Modeling Repeaters Explicitly Within Analytical Placement

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Modeling Repeaters Explicitly Within Analytical
Placement
Bill Halpin Synplicity, Inc. Sunnyvale, CA
Prashant Saxena Intel Labs (CAD
Research) Hillsboro, OR
41st Design Automation Conference San Diego,
CA June 10, 2004
formerly with Intel Corp.
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Outline

• Motivation
• Traditional approach and its problems
• A Quadratic Placement Primer
• Repeater Force Models and Usage
• Experimental Data
• Concluding remarks

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Motivation

• Todays focus on buffered placement
  Which nets should I
  buffer? How?
• Repeater instantiation swept under ECO placement
  rug
• Too many netlist changes gt ECO placement fails
• Increasing wire resistivity gt growing
  fraction of cells is repeaters
• . independent of frequency!

• Control placement perturbation due to repeaters
• As placement evolves, keep repeaters electrically
  meaningful
• One of top problems identified in recent scaling
  study

Saxena et al., TCAD, Apr 04
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The Interleaved ECO Approach
This works great at the 90 nm node (esp. for
sizing) so, is repeater insertion any
different?
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Problems with Interleaved Flow

• (Many) netlist changes break ECO placement
  (unlike sizing)
• Repeaters treated as first-order objects just
  like other cells
• Their existence should be contingent on their
  placement for wire RC alleviation
• Nets fragmented during repeater insertion
• Intended connectivity not visible to placer
• Artificial restriction of solution space due to
  granularity of interleaving
• Interleaving overhead

X
X
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The MorePlace Approach

• Modify placer core to explicitly model repeaters
  as transients
• Enable on-the-fly repeater insertion/deletion as
  placement evolves
• without modifying netlist
• Keep repeaters electrically relevant at all
  times
• Which global placement engine?
• Force-directed quadratic placement (KraftWerk)
• High quality, ECO-friendly, industrial-strength
  algorithm

Eisenmann Johannes, DAC98
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A Quadratic Placement Primer
Sigl et al., DAC91
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Overlap Removal in QP (KraftWerk)

• Pushing the springs analogy further
• use e for overlap
  removal

Can we capture repeater semantics without
breaking niceproperties of force computation?
Eisenmann Johannes, DAC98
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Repulsive Repeater Model

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Attractive Repeater Model

• Allow repeater forces to remain quadratic
  attractive (even as other connectivity forces are
  linearized)
• Allows equi-spacing of repeaters on net

• Making all nets quadratic doesnt work (Why?
  stay tuned)

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Using the Repeater Force Model
Goal Repeaters should stay close to their
desired locations even after going through solver
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Repeated Net Trajectory
Repeater stays very close to its original location
Typical net from Ckt_C testcase
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Repeater Prediction Model

• Optimal inter-repeater lengths obtainedby
  simulation
• for different metal layers and process nodes
• Short (lt 4lM3) wires on M3, long wires on M6
• Upper metal layers usually not available for
  synthesis
• Add repeater only if lsep gt 1.4lM
• Delete repeater only if lsep lt 0.7lM
• Model validated as conservative against90 nm
  tape-out data
• Undercounts reps for each wirelength bucket

Saxena et al., TCAD, Apr 04
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A MorePlaced Layout

• 5 testcases
• Median-sized Ckt_C
• 12.3K cells (90 nm)
• 13K nets
• Inter-repeater lengths correspond to 32 nm

• Red cells repeaters
• Runtime almost same as one-pass run (30 faster
  than interleaved flow)
• Wirelength worsens marginally
• So, is it good?

Repeater distribution not uniform
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Success Criterion

• When placement converges physically, repeater
  convergence should only require small ECOs
• KraftWerk convergence no large cell movements
  across iterations
• Repeater convergence only few nets require
  further repeater addition
• Legalizable placement (small ECO changes)

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Convergence Comparisons
Deletions not plotted for MorePlace
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Cumulative Repeater Count
Traditional flows fail to converge!
3-point flow is best among traditional flows
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Convergence Data
MorePlace runtime around 20-30 better than
3-point
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Traditional Repeated Net Trajectory
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Convergence with Quadratic Nets?

• Unstable equilibrium not an issue
• But forces shrink due to wirelength fracturing
  
• So, repeaters drift apart, causing net length to
  grow and demand yet more repeaters
• Furthermore, 20 wirelength deterioration due to
  quadratic function
• Ckt_C (32 nm, 3 break-pts) Reps 1129, 1834,
  1469 23.2 worse wirelength

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Summing Up

• Interleaved ECO placement repeater insertion
  fails to converge (even at 45 nm)
• MorePlace convergence order-of-magnitude better
• MorePlace scales better on both convergence and
  wirelength (with increasing design size, process)