Prediction of Interconnect Fanout Distribution Using Rents Rule
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
What is the fan-out distribution? Fo=2 Fo=1 ··· 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 T = # of IO’s k and p are empirical constants Georgia Institute of Technology, Microelectronics Research Center System of N gates
Conservation of I/O’s in a random logic netw Conservation of I/O’s for three blocks Conservation of I/O’s for two blocks Georgia Institute of Technology, Microelectronics Research Center
Derivation of fan-out distribution Conservation of I/O’s for m block: Applying Rent’s rule: Setting up the recursive equation: The solution: Georgia Institute of Technology, Microelectronics Research Center
The closed-form fan-out distribution m Substituting m by Fo+1 gives the fan-out distribution (number of nets versus fan-out) Where Ng is the total number of gates and k and p are the Rent’s parameters Georgia Institute of Technology, Microelectronics Research Center
Model verification - systems with no intern The case with p=1 The case with k=0 p=1 k=0 Georgia Institute of Technology, Microelectronics Research Center Net(Fo)=0 for all fan-out
How does the fan-out distribution look lik [Stroobandt and Kurdahi GLVLSI’ 98] Ng=15, 000, k=2. 0, p=0. 6 Georgia Institute of Technology, Microelectronics Research Center
Comparison with Previous Model Actual data Numerically evaluated model [Stroobandt and Kurdahi GLVLSI’ 98] New closed-form model Ng=23, 815, k=2. 41, p=0. 28 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
Characterization of the interconnect struc Maximum Fanout: Total Number of Nets: Average Fanout: Wher e: Georgia Institute of Technology, Microelectronics Research Center
Prediction of the interconnect struct Data from ISCAS benchmark in [Stroobandt and Kurdahi GLVLSI’ 9 Georgia Institute of Technology, Microelectronics Research Center
Variation of the average fan-out as a function of p, k and Ng Georgia Institute of Technology, Microelectronics Research Center
Estimation of Rent’s exponent Ng=44, 803, k=3. 36, p=0. 6 Georgia Institute of Technology, Microelectronics Research Center
Heterogeneous netlist information ~ ~ Ng=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 fanout Georgia Institute of Technology, Microelectronics Research Center
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