Delay and Slew Metrics Using the Lognormal Distribution

1
Delay and Slew Metrics Using the Lognormal
Distribution

• Charles J. Alpert
• Chandramouli Kashyap
• Frank Liu
• Anirudh Devgan
• IBM Corp., Austin, Texas

2
The Path to Enlightenment
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Whats Been Done Before . . .
Bakoglu Standard Deviation
4
Matching a Distribution
t
5
Life is Lognormal

• Stock option valuation
• Age of marriage
• Personal income distribution
• Survival times after cancer diagnosis
• Lengths of spoken words

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Statistical Distribution Facts
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The Lognormal Delay Formula
Match mean and variance
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First Slew Formula
Match mean and variance
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Second Slew Formula
Match variance and skewness
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Slew Formula Proposal

• LnS23
• Accurate at far end
• Overestimates at near end
• LnS12
• Consistent underestimator
• LnS smooth trade-off between them

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Example Results for an RC Ladder
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Experimental Setup

• Routed nets from an ASIC
• 432 difficult nets with 2313 sinks
• Partition sinks into three groups

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Far End Slew Results
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Middle End Slew Results
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Near End Slew Results
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How Will You get to Enlightenment?

• Elmore Expressway
• Rice Road
• Lognormal Lane

17
Delay and Slew Metrics Using the Lognormal
Distribution

• Charles J. Alpert
• Chandramouli Kashyap
• Frank Liu
• Anirudh Devgan
• IBM Corp., Austin, Texas