system level interconnect prediction (slip) 20081 sidewinder: a scalable ilp-based router jin hu,...

System Level Interconnect Prediction (SLIP) 2008 1

Sidewinder:Sidewinder:A Scalable ILP-Based RouterA Scalable ILP-Based Router

Jin Hu, Jarrod Roy, and Igor Markov

Dept. of Computer Science and EngineeringUniversity of Michigan


Why is Global Routing Important?High-level

• Abstract away design rules

• Chip routing grid

• Nets set of points

• Connect net points and assign to routing edges

Low level

• Uses global routing solution

• Assigns routes to routing tracks

• Must obey design rulesMust be certain distance apart

Global RoutingGlobal Routing

Detail RoutingDetail Routing

Final solution quality heavily dependent on global routing solution


Given:Routing grid G

with capacities

Net list N with n nets

Global Routing Problem

. . .

Net 1 Net 2 Net n

X

Y

g(x,

y)

cg(x,y)→g(x+1,y

)

…

cg(x,y)→g(x-

1,y)

cg(x,y)→g(x,y+

1)

…

cg(x,y)→g(x,y-

1)

…

…


Objective – route all nets while minimizing: Overflow: exceeded

(violations) grid capacities

Wirelength: total routed distance of nets

(traditional goal of routers)

Bends: changes in routing direction

(additional goal due to technology scaling)

Global Routing Problem

capacity = 2

overflow = 1

wirelength = 4

bends = 2


Directional preference on each metal layer

Bends require change in metal layers viasTungsten vs. copper or aluminumMore resistant, larger area, less reliable ISPD 2007 Routing Contest (IBM)

heavily penalizes vias: 3x more than WL

Why Minimize Bend Count?

Metal 1: Local routing (not shown)

Metal 3: Horizontal tracks

Metal 2: Vertical tracks

via


Outline

Common routing approaches Sidewinder

MethodologyExample

Results Conclusion

Our Contributions


Rip-up and Reroute (RRR)Route one net at a timeRip-up congested nets and

reroute in less congested areas

Routing Nets in Series

Net orderingvery important!

capacity = 2Blue BlackRed

BlueRed

Black

violationviolation

Maze Maze routeroute

Reroute with

different order


Routing nets in Parallel

Integer Linear Programming (ILP)Considers all variables simultaneouslyFinding optimal solutions is NP-Complete

Historically unscalable but have improved ILP solver technology: CPLEX v9, v10, v11More powerful CPUs

Significant progress in ILP formulationsPrevious work: BoxRouter 1.0 [Cho DAC06]


Sidewinder MethodologyInitial Routing

Improve?

Path Selection for ILP

yes

Final Routing

no

Generate Congestion Map

ILP Routing

• Breaks up multi-pin nets into subnets

• Routes with L-shape initially

• Calculates total congestion

• Chooses best 2 options for each net

• ILP route for new solution New solution is never worse than previous

• Repeats until no improvement

• Routes remaining nets with maze router

• Allows overflow


Initial Routing

Decompose 3+ pin nets into 2-pin subnets

Route all subnets with only LsSome nets may be unrouted

capacity = 2

Routed Nets: Blue, Red

Unrouted Nets: Black

Net Subnet 1Net topology

Subnet 2 Subnet 3


Generate Congestion Map

Use current solution to see congestion For each routed net, subtract 90% of usage

from total capacitiesLater account for 2nd path candidate

capacity = 2

2

2

0.2

0.2

capacity


Path Selection

For each net, consider possible patterns

LL-shapes-shapes ZZ-shapes-shapes CC-shapes-shapes(Potential)(Potential)

Maze RouteMaze Route


Path Selection

Use legal choices only

For each legal choice, calculate priority Pif all path segments have space

P = min(each grid edge);

else

P = -total overflow;

Use total available space for tie-breaker


Path Selection

Path Type Priority Tiebreaker

L1 (over, up) 0.2 0.4

L2 (up, over) ILLEGAL ILLEGAL

Z1 (vertical) ILLEGAL ILLEGAL

Z2 (horizontal) ILLEGAL ILLEGAL

C1 (+1N) ILLEGAL ILLEGAL

C2 (+1S) ILLEGAL ILLEGAL

C3 (+1E) 2 8

C4 (+1W) 2 8

C5 (+1N, +1E) ILLEGAL ILLEGAL

C6 (+1S, +1W) ILLEGAL ILLEGAL

Maze 0.2 0.4

Consider all unrouted nets first: Black Path

L1 C3 C4

• Pick top 2 choices as candidates

• Update congestion map each with usage of 50%

0.2

0.2

0.2

0.2

1.5 1.5

1.5

1.5

1.5

1.5

1.5 1.5

Maze

2 2

2

2

22

2

2


Path Selection

L1 C3 C4 Maze

0.2

0.2

1.5 1.5

1.5

1.5

1.5

1.5

1.5 1.5


L1 (over, up) 0.2 0.4






C3 (+1E) 1.5 6

C4 (+1W) 1.5 6



Maze 0.2 0.4

Consider all routed nets next: Red Path

0.2

0.2

1.5 1.4

1.4

1.4

1.5

1.5

1.5 1.4

• Pick top 1 choice as candidate

• Update congestion map with usage of 10%


Path Selection

L1 C3 C4 Maze


L1 (over, up) 0.2 0.4






C3 (+1E) 1.4 5.8

C4 (+1W) 1.5 6



Maze 0.2 0.4

Consider all routed nets next: Blue Path

• Pick top 1 choice as candidate

• Update congestion map with usage of 10%

0.2

0.2

1.5 1.4

1.4

1.4

1.5

1.5

1.5 1.4

0.2

0.2

1.4 1.4

1.4

1.4

1.4

1.4

1.4 1.4


ILP Formulation n

nnnn xwxwMaximize )( : 2211

Maximizes total number of nets routed

nnnn

nn

xxww

Nnxx

Where

2121

21

,for snet weight the: ,

netlist net each for paths 2 the: ,

:

nxx

nxx

toSubject

nn

nn

}1,0{,

1

:

21

21 Ensures at most 1 path is selected

10 ,0 ,),( )()1,(),(,

)1,(),(21

21

YjXiGjigcxxjigjigxx

jigjignn

nn

Capacity constraint in N direction

),(each for sconstraintcapacity 4 the:

x size of in cell grid the: ),(

)1,1(),( jigc

YXGjig

jigjig

YjXiGjigcxxjigjigxx

jigjignn

nn

0 ,0 ,),( )()1,(),(,

)1,(),(21

21

Capacity constraint in S direction

Capacity constraint in E direction

Capacity constraint in W direction

YjXiGjigcxxjigjigxx

jigjignn

nn

0 ,10 ,),( )(),1(),(,

),1(),(21

21

YjXiGjigcxxjigjigxx

jigjignn

nn

0 ,0 ,),( )(),1(),(,

),1(),(21

21


Choosing the Net Weights

Objective Function

Prioritizes choices by lowest wirelengthand number of bends

Path Type +WL +bends

L-shapes 1.00 +0 +0

Z-shapes 0.99 +0 +1

C-shapes 0.98 +2/+4 +2

Maze Route 0.97 variable variable

n

nnnn xwxwMaximize )( : 2211

nw


Iterative Improvement

Recall: for each routed net, 1 choice is from previous solutionWorst Case: New solution = Previous solution

Iterations stop when no improvement Final Routing: route all remaining nets with m

aze router (Dijkstra’s)

Every new solution is no worse than previous


Empirical Validation (ILP Only)

ISPD98 Benchmark Suite

• Real designs from IBM

• Standard suite in global routing

• Experiments ran on AMD Opteron 2.4 GHz with 4 GB of RAM

• ILP solver: CPLEX

• Net Decomposition: FLUTE [Chu TCAD07]


Results - Overflow

• Able to fully route 7/107/10 benchmarks

• Better than BoxRouter 1.0 [DAC06] on 8/108/10 benchmarks


Results - Wirelength

On Average: 0.5%0.5% Less Wirelength Than BoxRouter 1.0

ibm01 ibm02 ibm03 ibm04 ibm05 ibm06 ibm07 ibm08 ibm09 ibm100.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

Benchmark

SidewinderBoxRouter 1.0GeoSteiner

Normalized to GeoSteiner

GeoSteiner: Steiner tree generator

• Best lower bound for WL

• No capacity restrictions (routing solutions illegal)

• Impractically slow


Results – Bends

On Average: 6.4%6.4% Fewer Vias Than BoxRouter 1.0

ibm01 ibm02 ibm03 ibm04 ibm05 ibm06 ibm07 ibm08 ibm09 ibm100.9

0.95

1

1.05

1.1

1.15

Benchmark

SidewinderBoxRouter 1.0

Normalized to Minimum of Both Routers

Significantly fewer bends

• Vast majority of routes are patterns – L, Z, C

• Better bend count on every benchmark


Sidewinder: Summary

Scalable global router based on ILPUses dynamically updated congestion mapFirst ILP-based router to have global scope – lo

oks at entire routing grid Produces better solution quality

Average of 0.5% less wirelengthAverage of 6.4% fewer vias

system level interconnect prediction (slip) 20081 sidewinder: a scalable ilp-based router jin hu,...

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