Intrinsic Shortest Path Length: A New, Accurate A Priori Wirelength Estimator

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Intrinsic Shortest Path Length A New, Accurate A
Priori Wirelength Estimator
Andrew B. Kahng Sherief Reda abk_at_ucsd.edu
sreda_at_ucsd.edu VLSI CAD
Laboratory University of CA, San
Diego http//vlsicad.ucsd.edu/sreda
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Outline

• Previous work and motivation
• Intrinsic Shortest Path Length (ISPL) definition
• Validation of ISPL as wirelength estimator
• Practical Applications
• A Priori Total wirelength estimation
• A Priori Global interconnect prediction
• Relationship to Rent parameter

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Definition and Applications

• A priori wirelength estimation is the process of
  estimating and predicting the wirelength
  characteristics of VLSI netlists without
  knowledge of the netlist placement or
  floorplanning.

• Applications that benefit from a priori
  wirelength estimation
• Physical driven synthesis ? Faster timing
  convergence
• Early system planning
• Determining amount of necessary whitespace
• VLSI netlist characterization/reverse
  engineering/creation

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Previous Work

• Previous approaches
• Correlators
• If some measure e correlates with net length l
  then e can be used in relevant applications,
  e.g., clustering. Typically no analytical
  modeling between l and e.
• Examples mutual contraction and edge
  separability.
• Average wirelength estimators
• Rent parameter-based.
• Predict aggregate wirelength characteristics,
  e.g., wirelength distribution and total
  wirelength.

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Motivation

• Wanted
• Estimator has intuitive physical meaning
• Handles hypergraphs transparently
• Individual net length estimator If l1 gt l2 then
  e1 gt e2
• Analytical modeling between li and ei, e.g., li
  f(ei)
• Estimator and wirelength have similar
  distributions
• Total wirelength estimation
• Practical runtime for calculation

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A Motivating Observation
Input Netlist
b
a

• Nodes a and b are directly connected by an edge.
• Does this mean a and b will be placed spatially
  close in a good placement?

Observation Unlikely. Despite edge a, b, a
and b are structurally far from each other
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Intrinsic Shortest Path Length (ISPL)
Input Netlist
Will edge a, b be short?
b

• analyze the structural proximity of a and b

• structural proximity ? shortest path

• shortest path between nodes a and b that does not
  include a, b.

a
To estimate the Intrinsic Shortest Path Length
ISPL of edge a, b delete a, b and
calculate the shortest path length (number of
edges) between a and b

• Example ISPL of a, b 8. a, b and its ISP
  form a cycle

• BUT Netlists are hypergraphs ? a transparent
  mechanism is needed

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ISPL in Hypergraphs

• Set the distance or weight of a k-pin
  hyperedge by k/2

h
a
b
u
c
v
ISPL of u, v 11.51 3.5
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Outline

• Previous work and motivation
• Intrinsic Shortest Path Length (ISPL) definition
• Validation of ISPL as wirelength estimator
• Practical Applications
• A Priori Total wirelength estimation
• A Priori Global interconnect prediction
• Relationship to Rent parameter

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Validation of ISPL as Wirelength Estimator

• To validate our observation
• Correlation between the placed net length and net
  ISPL?
• Correlation between the effect of net pin count
  on average net length and average net ISPL?
• 3. Correlation between the average/total netlist
  wirelength and the average/total ISPL over a
  range of benchmarks?
• 4. Given two individual nets of some netlist, can
  we predict which individual net will be placed
  with greater wirelength?
• 5. Relationship between the distribution, or
  profile, of ISPL and the wirelength distribution?

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Validation 1. ISPL and Net Length
Objective validation of the relationship between
ISPL and net length Given a netlist (ibm01)
1. Calculate the ISPL of every hyperedge 2.
Place the netlist using some placer (Dragon) 3.
Plot ISPL versus Half-Perimeter Wirelength (HPWL)
of every net

• As ISPL increases, HPWL increases
• Correlation coefficient 0.91

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Validation 1. ISPL and Net Length

• Calculate correlation coefficients between ISPL
  and wirelength
• For comparison, calculate correlation coefficient
  between
• Mutual Contraction (UCSB) and HPWL
• Edge Separability (UCLA) and HPWL

correlation coefficients MC is mutual
connectivity ES is edge separability
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Validation 2. Effect of Pin Count
Objective Test the effect of pin count on both
average wirelength and ISPL

• For every k (2) on ibm01
• Calculate the average ISPL of all k-pin net
• Run a placer and calculate the average placed
  wirelength of all k-pin nets
• Correlation coefficient of 0.95 between average
  HPWL and average ISPL (typical result)

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Validation 3. Average ISPL and Total Wirelength
Objective Is the average ISPL correlated with
the total wirelength?

• Synthesize netlists (10k nodes/nets) with
  varying Rent parameter with GNL
• A higher rent parameter ? more global
  communication ? larger wirelength
• Calculate the average ISPL of each netlist
• Place the netlists using mPL and measure the HPWL

• Perfect correlation between average ISPL and
  total wirelength

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Validation 4. Individual Net Length Prediction
Objective Given two arbitrary nets i and j with
the same number of pins, can we a priori decide
which net will be longer?
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Validation 4. Individual Net Length Prediction
The success of prediction in percentage
MC Mutual Contraction ISPL Intrinsic Shortest
Path Length
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Validation 5. ISPL and Net Length Distribution

• Objective Examine the relationship between ISPL
  and HPWL profiles

• Sort all nets according to their ISPL and their
  HPWL
• Plot all sorted HPWL normalized to the maximum
  HPWL value
• Plot all sorted ISPL normalized to the maximum
  ISPL value
• ISPL and HPWL have roughly similar profiles

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Outline

• Previous work and motivation
• Intrinsic Shortest Path Length (ISPL) definition
• Validation of ISPL as wirelength estimator
• Practical Applications
• A Priori Total wirelength estimation
• A Priori Global interconnect prediction
• Relationship to Rent parameter

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Applications 1. A Priori Wirelength Total
Estimation

• Devise an analytical model between ISPL and HPWL

• Using empirical data, we find an exponential
  relationship between ISPL and wirelength

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Applications 1. A Priori Total Wirelength
Estimation

• How to determine ak and gk?

• Ideal modeling (not a priori) based on the
  netlist characteristics from the placement (only
  useful for model validation and calibration)
• Static modeling (a priori) fixed values for all
  netlists based on values typically encountered

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Applications 1. A Priori Total Wirelength
Estimation
Objective Given m ideal models, how to calculate
an approximate static model
?
m ideal exponential fits (from typical netlists)
linearize
An estimate function that minimizes the total
square error
calculate exp model
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Applications 1. A Priori Total Wirelength
Estimation

• Calculate the total wirelength of the IBM
  (version 1) benchmarks (unit size cells) using
  ideal model
• Calculate typical values and use it for a priori
  static modeling.

• On the average, ideal modeling is 3.61 accurate
  compared to actual HPWL. Static modeling is
  16.60 accurate

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Applications 2. A Priori Global Interconnect
Prediction
Global interconnects hurt performance and are
typically buffered
Definition a net is global (long) if it is in
the top 5 of the longest nets in the final
placement

• Objective
• Can we a priori decide which nets are going to
  be long before placement?

Given a netlist 1. Calculate the ISPL of all
nets 2. Sort all nets based on their ISPL 3.
Plot net count vs ISPL
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Outline

• Previous work and motivation
• Intrinsic Shortest Path Length (ISPL) definition
• Validation of ISPL as wirelength estimator
• Practical Applications
• A Priori Total wirelength estimation
• A Priori Global interconnect prediction
• Relationship to Rent parameter

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Relationship to Rent Parameter

• We develop a characterization, Range Parameter,
  of VLSI netlists

Definition 1 The range of a node u is the
average ISPL of all nets incident to it.

• The larger a nodes range , the more wirelength
  it needs to communicate with its neighbor

Definition 2 The Range of a netlist is the
average range of all nodes V.
? A large Range parameter predicts that a netlist
would require a large amount of global
communication.
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Relationship to Rent Parameter
Intuitive connection to Rent parameter a netlist
with large Rent parameter ? requires more global
communication in any good placement
Correlation coefficient of 0.701
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Rent Parameter
Range Parameter

• Calculated in top-down fashion

• Calculated in bottom-up fashion

• Useful for complete netlist characterization

• Useful for complete netlist characterization

• Useless for individual net prediction

• Useful for individual net prediction

• Unstable value

• Stable value (same topology)

• works on graphs or hypergraphs

• Hypergraph to graph transformation

? Runtime normalized with respect to FengShui
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Conclusions

• Developed the new concept of Intrinsic Shortest
  Path Length (ISPL)
• Demonstrated strong correlation between ISPL and
  HPWL
• Used it for individual net length predictor
• Correlated average ISPL with total wirelength
• Studied the relationship between ISPL and HPWL
  distributions
• Developed a characterization to VLSI netlists and
  studied its relation to Rent parameter
• Used ISPL for two practical applications
• Total wirelength estimation
• Global interconnect prediction

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Future Work

• Runtime improvement
• Studying the effect of different net weights on
  ISPL performance
• Better wirelength models
• Synthetic benchmark generation based on ISPL
• Analytical relationship between Range and Rent
  parameters
• Fixed blocks/white space effects
• Deducing wirelength distribution, pin-effect
  count from the analytical models
• Estimating RSMT by using weighting coefficients

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Thank you