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1 ITC-07 Paper 26.110/25/2007 Estimating Stuck Fault Coverage in Sequential Logic Using State Traversal and Entropy Analysis Soumitra Bose Design Technology,

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Presentation on theme: "1 ITC-07 Paper 26.110/25/2007 Estimating Stuck Fault Coverage in Sequential Logic Using State Traversal and Entropy Analysis Soumitra Bose Design Technology,"— Presentation transcript:

1 1 ITC-07 Paper 26.110/25/2007 Estimating Stuck Fault Coverage in Sequential Logic Using State Traversal and Entropy Analysis Soumitra Bose Design Technology, Intel Corp. Folsom, CA 95630 Vishwani D. Agrawal Dept. of ECE, Auburn University Auburn, AL 36849

2 2 ITC-07 Paper 26.110/25/2007 Outline Problem & Approach Background State Sequence Analysis Entropy Analysis Algorithm Implementation Results Conclusion

3 3 ITC-07 Paper 26.110/25/2007 Problem and Approach Problem –Coverage estimation algorithms inaccurate due to iterative array model. –This results in optimistic estimates, particularly for hard to test designs and when insufficient test vectors are available. Approach –Use state graph instead of iterative array model. –Reduce size of graph by entropy analysis.

4 4 ITC-07 Paper 26.110/25/2007 Background Approximate fault simulation –Per-vector analysis Critical path tracing (CPT), Abramovici et al., IEEE D&T 1984. Necessary conditions, Akers et al., ITC 1990. –Post-simulation analysis, Stafan, Jain and Agrawal, IEEE-D&T 1985. Dominator analysis in ATPG, Kirkland and Mercer, ITC 1987. Fault detection at fanout stem depends on signal states in this part and the observability of the dominator. Fanout stem Dominator

5 5 ITC-07 Paper 26.110/25/2007 Stafan: A Tutorial Example 11001 00110 00000 C0=0.4 C1=0.6 C0=1.0 C1=0.0 C0=0.6, C1=0.4 S=0.6 C0=0.4 C1=0.6 S=1.0 C0=0.4, C1=0.6 (controllabilities) S=0.4 (sensitization count) sa1 sa0 sa1 Detected faults Incorrectly detected faults OB0=1.0 OB1=1.0 OB0=0.0 OB1=1.0 OB0=1.0, OB1=0.0 (observabilities) OB0=1.0 OB1=1.0 OB0=1.0, OB1=0.0 pd: Prob(sa0 detected) = C1 × OB1, Prob(sa1 detected) = C0 × OB0 Threshold detection by N vectors: PD(N) = 1 – (1 – pd) N ≥ 0.5

6 6 ITC-07 Paper 26.110/25/2007 Sequential Logic: Iterative Array Model Fix-point evaluation: (1) Find observabilities at POs from latch outputs While latch observabilities change { assign latch input observabilities from latch outputs propagate observabilties from latches across combinational frame } Observability(i) = Detectability(i) + Observability(i+1) (i-1) (i) (i+1) last frame

7 7 ITC-07 Paper 26.110/25/2007 Motivation: Sequential Logic Example G6 000 001 010 100 011 010 110 100 G3 G4 G5 G7 G8 G10 G9 G11 sa0 Assumptions: (1) G11=1 initially. (2) Gate input states are stored (ITC 2006). (3) Iterative array model used. 101 Non-zero 0-observability at G9 => non-zero 1-observabilty at G11. Iterative array model implies G10 sa0 fault is detectable. Cause for error: Stafan Does not remember G11 = 1 in first vector.

8 8 ITC-07 Paper 26.110/25/2007 State Sequence Analysis - I (1) Remember preceding states while performing simulation. (2) However, state graph may be too big (max = number of vectors). (3) Collapse states to minimize graph size. States: (f1,f2,f3) Inputs: (i1,i2) 011 001 110 000 111 100 010 101 11 0*,11 10 01 11 00 10 01 00 01 1* 10 1* Collapse variable f3: (1) Merge states{011,010}. (2) Merge states {001,110}. (3) Original transitions: {1*, 11, 10} (4) New transitions: {1*0,101,111} = {10*,11*}

9 9 ITC-07 Paper 26.110/25/2007 State Sequence Analysis - II 01 00 10 11 10*,11* 1*1,0*1 0*0 0** State: (f1, f2) Inputs: (i1,i2,f3) 011 001 110 000 111 100 010 101 11 0*,11 10 01 11 00 10 01 00 01 1* States: (f1,f2,f3) Inputs: (i1,i2) 10 1* Result of collapsing f3: transitions from {010,010} to {001,000} : {1*, 11, 10} -> { 10*, 11*}

10 10 ITC-07 Paper 26.110/25/2007 Entropy Analysis State graph minimization done by entropy analysis Definition:   1,0 2 ))((log).()= -( i ii spspsH 01 1 H(s) p(s) Low H(s): infrequent 0 (or 1) Do not collapse state variables with low values of H(s) Sample every N cycles during simulation and collapse those variables with H(s) > threshold 0.5

11 11 ITC-07 Paper 26.110/25/2007 Observabilities From Minimized Graphs 1.Assume: next state NS, current state CS, current observabilities (0-COBS,1-COBS) for all states reachable from NS. 2.How do we evaluate 0-CBS,1-COBS for CS? 3.Use restrictor functions: latches that are 1 (0) in CS cannot have non-zero 0-observability (1-observability). 4.Three steps: (i) Restrict COBS values using NS, (ii) Trace back to derive new values for CS, and restrict the result (NewOBS), and (iii) Update COBS = max(COBS,NewOBS). NS CS COBS NewOBS Max(COBS, NewOBS)

12 12 ITC-07 Paper 26.110/25/2007 Accuracy And Speed Tradeoff Derivation of NewOBS uses partially specified circuit state CS. If no variables are collapsed, and all inputs are stored => accurate fault simulation by post processing is obtained. If all state variables are collapsed, and no inputs are stored => iterative array model is obtained. Observed accuracy and speed depends on entropy threshold used for minimization. NS CS COBS NewOBS Max(COBS, NewOBS)

13 13 ITC-07 Paper 26.110/25/2007 Exact Coverage/Estimate Comparison Circuit Exact fault sim Iterative arrayState exploration Cov (%)Time(s)Est (%)Time (s)Est (%)Time (s) s38666.110.9368.060.0766.280.10 s64186.612.6287.040.0986.831.89 S119695.832.0696.750.1396.500.69 S537868.1536.471.570.5469.4642.53 S923433.5778.7841.520.7036.1391.32 S1320729.75336.539.101.0534.32266.4 S3593282.92180.494.142.185.65192.6 S3841711.94215225.62.8317.52362.5 S3858462.84668.471.542.5766.6540.3  Improved accuracy with increased runtimes. Number of states approach length of test (20K).

14 14 ITC-07 Paper 26.110/25/2007 Graph Size vs Runtime Comparison circuitfsim (s)state graph sizeruntime (s) S3860.9311140.1 0.12 S6412.621110890.410.390.450.47 S11962.0611421650.14 0.220.38 S537836.42783054715563.864.215.016.52 S923478.84755263406313.813.620.035.6 S132073377853444291231717.220.660.6135.2 S35932180192314714298.410.212.125.7 S3841721523942852021758.323.222.661.5 S3585466851516843553716923.254.9111223 Different entropy thresholds chosen: 0.1, 0.2, 0.3, 0.4

15 15 ITC-07 Paper 26.110/25/2007 circuitcov (%)state graph sizeestimate(%) s38666.1111468.1 s64186.611108987.04 s119695.8114216596.75 96.58 s537868.227830547155671.2571.3271.39 s923433.64755263406339.4438.6537.5536.72 s1320729.87853444291231738.1237.0335.5735.48 s3593282.91923147142994.1092.9992.9888.77 s3841711.939428520217523.8923.2 15.82 s3585462.851516843553716971.1769.869.0166.4 Graph Size vs Estimate Comparison Different entropy thresholds chosen: 0.1, 0.2, 0.3, 0.4

16 16 ITC-07 Paper 26.110/25/2007 Conclusion State graph extracted during logic simulation can be used to improve accuracy of fault coverage estimation. Entropy measures can reduce the size of the graph, and trade off accuracy for speed. Iterative array estimate and exact fault coverage are two extremes of this algorithm: (1) Iterative array model: single state model (2) Exact fault simulation: fully expanded version that stores all state variables and inputs. Unaddressed outstanding problems: effective length of detection, structure of extracted graphs etc …

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