1. © 2005 Altera Corporation © 2006 Altera Corporation Placement and Timing for FPGAs Considering Variations Yan Lin 1, Mike Hutton 2 and Lei He 1 1 EE Department, UCLA 2 Altera Corporation, San Jose

2. © 2006 Altera Corporation 2 Outline Preliminaries and Motivation Timing with Guard-banding/Speed-binning Stochastic Placement Experimental Results Conclusions and Discussions

3. © 2006 Altera Corporation 3 Background Process variations  more and more significant in nanometer technology  affect timing and power in both ASICs and FPGAs Delay with variations  Variation sources Threshold voltage (V th ) and effective channel length (L eff )  Independent Gaussians for global/local variations  First order canonical form Related work  FPGA device and architecture evaluation with process variations [Wong et al, ICCAD’05]  SSTA [Chang et al, ICCAD ’ 03] [Viseswariah et al, DAC ’ 04]  Statistical criticality analysis [Viseswariah et al, DAC ’ 04] [Li et al, ICCAD ’ 05] [Xiong et al, TAU ’ 06]  Statistical gate sizing for ASICs [Guthaus et al, ICCAD ’ 05] [Sinha et al, ICCAD ’ 05]

4. © 2006 Altera Corporation 4 Motivation STA is inaccurate with variation  Slack ignores near criticality  Near-critical paths may be statistically timing critical Deterministic timing-driven placer (e.g. T-VPlace in VPR)  Based on STA  Optimize for static critical path  May not optimize timing with variation Stochastic placer is needed with variations  Same placement for one application across chips

5. © 2006 Altera Corporation 5 Pre-routing Interconnect Uncertainty vs. Process Variation in Placement Clearly, process variation leads to a more significant delay variance in placement stage  Therefore, only consider process variation for placement Existing timing- driven placer  Leverages timing slack in STA  With interconnect delay estimated  May incur uncertainty along with process variation

6. © 2006 Altera Corporation 6 Outline Preliminaries and Motivation Timing with Guard-banding/Speed-binning Stochastic Placement Experimental Results Conclusions and Discussions

7. © 2006 Altera Corporation 7 Uniqueness for Timing in FPGAs FPGAs vs. ASICs  Similarity Susceptible to process variations  Advantages Long switching paths dampen (average out) local variation Binned for speed-grades to isolate global variation Can be programmed repeatedly and differently during timing chip-test  Disadvantages Critical paths unknown at test time Same timing model to be applied to unknown applications at unknown clock frequency and varied conditions Guard-banded timing model can be arbitrarily conservative or aggressive

8. © 2006 Altera Corporation 8 Timing with Guard-banding A guard-band is applied for individual node to model uncertainty in STA A constant guard-banded delay is µ + cσ µ and σ are the nominal delay and standard deviation, respectively  c is constant for all circuit elements Guard-band cost (T grd /T norm )-1  T grd : critical path delay in STA w/ guard-banding  T norm : critical path delay in STA w/ nominal timing model  Pessimistic/optimistic for designs with longer/shorter critical path  Actual timing yield analyzed by SSTA

9. © 2006 Altera Corporation 9 Timing with Speed-binning Test and eliminate local variation by testing multiple similar paths across the test chip Model global variation Gaussians ΔX i as a single ΔG a Speed-binning = Categorizing ΔG a All chips fell into the same bin share the same guard- banded timing model  e.g., µ -σ g / µ +σ g / µ +3σ g for fast/medium/slow bin  STA for the circuit delay T bin for each bin

10. © 2006 Altera Corporation 10 Yield Analysis with Speed-binning Yield loss due to ignored local variation Yield loss due to unknown critical paths Timing yield analysis for a bin  circuit delay T µ +σ Tg ΔG a +σ Tl ΔR a  bin k [G low (k), G up (k) ]  cut-off delay γT bin (k)  timing yield for bin k is The overall timing yield is

11. © 2006 Altera Corporation 11 Outline Preliminaries and Motivation Timing with Guard-banding/Speed-binning Stochastic Placement Experimental Results Conclusions and Discussions

12. © 2006 Altera Corporation 12 Timing-Driven Placement T-VPlace [Marquardt et al, FPGA 2000] Simulated annealing based placement Both wiring and timing are considered in the cost function  Wiring cost  Timing cost for a connection for a placement solution  Overall cost STA is performed at each annealing temperature to update critical path delay and slack

13. © 2006 Altera Corporation 13 Stochastic Placement ST-VPlace Main differences between ST-VPlace and T-VPlace  Estimate delay matrix in canonical form instead of just nominal delay matrix Used in SSTA for statistical timing cost during placement  Perform SSTA instead of STA at each temperature in simulated annealing framework  Using statistical criticality instead of static criticality in cost function Statistical criticality for an edge/node is the probability that this edge/node is statistically timing critical in SSTA  Statistical criticality exponent θ Static criticality is based on slack and the longest path delay in STA

14. © 2006 Altera Corporation 14 Outline Preliminaries and Motivation Timing with Guard-banding/Speed-binning Stochastic Placement Experimental Results Conclusions and Discussions

15. © 2006 Altera Corporation 15 Experimental Settings Variation and device setting  10% as 3 sigma for global and local variation in V th and L eff at IRTS 65nm technology node  Min-ED device setting V dd =0.9v V th =0.3v [Wong et al, ICCAD ’ 05] Architecture similar to Altera ’ s Stratix TM  Island style FPGA architecture  cluster size 10 and LUT size 4  60% length-4 and 40% length-8 wire in interconnects  1.2X routing channel width obtained by T-VPlace Yield loss in failed parts per 10K parts (pp10K) Evaluated using MCNC and QUIP designs

16. © 2006 Altera Corporation 16 Cost Function Tuning Perform ST-VPlace and SSTA to obtain mean delay and standard deviation over all designs for each statistical criticality exponent θ θ=0.3 leads to the smallest mean and deviation  the highest timing yield

17. © 2006 Altera Corporation 17 T-VPlace vs. ST-VPlace Some correlation between mean delay and deviation ST-VPlace achieves  smaller mean delay for all designs  smaller variance for most designs   a higher timing yield

18. © 2006 Altera Corporation 18 Statistical Criticality vs. Static Criticality Statistic criticality vs. static criticality  Statistical criticality does not increase monotonically with static one  Statistical criticality may vary significantly with similar static one ST-VPlace considers statistical criticality explicitly  Optimizes near-critical paths under variations  Leads to a higher timing yield

19. © 2006 Altera Corporation 19 Impact on Path-length Distribution Path-length distribution in ST-VPlace is almost on top of that in T-VPlace ST-VPlace reduces top 10% near-critical paths from 1.3% to 0.8%  Although has a larger nominal delay  But has a smaller mean and variance  a higher timing yield

20. © 2006 Altera Corporation 20 Effect of Guard-banding Variation (3sigma) global 5% local 5% 0% 20% 40% 60% 80% 100% 120% 01234 Guard-band factor Guard-band cost 0.1 1.0 10.0 100.0 1000.0 10000.0 Yield loss (pp10k) guard-band cost T-Vplace yield lost STV-Place yield lost Variation (3sigma) global 20% local 20% 0% 20% 40% 60% 80% 100% 120% 01234 Guard-band factor Guard-band cost 0.1 1.0 10.0 100.0 1000.0 10000.0 Yield loss (pp10k) guard-band cost T-Vplace yield lost ST-VPlace yield lost ST-VPlace obtains a higher timing yield under varied variations and guard-band factors  Larger gain with smaller variation

21. © 2006 Altera Corporation 21 Effect of Guard-banding Variation (3sigma) global 5% local 5% 0% 20% 40% 60% 80% 100% 120% 01234 Guard-band factor Guard-band cost 0.1 1.0 10.0 100.0 1000.0 10000.0 Yield loss (pp10k) guard-band cost T-Vplace yield lost STV-Place yield lost Variation (3sigma) global 20% local 20% 0% 20% 40% 60% 80% 100% 120% 01234 Guard-band factor Guard-band cost 0.1 1.0 10.0 100.0 1000.0 10000.0 Yield loss (pp10k) guard-band cost T-Vplace yield lost ST-VPlace yield lost ST-VPlace obtains a higher timing yield under varied variations and guard-band factors  Larger gain with smaller variation  Similar gain with varied local variation when no global variation is considered Yeild loss reduced by 3.4X with 3 sigma guard-banding under 10%/10% variations

22. © 2006 Altera Corporation 22 Effect of Speed-binning Fast/Medium/Slow = 40%/30%/29.999% Discard the slowest 0.001% (0.1pp10K) chips T bin may be relaxed by γ for a higher timing yield Yield loss due to local variation and unknown critical paths ST-VPlace consistently achieves higher timing yield Yield loss is reduced by 25X with γ=5%

23. © 2006 Altera Corporation 23 Conclusions and Discussions Conclusions  Quantified the effects of guard-banding and speed- binning with variations  Developed a novel stochastic placer  Evaluated with MCNC and QUIP designs, reduced yield loss by 3.4X with guard-banding 25X with speed-binning Ongoing and future work  Extend timing models with spatial correlated variations  Develop stochastic physical synthesis algorithms, e.g., clustering, routing, re-timing