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A Semi-Persistent Clustering Technique for VLSI Circuit Placement

A Semi-Persistent Clustering Technique for VLSI Circuit Placement. Charles J. Alpert 1 , Andrew Kahng 2 , Gi-Joon Nam 1 , Sherief Reda 2 and Paul G. Villarrubia 1 1 IBM Corp. 2 Department of CSE, UCSD. bigblue4 design from ISPD2005 Suite. Implications in Placement. Scalability Tractability

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A Semi-Persistent Clustering Technique for VLSI Circuit Placement

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  1. A Semi-Persistent Clustering Technique for VLSI Circuit Placement Charles J. Alpert1, Andrew Kahng2, Gi-Joon Nam1, Sherief Reda2 and Paul G. Villarrubia1 1IBM Corp. 2Department of CSE, UCSD

  2. bigblue4 design from ISPD2005 Suite

  3. Implications in Placement • Scalability • Tractability • Runtime vs. quality trade-off • SoC (System-on-Chip) designs • Mixed-size objects • White space

  4. Problem Statement • What is the most effective and efficient clustering strategy for analytic placement? • Quality of solution • CPU time

  5. B B Cluster A with its “closest neighbor” B C C Update the circuit netlist D D D AC A A E E E F F F  wij conn(u,v) Clustering Score Function: d(u, v) = [ size(u) + size(v) ]k Clustering Concept

  6. Clustering Literature • Tremendous amounts of research here • Edge-Coarsening (EC) • First-Choice (FC) • Edge-Separability (ESC) • Peak-Clustering • Etc… • General drawbacks • Clique transformation • Edge weight discrepancy • Pass-based iteration • Lack of global clustering view

  7. Best-Choice Clustering • Avoid clique transformation • Avoid pass-based iterations • More global view of clustering sequence • Priority-queue management • Lazy-update speed-up technique • Area-controlled balanced clustering

  8. Best-Choice Clustering • Initialize the priority-queue PQ: • - For each cell u: calculate its clustering score c with its closest neighbor v. • - Insert the pair (u, v) into PQ based on their cost c. • Until the target cell number is reached: • - Pick the top of the heap (m, n) • - Cluster (m, n) into a new object mn; update the netlist • - Calculate mn closest neighbor k; insert (mn, k) into PQ • - Recalculate the clustering cost of all the neighbors to m and n

  9. Assume N-pin net weight = 1 / (n-1) Each object size = 1 Timing criticality is 1 for all nets B C A D E F Best-Choice Example

  10. A=1/2 CD=2/3 B B D=1 C A A B=1/2 B=1/2 CD D C=1 B=2/3 E E D=3/4 F F F=1/2 D=1/2 E=1/2 Best-Choice Example

  11. A=3/8 A=3/8 BCD=3/8 BCD BCD BDC=3/8 A A E F=1/2 EF F E=1/2 BCD=3/10 Best-Choice Example

  12. ABCD EF Best-Choice Example ABCDEF EF=1/3 ABCD=1/3  clustering_score = 2.875

  13. Best-Choice Clustering Summary • Globally optimal clustering sequence via priority-queue data structure • Produce better quality of results • Clustering framework • Arbitrary clustering score function can be plugged in

  14. (1) (2) Best-Choice Clustering • Clustering score distribution • First-choice (FC) :  clustering_score = 5612.83 • Best-choice (BC) :  clustering_score = 6671.53

  15. Lazy Update Speed-up Technique Priority Queue PQ Top of the PQ Node A • Observations: • Node A might be updated a number of times before making it to the top of the PQ (if ever), but the last update is what determines its final position in PQ • Statistics indicate than in 96% of our updating steps, updating node A score pushes A down in PQ

  16. Lazy Update Speed-up Technique Main Idea: Wait until A gets to the top of the priority-queue and then update its score if necessary Until the target cell number is reached: - Pick the top of the heap (m, n) - If (m, n) is invalid then - recalculate m closest neighbor n’ and insert (m, n’) in the heap else - Cluster (m, n) into a new object mn; update the netlist - Calculate mn closest neighbor k; insert (mn, k) in the heap - Mark all neighbors of m and n invalid

  17. Lazy Update Runtime Charateristic Note: Practically no impact to solution quality

  18. Experiments • IBM CPLACE • Analytic placement algorithm • Semi-persistent clustering paradigm • Up-front clustering • Selective unclustering during main global placement • Full unclustering before detailed placement • Order-of-magnitude reduction by clustering • Industrial ASIC designs • Size ranges from 56K to 880K placeable objects

  19. Placement Results w/ Clustering • Average 4.3% WL improvement over EC • BC is x8.76 slower than EC

  20. No Clustering vs. BC+Lazy Clustering

  21. Conclusions • Globally optimal clustering sequence framework • Independent of clustering scoring function • Better clustering sequence • Allow significant placement speed-up • Almost no loss of quality of solution • Size control via clustering scoring function • Effective for dense design

  22. Future Work • Handling fixed blocks during clustering • Ignoring nets connected to fixed objects • Ignoring pins connected to fixed objects • Including fixed blocks during clustering • Etc…. • No visible improvement at the moment

  23.  wij conn(u,v) • d(u, v) = [ size(u) + size(v) ]k Cluster Size Control Results Standard : k = 1 Automatic: k = size(u) + size(v) /  where  = expected avg. size

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