1. FPGA Logic Cluster Design Dr. Philip Brisk Department of Computer Science and Engineering University of California, Riverside CS 223

2. How Much Logic Should Go in an FPGA Logic Block? Vaughn Betz, Jonathan Rose IEEE Design & Test of Computers 15(1): 10-15 (1998)

3. Three Questions How many inputs should the FPGA routing provide to a cluster of LUTs? (I) – Routing flexibility vs. area As the number of LUTs in a logic cluster changes, how should the FPGA’s routing architecture change? (F c ) How many LUTs should be included in a cluster? (N)

4. Experimental Methodology 20 MCNC Benchmarks – Well-established – A bit old, even by 1998 standards – Sadly, still in use 4-LUT Architecture F s = 3 – Vary other parameters to see what works best

5. Area Model Count the number of min-width transistors required to implement a benchmark circuit in an FPGA architecture Normalized Area (Num min-width transistors used) / (Num BLEs used)

6. How many cluster inputs do we need? We hit near 100% utilization when I = 50-60% of the total number of BLE inputs We can pack BLEs together to share common inputs Re-use locally generated outputs Works because the packing algorithm was effective! Input sharing and output re-use within a logic cluster

7. Visual Depiction I = ~0.6KN is pretty good Use the feedbacks! Fanout

8. The Packer was Effective! It packed BLEs together to share common inputs It re-use locally generated outputs via the feedbacks

9. Cluster inputs vs. Cluster size Approx. (2N + 2) N = 1 BLE uses 3.5/4 inputs (on average) N = 16 BLEs uses 19.7 / 64 inputs, on average

10. Commercial FPGAs Altera Flex 8000 FPGA uses a cluster of size N=8 with I=24 – Results suggest to reduce I to 18 (save area) Xilinx 5200 FPGA uses a cluster of size N=4 with I=16 – Results suggest to reduce I to 10 (save area)

11. Routing Flexiblity vs. Cluster Size Set F c = W/N – Each routing track is driven by one LUT output pin in the cluster

12. Area Efficiency vs. Cluster Size I is set to achieve 98% logic utilization N=2 BLEs introduces intra-cluster routing Reduce routing between logic blocks Area efficiency rapidly degrades beyond this point

13. Conclusions I = 2N + 2 for N < 16 – Slow, linear growth Reduce F c – Works because LUT inputs are equivalent Cluster area efficiency is within 10% for 1 < N < 8 Large clusters reduce the size of the placement problem and increase FPGA speed

14. The Effect of LUT and Cluster Size on Deep-Submicron FPGA Performance and Density Elias Ahmed, Jonathan Rose IEEE Transactions on VLSI Systems 12(3): 288-298 (2004)

15. Contributions Vary LUT size (K) from 2 to 7 Vary cluster size (N) from 1 to 10 LUTs – Experimentally determine the number of cluster inputs (I) as a function of K and N – Clustering small LUTs (K=2,3) produces good area results, but bad performance (~2x worse) – LUTs of size (K=4,5,6), clusters of size (N=3…10) yield the best area-delay product

16. CAD Flow

17. Inputs Req.’d for 98% Area Utilization I = ½K(N+1)

18. Total Area LUT sizes of K = 4,5 are the most area efficient for all cluster sizes Reduction in total area as cluster size increases from 1-3 for all LUT sizes As clusters are made larger (N > 4) there is little impact on total FPGA area Intra-cluster routing area is 25-35% of the total area

19. Total Intra-cluster Routing Area The increase in cluster size far outweighs the rate of decrease in the number of clusters: hence the upward trend

20. #Clusters and Area/Cluster vs. K 25-35% N = 1 BLE per Cluster

21. LUT area vs. Intra-cluster Mux Area Intra-cluster routing area is 25- 35% of logic cluster area LUT area dominates

22. Intra-cluster Routing Area as a Function of LUT Size Total intra-cluster routing area decreases near-linearly from K = 3 to 7

23. Total Intra-cluster Routing Area The product of these two curves gives the total inter-cluster routing area. Routing area decreases linearly with LUT size Increasing LUT sizes decreases the number of clusters used faster than the rate of increase in routing area per cluster Depends on good CAD tools

24. Critical Path Delay vs. LUT Size Increasing both N and K has a positive effect Benefits saturate as N and K get large As N and K increase LUT delay and the delay through a single cluster increases The number of LUTs and clusters in series on the critical path decreases Reduced global routing delay

25. Intra-cluster Delay vs. LUT Size Intra-cluster delay decreases as K increases Reduction in number of BLE levels on critical path Intra-cluster delay increases as N increases Larger intra-cluster cluster muxes are slower The delay through these muxes is still much faster than global routing delay

26. BLE Delay vs. K BLE delay increases linearly as K increases (intuitive) Number of BLEs on the critical path decreases quadratically as K increases Fewer, but larger, BLEs

27. Global Routing Delay vs. K As K increases Fewer LUTs on the critical path Fewer global routing links As N increases More opportunities to use faster intra-cluster routing

28. Critical Path Delay (K = 4) K remains constants – No reduction in number of BLEs on critical path N increases – BLE and intra-cluster routing delay increase – More logic implemented internally within clusters – Can use faster intra-cluster routing instead of global routing

29. Critical Path Delay vs. LUT Size (Recap) Increasing N beyond 3 has minimal effects Limited effectiveness of clustering Architectural weakness? Semi-effective CAD tools?

30. Number of Logic Clusters on Critical Path The number of logic levels decrease with increasing N and K For a given K, most of the reduction is from N = 1 to 3 The majority of the critical path delay was reduced in this range Increasing N is less effective when K is large

31. BLE Fanout vs. LUT Size Smaller LUTs have better response to increasing N because each LUT has a relatively small fanout Adding an extra BLE to the cluster guaranteed some reduction in the number of logic levels Larger LUTs have larger average fanout Harder to ensure that increasing N will result in fewer cluster levels on the critical path

32. Area-Delay Product Large Delays Many BLEs on critical path Slightly larger area requirement Large area cost for K=7 outweighs marginal delay improvement

33. Caveats Quality of CAD tools Mix of benchmark circuits Limited exploration of routing parameter design space – Parameters were derived from N = K = 4

34. Best Overall Results and Summary To achieve 98% LUT utilization, set I = ½K(N+1) Small LUT sizes are not area efficient and have poor performance characteristics Future challenges – Reduce number of BLEs on critical path without resorting to larger LUTs – Reduce intra-cluster routing delays