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Wirelength Estimation based on Rent Exponents of Partitioning and Placement

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hwakeland
22 diapositives · 244 Views · Dec 20, 2019

Explore wirelength estimation based on Rent's rule, extracting Rent exponents, and the relationship between partitioning and placement Rent exponents. Experimental observations and implications for total wirelength estimation. Discuss the potential of Rent exponent as a metric for placement quality.

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  1. Wirelength Estimation based on Rent Exponents of Partitioning and Placement Xiaojian Yang Elaheh Bozorgzadeh Majid Sarrafzadeh Embedded and Reconfigurable System Lab Computer Science Department, UCLA 1

  2. Outline • Introduction • Motivation • Rent Exponents of Partitioning and Placement • Wirelength Estimation based on Rent’s rule • Rent Exponent and Placement Quality • Conclusion 2

  3. Introduction • Rent’s rule and its application • P = TB r • Introduced by Landman and Russo, 1971 • Used for Wirelength estimation • Rent Exponent • Key role in Rent’s rule applications • Extracted from partitioning-based method • “Intrinsic Rent exponent”, Hagen, et.al 1994 3

  4. Introduction (cont’d) • Two Rent Exponents • Topological and Geometrical (Christie, SLIP2000) • Partitioning and Placement • Questions: • Same or different? • Which one is appropriate for Rent’s rule applications? • Relationship? 4

  5. Partitioning Rent Exponent log P log B B – Number of cells P – Number of external nets 5

  6. Partitioning Rent Exponent log P slope = r log B B – Number of cells P – Number of external nets 6

  7. Placement Rent exponent slope = r’ log P log B 7

  8. Difference between two exponents Placement Partitioning • Partitioning objective: Minimizing cut-size • Embed partitions into two-dimensional plane • Cut-size increases in placement compared to partitioning log P Placement r’ > Partitioning r log B 8

  9. Relation between two Rent exponents • Based on min-cut placement approaches (recursively bipartitioning) • Different partitioning instances • Partitioning tree approach: Pure Partitioning • Partitioning in Placement: terminal propagation 9

  10. Pure Partitioning Cut-size = C 10

  11. Terminal Propagation Cut-size = C’ > C 11

  12. Cut size increases cut-size : C  C’ B1 C B2 P P2 u P1 P1+C = TB1r = P P1= 2r-1 P P1+P2 = T(B1+B2)r  --- effect of external net 12

  13. Relationship r --- Partitioning Rent exponent r’ --- Placement Rent exponent B --- number of cells  --- 0    1, effect of external net • Limited Range • Rough Estimation from r to r’ 13

  14. Experiment Background • Benchmark: MCNC+IBM • IBM: Derived from ISPD98 partitioning benchmark • Size from 20k cells --- 220k cells • Partitioning: hMetis • Placement: wirelength-driven • Capo, Feng Shui, Dragon • Rent exponent extraction • Linear regression • Each point corresponds to one level in partitioning or placement 14

  15. Experimental Observation (1) • Example: ibm11, 68k cells Partitioning r Estimated Placement r’ Placement r’ Capo Feng Shui Dragon 15

  16. Wirelength Estimation based on Rent’s rule • Classical problem • Donath 1979 • Stroobandt et.al 1994 • Davis et.al 1998 • Needs geometrical (placement) Rent exponent • Comparison • Estimated WL using Partitioning Rent exponent • Estimated WL using Placement Rent exponent • Total Wirelength after global routing (maze-based) 16

  17. Experimental Observation (2) • Example: ibm13, 81k cells • Overall: Estimation based on Partitioning Rent exponent under-estimate total wirelength 19% --- 32% Partitioning r = 0.600 Actual WL Capo FS Dragon Placement Rent r’ Capo FS Dragon 17

  18. Estimation based on r’ Derivation of Placement Rent exponent Recursively bipartitioning circuit r (partition r) r’ (place r) Wirelength Estimation Estimated total wirelength 18

  19. Estimation based on r’ • Estimation results: • -12% --- +14% • Total wirelength estimation is hard • Rent exponent • Placement approach • Routing approach • Congestion --- unevenly distributed wires 19

  20. Rent exponent, a placement metric? • Hagen et.al • Rent exponent is a measurement of partitioning approach • Ratio-cut gives the smallest Rent exponent • Similar case in Placement? • Ordinary placement measurement Total bounding box wirelength or routed wirelength • Correlation between wirelength and Rent exponent? 20

  21. Experimental Observation Bounding box wirelength Routed wirelength Rent exponent • Weak correlation: most shorter wirelengths • correspond to lower Rent exponents • Open question 21

  22. Conclusion • Topological (partitioning) Rent exponent and Geometrical (placement) Rent exponent are different. • Relationship between two Rent exponents. • Wirelength Estimation should use Geometrical Rent exponent. • Open question: Is Rent exponent a metric of placement quality? 22