1. Enhanced Dual-Transition Probabilistic Power Estimation with Selective Supergate Analysis Fei Huand Vishwani D. Agrawal Department of ECE, Auburn University, Auburn, AL 36849

2. 10/04/2005ICCD 2005, San Jose, CA2 Problem Statement Enhance the probabilistic power estimation technique for signal correlations to improve the estimation of dynamic power and, in particular, account for glitch suppression by inertial delays.

3. 10/04/2005ICCD 2005, San Jose, CA3 Outline  Background Probability waveform Tagged probability waveform simulation (TPS) Dual-transition glitch filtering (Dual-trans)  Present Contributions Motivation Supergate and timed Boolean function (TBF) Modifications of TPS and Dual-trans  Using TBF  Adaptive application of supergate Experimental results  Conclusions

4. 10/04/2005ICCD 2005, San Jose, CA4 Background: Probability Waveform Input vector applied Next input vector applied Vector period Transient interval 0 Steady state Samples of signal, s(t) 0 Prob. waveform, P(t) 1.0 P(t)=0.25 P(t) =0.25 0.25 0.5 0.25 0.5 0.25 0.5 Transition probabilities time

5. 10/04/2005ICCD 2005, San Jose, CA5 Background: Tagged Probability Waveform  Partition of a probability waveform for one vector period according to the steady state signal values Four tagged waveforms  Approximate exact spatial correlations with the macroscopic spatial correlations between steady state signal values (tags)  Reference: C.-S. Ding, et al., “Gate-level power estimation using tagged probabilistic simulation,” IEEE Trans. on CAD, vol. 17, no. 11, pp. 1099–1107, Nov. 1998.

6. 10/04/2005ICCD 2005, San Jose, CA6 Background: Dual-Transition Glitch Filtering t1 < t2 < t3 < t1+d Actual waveform TPS glitch filteringDual-transition glitch filtering Reference: F. Hu, V. D. Agrawal, “Dual-Transition Glitch Filtering in Probabilistic Waveform Power Estimation,” Proc. GLSVLSI, 2005, pp. 357-360. Dual-transition probability: probability of joint event at two time instance

7. 10/04/2005ICCD 2005, San Jose, CA7 Motivation: Reconvergent Fanouts  Effectiveness of dual-transition glitch filtering is limited by the underlying TPS method  The major sources of errors in TPS is its approximation of spatial correlation among signals

8. 10/04/2005ICCD 2005, San Jose, CA8 Supergate and TBF  Supergate partitioning of circuits in a way that all inputs to a partition are externally independent Limit to maximum 3 levels and 3 input, to avoid exponentially increased complexity  Reference: S. C. Seth and V. D. Agrawal, “A new model for computation of probabilistic testability in combinational circuits,” Integration, the VLSI Journal, vol. 7, pp. 49-75, 1989. supergate a b c 1 2 3 4

9. 10/04/2005ICCD 2005, San Jose, CA9 Timed Boolean Function  Need to use timed Boolean function (TBF) Existence of multiple propagation delay paths inside a supergate  Assuming same gate delay  state of node c determined by the values on inputs a and b at times t-2 and t-3.  Reference: E. J. McCluskey, “Transients in combinational logic circuits,” in Wilcox and Mann, editors, Redundancy Techniques for Computing Systems, Spartan Books, 1962, pp. 9-46. supergate a b c 1 2 3 4

10. 10/04/2005ICCD 2005, San Jose, CA10 Present Contributions  Reformulate TPS using timed Boolean functions (TBF).  Compute dual-transition probabilities using TBF Reformulate the dual-transition probability Approximate higher-order probabilities as function of dual-transition probabilities  This allows application of supergate structures for improving signal and transition probabilities.

11. 10/04/2005ICCD 2005, San Jose, CA11 Selective Application of Supergate  Motivation TBF not accurate when inertial glitch filtering effect is not negligible Inertial glitch filtering effect  The glitch filtering by internal gates of a supergate

12. 10/04/2005ICCD 2005, San Jose, CA12 Selective Application of Supergate  Static decision making Quick analysis based on the time instances subject to glitch filtering D = average number of time instants requiring glitch filtering Apply supergate if D> D T (inertial filtering negligible)  D T, experimentally determined threshold (0.9)

13. 10/04/2005ICCD 2005, San Jose, CA13 Experimental Results – Fanout Delay Assignment Circuit TPSDualTransSupergate method E avg σE tot E avg σE tot E avg σE tot c172.32.60.12.32.60.12.32.60.1 c43229.938.835.89.511.86.511.516.611.5 c4996.814.07.03.68.20.62.33.0 c8808.315.31.68.015.75.24.89.00.0 c135524.231.632.95.811.25.45.09.50.5 c190815.023.14.117.727.911.27.016.32.0 c267016.629.87.216.728.39.913.223.66.2 c354013.826.39.810.325.62.410.526.43.7 c531511.824.42.313.431.510.111.327.03.4 c628827.427.532.115.718.84.112.715.40.2 c755214.527.53.214.831.47.814.127.61.3 Avg.15.523.712.410.719.45.78.616.12.9

14. 10/04/2005ICCD 2005, San Jose, CA14 Experimental Results – Unit Delay Assignment Circuits TPSDualTransSupergate method E avg σE tot E avg σE tot E avg σE tot c170.60.40.10.60.40.10.60.40.9 c4327.99.69.05.68.74.83.46.32.2 c49911.126.916.011.126.616.11.02.10.8 c8807.815.34.77.715.34.74.06.82.6 c135510.020.89.910.020.610.110.324.212.7 c190821.631.518.621.531.518.76.013.72.0 c267011.232.47.08.830.71.07.329.41.8 c35409.525.03.09.927.04.89.526.84.3 c531518.044.714.018.545.515.613.640.49.2 c628827.936.315.428.536.916.427.637.315.0 c755215.539.58.815.839.99.413.936.03.8 Avg.12.825.79.712.525.79.28.820.35.0

15. 10/04/2005ICCD 2005, San Jose, CA15 Conclusions  Effectiveness of dual-transition glitch filtering method is limited by the underlying probabilistic simulation method  Proposed an enhanced dual-transition power estimation method: Incorporates supergate to handle the spatial correlation at reconvergent fanouts Describes supergate by timed Boolean function Uses selective application of supergate when inertial glitch filtering effect is negligible  Improved estimation accuracy over previous approaches (TPS and DualTrans) The average estimation error of total power is now less than 5% for ISCAS’85 benchmark circuits

16. Questions ? For questions and comments, please contact hufei01@auburn.eduhufei01@auburn.edu