Georgia Institute of Technology, Microelectronics Research Center Prediction of Interconnect Fan-out Distribution Using Rent’s Rule Payman Zarkesh-Ha,

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Presentation transcript:

Georgia Institute of Technology, Microelectronics Research Center Prediction of Interconnect Fan-out Distribution Using Rent’s Rule Payman Zarkesh-Ha, Jeffrey A. Davis, William Loh *, and James D. Meindl Georgia Institute of Technology Microelectronics Research Center * LSI Logic Corporation Device Technology Group

Georgia Institute of Technology, Microelectronics Research Center Outline  Motivation  Derivation of Fan-out Distribution  Comparison with a Previous Model  Applications of Fan-out Distribution  Conclusion

Georgia Institute of Technology, Microelectronics Research Center Motivation How can a closed-form fan-out distribution model be useful? - Prediction of fan-out distribution Characterization of the interconnect structure Prediction of the average fan-out Prediction of the total number of nets - Estimation of Rent’s exponent Easy estimation with no clustering - Heterogeneous netlist information Fast computation for approximation

Georgia Institute of Technology, Microelectronics Research Center Fo=2 Fo=1 What is the fan-out distribution? ···

Georgia Institute of Technology, Microelectronics Research Center Derivation of Fan-out Distribution Rent’s Rule: Underlying assumption for prediction of a priori fan-out distribution System of N gates T = # of IO’s k and p are empirical constants

Georgia Institute of Technology, Microelectronics Research Center Conservation of I/O’s for two blocks Conservation of I/O’s for three blocks Conservation of I/O’s in a random logic network

Georgia Institute of Technology, Microelectronics Research Center Conservation of I/O’s for m block: Applying Rent’s rule: Setting up the recursive equation: The solution: Derivation of fan-out distribution

Georgia Institute of Technology, Microelectronics Research Center Substituting m by Fo+1 gives the fan-out distribution (number of nets versus fan-out) Where N g is the total number of gates and k and p are the Rent’s parameters The closed-form fan-out distribution model

Georgia Institute of Technology, Microelectronics Research Center Model verification - systems with no internal net The case with p=1 The case with k=0 Net(Fo)=0 for all fan-out p=1 k=0

Georgia Institute of Technology, Microelectronics Research Center N g =15,000, k=2.0, p=0.6 How does the fan-out distribution look like? [Stroobandt and Kurdahi GLVLSI’98]

Georgia Institute of Technology, Microelectronics Research Center Actual data Numerically evaluated model New closed-form model Comparison with Previous Model N g =23,815, k=2.41, p=0.28 [Stroobandt and Kurdahi GLVLSI’98]

Georgia Institute of Technology, Microelectronics Research Center Applications of Fan-out Distribution - Prediction of fan-out distribution Characterization of the interconnect structure Prediction of the average fan-out Prediction of the total number of nets - Estimation of Rent’s exponent Easy estimation with no clustering - Heterogeneous netlist information Fast computation for approximation

Georgia Institute of Technology, Microelectronics Research Center Maximum Fan-out: Total Number of Nets: Average Fan-out: Where: Characterization of the interconnect structure

Georgia Institute of Technology, Microelectronics Research Center Prediction of the interconnect structure Data from ISCAS benchmark in [Stroobandt and Kurdahi GLVLSI’98]

Georgia Institute of Technology, Microelectronics Research Center Variation of the average fan-out as a function of p, k and N g

Georgia Institute of Technology, Microelectronics Research Center Estimation of Rent’s exponent N g =44,803, k=3.36, p=0.6

Georgia Institute of Technology, Microelectronics Research Center Heterogeneous netlist information N g =20, K=738.4, P=0.34 ~~ 90 sec <0.1 sec

Georgia Institute of Technology, Microelectronics Research Center Conclusion  A closed-form model for fan-out distribution is derived based on Rent’s rule  The closed-form model is verified through comparison with actual data from ISCAS  Applications of the closed-form fan- out distribution model are presented