Cross-layer Optimized Placement and Routing for FPGA Soft Error Mitigation

1. Cross-layer Optimized Placement and Routing for FPGA Soft Error Mitigation Keheng Huang1,2, Yu Hu1, and Xiaowei Li1 1Key Laboratory of Computer System and ArchitectureInstitute of Computing Technology Chinese Academy of Sciences 2Graduate University of Chinese Academy of Sciences

2. Outline • Background • Motivation • Cross-layer optimized placement and routing • Experimental results • Conclusions

3. Background • Architecture of SRAM-based FPGAs

4. Background • Architecture of SRAM-based FPGAs Segments

5. Background • Architecture of SRAM-based FPGAs Segments

6. Background • Architecture of SRAM-based FPGAs • Configuration bits (>98% of all SRAM bits) • Routing resources (80% of configuration bits) • User bits (<2% of all SRAM bits) Segments • The reliability of routing resources needs to be seriously considered during placement and routing

7. Reliability Oriented EDA Flow Design specification • Application design level • Physical design level Synthesis and mapping • RoRA[TC’06] • TMR designs only Gate-level netlist • SEU-Aware P & R[ISQED’07] • Dimensions of bounding box • SEU-Aware Router [DAC’07] • Number of configuration bits Placement and routing • Reliability-aware P & R[ITC’10] • Dimensions of bounding box Bit Stream

8. Soft Error Rate (SER) SER evaluation criterion Application level factor (EPP) Propagation probability + Physical level factor • (Node error rate) Occurrence probability

9. Key Observation Prior P& R guidance criterion SER evaluation criterion Application level factor (EPP) All EPPs are equal? + Estimated SER Physical level factor • (Node error rate) Physical level factor (Bounding boxes, Configuration bits)

10. Key Observation • Application level factor (EPPs) varies significantly

11. Key Observation • Application level factor (EPPs) varies significantly

12. Cross-layer Optimized Placement and Routing • Overview

13. Cross-layer Optimized Placement and Routing • Overview

14. Cross-layer Optimized Placement and Routing • Overview

15. Cross-layer Optimized Placement and Routing • Overview

16. Cross-layer Optimized Placement and Routing • Overview

17. Cross-layer Optimized Placement and Routing • Overview

18. Cube-based EPP Analysis • Error propagation probability (EPP) • Monte Carlo simulation • Test vectors (high accuracy) • Traverse the design N times (high complexity) • Static analysis • Signal probability and error propagation rules (lower accuracy) • Traverse the design twice per fault (lower complexity)

19. Cube-based EPP Analysis • Error propagation probability (EPP) • Monte Carlo simulation • Test vectors (high accuracy) • Traverse the design N times (high complexity) • Static analysis • Signal probability and error propagation rules (lower accuracy) • Traverse the design twice per fault (lower complexity) • A method with high accuracy and low complexity?

20. Cube-based EPP Analysis • Besides 0 and 1, “X” bit is introduced • Introduce the cube and cover in logic synthesis • Covers adjoin V:(set union:∪) • Covers interface I:(set intersection: ∩) 0XX = {000,001,010,011} cube cover ={0XX, 1XX} adjoin :{00X} V {01X} = {0XX} interface: {00X} I {001} = {001}

21. Cube-based EPP Analysis • Forward traverse: compute the vectors that set the logic of the wire as 0 and 1 respectively

22. Cube-based EPP Analysis • Forward traverse: compute the vectors that set the logic of the wire as 0 and 1 respectively

23. Cube-based EPP Analysis • Forward traverse: compute the vectors that set the logic of the wire as 0 and 1 respectively • Backward traverse: compute the vectors that can propagate the fault to outputs

24. Cube-based EPP Analysis • Forward traverse: compute the vectors that set the logic of the wire as 0 and 1 respectively • Backward traverse: compute the vectors that can propagate the fault to outputs

25. Application level factor • Error propagation probability (EPP) • Compare with traditional Monte Carlo simulation • For each fault, traverse the design N times Ncare-cover: number of vectors stored in care-cover Ninputs: total number of input vectors

26. Application level factor • Comparison of computational complexity • N: number of input vectors • V: number of LUTs • E: number of interconnecting wires • g: number of configuration bits per LUT or wire • Cavg: average compression ratio of all covers

27. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

28. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

29. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

30. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

31. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

32. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

33. Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost SER cost= Phy cost * App cost

34. Cross-layer Optimized Routing • Finer granularity estimate of SER

35. Cross-layer Optimized Routing • Finer granularity estimate of SER

36. Cross-layer Optimized Routing • Finer granularity estimate of SER

37. Cross-layer Optimized Routing • Finer granularity estimate of SER

38. Cross-layer Optimized Routing • Finer granularity estimate of SER

39. Cross-layer Optimized Routing • Finer granularity estimate of SER

40. Experimental Setup MCNC benchmark set • Berkeley ABC mapper Logic resources: 4 6-input LUTs per CLB Routing channel width: 30% increase Gate-level netlist • VPR: Academic FPGA placement and routing tool Bit Stream

41. Experimental results • Comparison of EPP accuracy and run time • Monte Carlo simulation • DCOW: partial Monte Carlo simulation • Cube-based EPP analysis • Comparison of SER mitigation • Original VPR • Guided by physical level factor only (PPL) • Cross-layer optimized placement and routing algorithm (COPAR)

42. Comparison of EPP Accuracy and Run Time • Monte Carlo simulation (golden model) • DCOW: partial Monte Carlo simulation (DAC’10) • Cube-based analysis (our method) Ncube: number of test vectors computed by cube-based analysis Nsim: number of test vectors computed by Monte Carlo simulation Ninputs: total number of input vectors

43. Comparison of EPP Accuracy and Run Time

44. Comparison of EPP Accuracy and Run Time

45. Comparison of EPP Accuracy and Run Time

46. Comparison of SER Mitigation

47. Comparison of SER Mitigation 100% 93.53% 85.61%

48. Conclusions • Observe the gap between the SER evaluation criterion and guidance criterion for soft error mitigation (gini coefficient=0.646) • Introduce cube-based EPP analysis to compute the application level factor (gap<1%) • Propose a cross-layer optimized placement and routing algorithm (SER mitigation>14%)

49. Thank You for Your Attention • Question?