Statistical Leakage Power Minimization Using Fast Equislack Shell Based Optimization

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Statistical Leakage Power Minimization Using Fast
Equi-slack Shell Based Optimization

• Xiaoji Ye, Peng Li
• Department of ECE
• Texas AM University
• Yaping Zhan
• AMD, Austin, TX, US

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Power Density and Leakage

• Power is critical for IC design
• Leakage power becomes increasingly important

Patrick P. Gelsinger, ISSCC 2001
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Leakage Optimization

• Gate sizing problem

Objective Minimize leakage power Subject
to Circuit delay Timing constraint Gate
size ?Smin, S2, S3,, Smax Threshold voltage ?
Vthlow, Vthhigh
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Deterministic Leakage Optimization

• Process variations significantly impact the
  leakage power and timing
• Deterministic optimization
• Can not capture timing and leakage variability
• May miss the true performance-limiting corner
• Can not capture spatial correlations
• Incapable of guaranteeing a specific yield
• Perform statistical leakage optimization!

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Statistical Optimization

• Sensitivity-based incremental gate sizing
  technique
• M. R. Guthaus, N. Venkateswaran, C.
  Visweswariah,V. Zolotov, ICCAD 2005
• Use criticality as guidance to select candidate
  gates
• Size one gate in each iteration, runtime may be
  high
• Second-order conic programming
• M. Mani, A. Devgan, M. Orshansky, DAC 2005
• Gate size rounding is needed after each
  optimization
• Bottleneck is the SOCP computation

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Our Work

• Use SSTA as guidance for circuit optimization
• Capable of guaranteeing specific timing yield
• Timing, leakage, leakage/delay sensitivity fully
  parameterized in process variations
• Introduce a novel equi-slack shell based
  technique
• A number of gates are sized simultaneously
  ateach iteration
• Statistical timing information (slack) is updated
  efficiently at each iteration without re-running
  SSTA
• Timing yield is strictly maintained
• Smooth incremental optimization step

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Motivation

• Perform sizing on the basis of groups (equi-slack
  shells)

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Our IdeaEqui-Slack Shell Concept

• Group nodes by equal slacks
• Do optimization within a group

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Our ApproachSizing Within a Shell

• Nodes within a shell are divided into levels
• Level sensitivity is the sum of the leakage/delay
  sensitivities of all the nodes in this level
• Pick the level with the maximum leakage/delay
  sensitivity
• Size down nodes in a selected level

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2
2
2
2
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Our Approach Shell Update

• Efficiently update the slacks after each sizing
  step
• Merge the groups of the same slack

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Flowchart
Obtain statistical slacks for all gates
Initial run of SSTA
Shell initialization
Find shell with the largest slack Optimize
within shell
Slack update within shell Shell update
Timing violated?
Post tuning
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Atomic operations on the shell

• Initialization
• Expansion
• Merge
• Levelization
• Sizing within the shell
• Slack update
• Shell update

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Shell Initialization

• Conduct initial forward and backward SSTAs to
  compute statistical slacks for all gates
• Gates with the largest mean-3sigma slack are
  selected as seeds

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Shell Expansion

• For each seed, check its neighbor gates
• If
  ? absorb the neighbor
• Guarantee the (mean /- 3sigma) points of the
  slack for gates inside and outside shell are not
  close with each other

Shell B
Shell A
Shell C
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Shell Merge

• Merge when two shells meet

Expand
Shell B
Merge
Shell A
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Shell Data Structure

• Shell boundary stored separately for fast
  operations

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Levelization

• Levelization within a shell
• Level sensitivity
• Pick the level with the largest mean-3sigma
  sensitivity

G3
G9
G6
G1
L2
L4
L1
L3
G4
G8
G2
G7
G12
G5
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Optimization Within A Shell

• Size down gates in the selected level to absorb
  the slack
• Gradually reduce the slack
• Safe bound
• Change gate size or Vth, guarantee
• Slack reduction for other gates within shell

?Slack'max?Slack1,?Slack2,...,?Slackk
?Slacki is slack reduction for gatei
gatei target level, i1,...,k
Î
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Slack Update Within A Shell

• Internal gates slack reduced by
• Boundary gates
• Fanin cone of level
• Fanout cone of level

G11
G10
G3
G9
G6
G1
L2
L4
L1
L3
G4
G8
G2
G7
G12
G5
G14
G13
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Shell Update

• Boundary gate if
• Remove it from the shell
• Form a new shell with a larger slack

G11
G10
G3
G9
G1
G6
L2
L4
L1
G4
G8
L3
G7
G2
G12
G5
G14
G13
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Flowchart
Obtain statistical slacks for all gates
Initial run of SSTA
Shell initialization
Find shell with the largest slack Optimize
within shell
Slack update within shell Shell update
Timing violated?
Post tuning
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Experimental Setup

• Six gate sizes 1x, 2x, 4x, 6x, 8x, 10x, and dual
  Vth
• Process variation range
• Model characterization using 45nm PTM
• Algorithm implemented in C, applied to ISCAS 85
  benchmark circuits
• Results compared with deterministic optimization
  under the same timing constraint

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Results

• Leakage vs delay for c499 for different timing
  constraints

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Results

• Delay-power product for c880 for different timing
  constraints

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Results

• Leakage distribution for c432

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Conclusion

• A novel equi-slack shell based statistical
  leakage optimization technique is proposed
• Level-based statistical sensitivities are used as
  guidance to simultaneously optimize multiple
  gates in a shell
• Fast slack update after each sizing step without
  re-running SSTA can be achieved
• Superior runtime and optimization results have
  been observed in the experiments

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Thank you!