Delay and Slew Metrics Using the Lognormal Distribution

Delay and Slew Metrics Using the Lognormal Distribution Charles J. Alpert Chandramouli Kashyap Frank Liu Anirudh Devgan IBM Corp. , Austin, Texas

The Path to Enlightenment Elmore Expressway Lognormal Lane Rice Road (AWE Avenue)

What’s Been Done Before. . . Delay Slew Step D 2 M PRIMO h-Gamma WED Bakoglu ? ? ? Standard Deviation Ramp PERI

Matching a Distribution V(t) Impulse Response PDF (Probability Density Function) t

Life is Lognormal l Stock option valuation l Age of marriage l Personal income distribution l Survival times after cancer diagnosis l Lengths of spoken words

Statistical Distribution Facts # parameters Closed-form median Lognormal 2 yes Exponential 1 yes Gamma 3 no Weibull 3 no

The Lognormal Delay Formula Match mean and variance

First Slew Formula Match mean and variance where

Second Slew Formula Match variance and skewness where f is closed form

Slew Formula Proposal l Ln. S 23 ¤ Accurate at far end ¤ Overestimates at near end l Ln. S 12 ¤ Consistent underestimator l Ln. S: smooth trade-off between them

Example Results for an RC Ladder

Experimental Setup l Routed nets from an ASIC l 432 “difficult” nets with 2313 sinks l Partition sinks into three groups Near Middle Far

Far End Slew Results

Middle End Slew Results

Near End Slew Results

How Will You get to Enlightenment? l Elmore Expressway l Rice Road l Lognormal Lane

Delay and Slew Metrics Using the Lognormal Distribution Charles J. Alpert Chandramouli Kashyap Frank Liu Anirudh Devgan IBM Corp. , Austin, Texas