1. Stochastic Physical Synthesis for FPGAs with Pre-routing Interconnect Uncertainty and Process Variation Yan Lin and Lei He EE Department, UCLA http://eda.ee.ucla.edu Partially supported by NSF and UC Micro sponsored by Actel

2. Motivation  Variations Pre-routing interconnect uncertainty Process variation  Impact Any near-critical paths  statistically timing critical STA ignores near-criticality  Related work for FPGAs Chipwise placement [Cheng, FPL’06] Stochastic placement [Lin, FPL’06] Stochastic routing [Sivaswamy, FPGA’07] Stochastic physical synthesis and the interaction have not been studied for FPGAs

3. Outline  Preliminaries  Stochastic Clustering  Stochastic Placement  Stochastic Routing  Interaction between Clustering, Placement and Routing  Conclusions

4. Model of Variations  Pre-routing interconnect uncertainty modeled as independent Gaussian distribution Standard deviation estimated with post-routing delay distribution  Again, Gaussian models for process variations Threshold voltage (V th ) Effective channel length (L eff ) Model these variation sources as independent Gaussians

5. Model of Variations  Pre-routing interconnect uncertainty modeled as independent Gaussian distribution Standard deviation estimated with post-routing delay distribution  Again, Gaussian models for process variations Threshold voltage (V th ) Effective channel length (L eff ) Model these variation sources as independent Gaussians models process variation models interconnect uncertainty are standard deviations  Delay with variations First order canonical form

6. Synthesis Flow

11. Experimental Settings  Variation and device setting 10%/10%/6% as 3 sigma for global/spatial/local variation in V th and L eff IRTS 65nm technology node  Island style FPGA architecture Cluster size 10 and LUT size 4 60% length-4 and 40% length-8 wire in interconnects  Yield loss in failed parts per 10K parts (pp10K) 2.5 sigma guard-banded delay as the cut-off delay Evaluated using MCNC designs

12. Outline  Preliminaries  Stochastic Clustering  Stochastic Placement  Stochastic Routing  Interaction between Clustering, Placement and Routing  Conclusions

13.  With statistical criticality Better seed BLE selection Better candidate BLE selection for the current cluster Stochastic Clustering ST-VPack  Based on T-VPack [Betz, FPGA book] An iterative approach  Select a seed BLE for a new cluster  Pack BLE into the current cluster STA with constant delay model to calculate slack  ST-VPack performs SSTA Statistical criticality of an edge/node is the probability of this edge/node being timing critical with variations  Statistical timing cost of BLE B

14. The Impact of the Combination of Two Uncertainty Sources  Timing gain mainly due to modeling interconnect uncertainty Modeling interconnect uncertainty leads to a better delay distribution than process variation Considering both does not have much further gain Process variation Interconnect uncertainty Both 0% 10%20%10%20% 10%20%0.0 10% Tmean22.522.621.621.521.821.7 Tsigma3.353.363.263.243.203.19

15. Interconnect Uncertainty vs. Process Variation in Clustering  Clearly, interconnect uncertainty leads to a more significant delay variance in clustering With process variation With interconnect uncertainty

16. Comparison between T-VPack and ST-VPack  ST-VPack on average reduces mean delay by 5.0% (up to 13.0%) standard deviation by 6.4% (up to 31.8%) yield loss from 50pp10K to 9pp10K  In addition, ST-VPack has virtually no wire length, area and runtime overhead

17. Outline  Motivation and Background  Stochastic Clustering  Stochastic Placement  Stochastic Routing  Interaction between Clustering, Placement and Routing  Conclusions

18. Pre-routing Interconnect Uncertainty vs. Process Variation in Placement  Clearly, process variation leads to a more significant delay variance in placement Only considering process variation is sufficient With process variation With interconnect uncertainty

19. Stochastic Placement ST-VPlace  Stochastic placement developed in [Lin, FPL’06] Based on T-VPlace [Marquardt, ISFPGA ’ 00] Replace SSTA with STA Replace statistical criticality with static criticality  Main improvement Consider spatially correlated variation with PCA

20. Comparison between T-VPlace and ST-VPlace  ST-VPlace on average reduces mean delay by 4.0% (up to 14.2%) standard deviation by 6.1% (up to 22.7%) yield loss from 50pp10K to 12pp10K virtually no wire overhead  On the other hand, ST-VPlace takes 3.1X runtime

21. Outline  Preliminaries  Stochastic Clustering  Stochastic Placement  Stochastic Routing  Interaction between Clustering, Placement and Routing  Conclusions

22. Stochastic Routing ST-PathFinder  Based on PathFinder [Betz, FPGA book] An iterative maze router, w/ congestion allowed Considering both timing and wiring costs  Interconnect estimation in routing Occurs when predicting delay to the target sink Has the highest accuracy  ST-PathFinder performs SSTA The new statistical cost function for node n is better tradeoff between timing and wiring costs

23. Comparison between PathFinder and ST-PathFinder  ST-PathFinder on average reduces mean delay by 1.4% (up to 7.8%) standard deviation by 0.7% (up to 5.2%) yield loss from 50pp10K to 35pp10K no runtime overhead  ST-PathFinder also reduces wire length by 4.5% on average

24. Outline  Preliminaries  Stochastic Clustering  Stochastic Placement  Stochastic Routing  Interaction between Clustering, Placement and Routing  Conclusions

25. Interaction between Clustering, Placement and Routing  The stochastic flow reduces yield loss from 50 to 5, but 3.0X runtime  Timing gain mainly due to clustering and placement, but w/ overlap  Stochastic clustering + deterministic P&R is a good flow Significant timing gains and slightly less runtime clusterDSDDSSDS PlacerDDSDSDSS RouterDDDSDSSS Tnorm21.2-3.7%-3.3%-1.4%-6.4%-4.1%-3.6%-6.3% Tmean22.9-5.0%-4.0%-1.4%-5.9%-4.7%-4.0%-6.2% Tsigma2.4-6.4%-6.1%-0.7%-8.8%-6.1%-6.3%-7.5% Yield loss50.29.311.835.25.310.311.05.4 runtime1X0.99X3.1X0.96X3.0X0.97X3.1X3.0X Wire1X0.8%1.3%-4.5%3.2%-3.4% -1.6%  Deterministic clusterer, placer + stochastic router is a good flow Significant wiring gains and less runtime

26. Conclusions  The timing gain mainly due to clusterer and placer modeling interconnect uncertainty for clustering considering process variation for placement  The stochastic flow reduces yield loss from 50 to 5pp10K mean delay by 6.2%, standard deviation by 7.5% but takes 3X runtime  Deterministic clusterer, placer + stochastic router reduces wire length by 4.5% also runs slightly faster than deterministic flow  Stochastic clusterer + deterministic P&R reduces yield loss from 50 to 9pp10K mean delay by 5.0%, standard deviation by 6.4% also runs slightly faster than deterministic flow