 / 9 9 / 9 7/ 13 13 / 15 14 / 18 22/22 18/22 15 / 15 7 / 15 Slack = required time - arrival time

27. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 4 0 8 4 0 8 2 0 6 2 4 0 4 4 0 8 Slack = required time - arrival time

28. Slack and Criticality Calculation PO1 PO2 PO3 PI1 PI2 PI3 1 3 1 4 6 4 6 6 5 5 7 4 0 / 4 0 / 0 0 / 8 1 / 5 3 / 3 1 / 9 7 / 9 9 / 9 7/ 13 13 / 15 14 / 18 22/22 18/22 Critical Path 18/22 15 / 15 7 / 15

29. Timing-Driven Clustering – T-VPACK °Cost metric now considers both connectivity and timing criticality °Perform an analysis of criticality at beginning considering all wires to be inter-cluster °Determine “Base” BLE criticality

30. Base Criticality

31. How to break ties? °Initially, many paths may have the same number of BLEs °Include “tie-breaking” in performance cost function

32. Results for T-VPACK versus VPACK Why does the gap between VPack and T-VPack increase as N increases?

33. Results for T-VPACK versus VPACK °T-VPack prefers to cluster a BLE with BLEs that are in its fan-in or fan-out °VPack favors input sharing °T-VPack completely absorbs many low-fanout nets Fewer nets to route!

34. Results for T-VPACK versus VPACK Why does area-delay product show an increasing trend beyond cluster size of 10?

35. Results for T-VPACK versus VPACK °Increased number of nets that are completely absorbed by T-Vpack °Area- delay product Cluster size 7-10 best choice (36-34% better than N=1) °N=7 vs N=1 30% less delay, 8% les area

36. Results for T-VPACK, DELAY !!! Why do we see a circuit speedup?

37. Results for T-VPACK, DELAY !!! 18% 40% °Intra-cluster: Fast, Inter-cluster: Slow ! °As N increases Number of internal connections on the critical path increase Number of external connections on the critical path decrease

38. Why are inter-cluster connections becoming faster? Reduction in Number of external connections (internal connections are faster) External connections on the critical path are becoming faster Reduction in routing requirements

39. Drawback of VPack and T-VPack