Fractional Cut: Improved Recursive Bisection Placement

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Fractional CutImproved Recursive Bisection
Placement

• Ameya R. Agnihotri Mehmet Can YILDIZ Ateen
  KhatkhateAjita Mathur Satoshi Ono Patrick H.
  MaddenSUNY Binghamton Computer Science
  Departmenthttp//vlsicad.cs.binghamton.edu
• pmadden_at_cs.binghamton.edu
• IBM Austin Research Labs
• Work supported by SRC Project 947.1, IBM Faculty
  Partnership Award, Intel, and NYSTAR
  Microelectronics Design Center

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Overview

• Recursive Bisection
• The "Narrow Region" problem
• Fractional Cuts
• Legalization of Placements
• Experimental Results
• Conclusion and Future Work

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Bisection Based Placement
Logic elements
Placement region
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Recursive Bisection Placement
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After Bisection

• Cells have been assigned to rows
• Relative horizontal positions are known, but
  there may be overlaps
• Overlap removal sort by X and pack
• For MCNC benchmarks, this works well
• For IBM and PEKO benchmarks some problems occur

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The Narrow Region Problem
Total cell area matches the available row space,
but... Its not possible to partition the cells
to fit within the boundaries
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The Narrow Region Problem
The problem may occur more than once
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Feng Shui 1.2 crash and burn.
Adya, Benchmarking for Large Scale Placement
and Beyond ISPD 2003
We were co-authors on this paper, and contributed
a H/V demand table that contained errors (trend
indicated was correct, and results were uniformly
skewed). TCAD version is fixed.
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Narrow Region Solutions

• Avoid them!
• Capo cut sequences are biased towards horizontal
• Cut sequence impacts HPWL
• White space
• Additional area gives greater freedom
• Post-Bisection Optimization
• Fix the problem by moving cells vertically
  after bisection is complete
• Fractional Cuts.

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Fractional Cut
We cant change where the cut line falls between
the cells We can move the cut line off of the row
boundary
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Ignoring Row Boundaries
Row boundaries are in blue Black outlined
rectangles are the regions Numbers indicate
total cell areas (there may be a number of cells
in each region).
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Fractional Cut
After bisection, cells are placed in non-legal
positions at the centers of their regions
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After Bisection
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After Bisection

• The cells must be row aligned
• Overlaps must be removed
• This is very much like legalization in analytic
  placement

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Legalization Method

• Process rows one at a time
• For each row
• Select a subset of cells such that the total
  horizontal WL of the packed subset, plus the
  penalty for the non-selected cells, is minimized
• Simple dynamic programming formulation obtains
  good results
• Example six cells, with space for four cells in
  the row

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Example
B
F
A
D
E
C
All the blocks are going to be packed to the
"left." The total distance things travel depends
on which blocks we choose.
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Some Observations

• If A is to the left of B before packing
• It should still be to the left after packing
• The distance that a block travels depends only on
  the number of blocks to the left of it
• We don't care which blocks to the left are
  taken--only how many

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Dynamic Programming
- A B C D E F
Position 0 -
Position 1 - -
Position 2 - - ??
Position 3 - -
Table contains total movement cost for
legalization Rows are filled to
location Columns are using some subset using up
to the given cell
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Dynamic Programming

• Optimal solution to fill three locations using a
  subset of ABCDE
• Contains E, with the optimal solution using two
  locations and a subset of ABCD
• or does not contain E, and the optimal solution
  using three locations and a subset of ABCD

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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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After Bisection
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Legalization
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Legalization
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Following Legalization

• Classic branch-and-bound sliding window
  optimization
• Both single and multiple row optimization
• Cell mirroring and space insertion are also
  supported

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Experimental Results
Feng Shui 2.0 Feng Shui 1.5 DP Feng Shui 1.5 Capo 8.6 Dragon 2.23 Kraftwerk mPL 2.0
Ibm01 0.52 0.54 1.85 0.57 0.51 0.70 0.64
Ibm02 1.50 1.51 5.63 1.60 1.44 2.15 1.61
Ibm07 3.30 3.36 16.72 3.71 3.31 5.12 4.07
Ibm08 3.60 3.72 13.66 3.89 3.39 4.66 4.25
Ibm09 3.02 3.22 16.95 3.31 2.96 4.26 3.81
Ibm10 5.66 5.88 40.00 6.34 5.61 7.61 6.61
Ibm11 4.48 4.80 31.73 4.89 4.43 5.80 5.96
Ibm12 7.74 8.08 42.85 8.76 7.60 10.41 9.44
Avg X1.042 X5.187 X1.102 X0.980 X1.379 X1.213
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Experimental Results
Opt. Feng Shui 2.0 Feng Shui 1.5DP Feng Shui 1.5 Capo 8.6 Dragon 2.20 Kraftwerk Kraftwerk DOMINO mPL 2.0
Peko01 0.81 1.25 1.30 4.59 1.29 1.46 1.39 1.74 1.10
Peko02 1.26 2.09 2.10 6.92 2.03 2.43 1.98 2.61 1.76
Peko03 1.50 2.62 2.61 8.18 2.66 2.93 3.02 3.78 2.05
Peko04 1.75 2.82 2.91 14.31 3.12 3.87 3.25 4.25 2.31
Peko05 1.91 3.01 3.14 15.70 3.16 3.79 3.92 4.79 2.57
Peko06 2.06 3.44 3.42 21.38 3.57 4.35 4.07 5.38 2.78
Peko07 2.88 4.91 4.98 38.54 5.07 6.24 5.73 7.56 3.95
Peko08 3.14 5.25 5.62 34.16 5.57 6.79 5.87 8.17 4.99
Peko09 3.64 5.98 6.32 36.03 6.47 7.72 8.52 10.00 4.76
Peko10 4.73 7.87 8.40 17.89 8.00 8.49 8.90 12.00 6.59
Avg X1.65 X1.70 X8.13 X1.72 X2.02 X1.93 X2.48 X1.38
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Experimental Results -- Summary

• Fractional Cut provides 4 improvement over
  row-based cut lines
• Roughly 10 improvement over typical recursive
  bisection approach
• DP legalization avoids pathological behavior
• Narrow region problem is eliminated
• A simple bisection approach
• Within 2 of Dragon (annealer)
• Lower HPWL than Capo, Kraftwerk
• Lower HPWL than MPL on non-synthetic benchmarks

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Current and Future Work

• Mixed Block placement
• Current version of the tool is on the webFeng
  Shui 2.2 supports mixed block.
• http//vlsicad.cs.binghamton.edu
• Improved Legalization and Detail Placement
• Feng Shui 2.2 uses a legalizer developed by
  colleagues
• Integration of routing and placement

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Thanks to

• SRC, IBM, Intel, NYSTAR MDC
• IBM TJW
• Prof. Roman Bazylevych/Lviv Polytechnic
• Dr. Bill Swartz/InternetCAD