Rent exponent prediction methods

摘要

A wide variety of models for estimating the distribution ofnon-chip net lengths assume an accurate estimate for an empiricalnparameter called the Rent exponent. Due to its definition as annexponent, these models are sensitive to its precise value, and carefulnselection is essential for good estimates of layout requirements andncycle times. In addition, it is also important to be able to predictnchanges in the Rent exponent with (possibly discontinuous) changes inninterconnect technology. This paper presents a range of methods fornestimating the Rent exponents of arbitrarily large gate placements as anfunction of optimization procedure and the level of fan-out present innthe netlist. The first part of the paper describes a rapid algorithmicnapproach which combines the self-similar, or fractal attributes of smallnwiring cells with a Monte Carlo sampling method. This method is shown tonaccurately account for variations in both the wiring signature of thennetlist and for the effects of most algorithms used for placementnoptimization. The second part of the paper presents an analytical modelnfor Rent exponent prediction, based on a renormalization groupntransformation. This transformation is designed to filter outninformation which does not contribute to the scale-invariant propertiesnof the optimized netlist enabling the derivation of a closed-formnexpression for the Rent exponent