Perimeter-degree: A Priori Metric for Directly Measuring and Homogenizing Interconnection Complexity in Multilevel Placement

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1 Perimeter-degree: A Priori Metric for Directly Measuring and Homogenizing Interconnection Complexity in Multilevel Placement Navaratnasothie Selvakkumaran (Selva) selva@cs.umn.edu 1

2 Authors Navaratnasothie. Selvakkumaran University of Minnesota Phiroze N.Parakh Monterey Design Systems Inc George Karypis University of Minnesota 2

3 Overview Background Placement is becoming harder Congestion Objective Motivation Experimental results Conclusions 3

4 Placement is becoming harder Support for physical synthesis Fast and accurate prototyping Focus on timing Presence of macro cells Ever increasing problem size Congestion elimination 4

5 Congestion Why Congestion? Measuring congestion. Existing techniques 5

6 Why Congestion? Demand exceeds supply Non homogeneous supply Location of bin Macro cells Lets assume uniform supply for the rest of the discussion Non homogeneous demand. 6

7 Measuring Congestion Half-perimeter wirelength Router based congestion estimation Stochastic congestion estimation 7

8 Measuring Congestion Half-perimeter Wirelength Good metric more wires => more congestion But insufficient regional variations? Bounding box of high fan-out net Vs low fan-out net? We need additional metrics Pin density? Bin degree? (no of external nets of a bin) 8

9 Measuring Congestion Router based estimates Accurate But computationally very expensive Stochastic estimates Relatively accurate Still expensive for fast prototyping 9

10 Existing Congestion Reduction Techniques Posteriori / online methods Established methods But too many constraints as the placement problem becomes harder Is priori feasible? Required for fast prototyping 10

11 Overview - recap Background Placement is becoming harder Congestion Objective Motivation Experimental results Conclusions 11

12 Objective To come up with priori techniques to aid half-perimeter wirelength objective to produce placements with lower regional variations. Use single objective of half-perimeter wirelength Quality is measured in terms of congested edges after global placement 12

13 Overview - recap Background Placement is becoming harder Congestion Objective Motivation Experimental results Conclusions 13

14 Motivation Known metrics for congestion control Pin density Bin degree Can we do better? 14

15 Motivation : known metrics Pin density dilute high pin density portions of netlist But equal pin density with varying demand possible Following clusters show equal pin density but different degree (demand) 15

16 Motivation : known metrics Bin Degree Impact of bin degree on regional wirelength Number of interconnects Gradient = 2* local Rent s exponent - 3 Interconnect length Doubling bin degree results in more than twice as much wirelength associated with that bin 16

17 Motivation : known metrics Degree of a cluster Good metric but captures only demand Following clusters have equal degree but differ in routing supply A B 17

18 Motivation : a better metric Degree is a demand at the perimeter of a cluster Supply is proportional to perimeter Thus we define a new metric perimeterdegree Perimeter-degree = degree / perimeter 18

19 Overview - recap Background Placement is becoming harder Congestion Objective Motivation Experimental results Conclusions 19

20 Experimental Results Allocate whitespace to clusters with high perimeter-degree Cell level (pin density is equally effective) Cluster level Combined method Direct use of perimeter-degree as capacity constraint 20

21 Whitespace based schemes Percentage reduction in mild and severe congested edges mild severe cell inflation cluster inflation combined method 21

22 Direct use of Perimeter-degree Set area of clusters in proportion of perimeterdegree of clusters so that total area does not change. Since actual area is not used. Bin capacity violations may occur. More legalization iterations Results Half-perimeter wirelength increased by 0.1% Mild congested edges reduced by 11% Severe congested edges reduced by 26% 22

23 Conclusion We have shown that congestion can be reduced substantially with negligible change in half-perimeter wirelength. Same amount of interconnects but substantially lower congestion => homogeneous routing demand Negligible computations required 23

24 Questions 24

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