congestion estimation in floorplanning
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Congestion Estimation in Floorplanning
Supervisor:
Evangeline F. Y. YOUNGby
Chiu Wing SHAM
Overview
IntroductionBackgroundCongestion ModelingExperimental ResultsFuture Works
IntroductionMotivations:
80% of the clock cycle consumed by interconnects
Interconnect optimization becomes the major concern in floorplanning
Appropriate interconnect estimation is required in floorplanning
Major Role of Floorplanning
Minimization of chip areaOptimization of interconnect cost
WirelengthTiming delayRoutability
Others:Heat dissipationNoise reductionPower consumption
Congestion Planning
Congestion planning is important to circuit designExcessive congestion may result in a local shortage
of routing resourcesA large expansion in areaFailure in achieving timing closure
Congestion modelingGiven a packing and netlistEstimating the congestion and routability instead
of real routing
Congestion Model A
The number of feasible routes for wire kpassing through each grid
6
61 3
3 4
3 1
3
The routes for wire k
The probability that wire k passing through this grid, Pk(x,y)=4/6=0.67
Congestion Model A
Congestion of the grid (x,y)
- Expected number of wires passing through the grid (x,y), weight(x,y):
k
k yxPyxweight wireall
),(),(
Limitations
The weighted number of feasible routes for wire kpassing through each grid
24
248 12
12 8
12 8
12
The routes for wire k
The probability that wire k passing through this grid, Pk(x,y)=8/24=0.33
Bends: 1,Weight: 8
Bends: 3,Weight: 1
Bends: 2,Weight: 3
Bends: 1,Weight: 8
Bends: 2,Weight: 3
Bends: 3,Weight: 1
Model A assumes that all feasible routes have the same probability of being selected
In real cases, the routes with less bends should have a higher probability of being selected
Congestion Model B
s
T
Divisions
1/3 1/2
1/2 1/3
1/2 1/3
1/2
The probability of wire kpassing through each grid
equal probability ineach division
Congestion Model B
where distk(x, y) is the distance from the source of wire k to the grid (x, y) and cntk(r) is the number of grids in the division that is r grids from the source.
)),((
1),(
yxdistcntyxP
kkk
Congestion of the grid (x,y) due to wire k
- the probability of wire k pass through the grid (x,y), Pk(x,y):
LimitationsRouting resources:
Both models assume that routing resources are equal at different locations
Routing resources should be different at different locations in real cases
Wirelength:Both models assume that all nets are routed in
their shortest Manhattan distanceSome nets may be routed with detours in real
cases
Our ApproachesCongestion Model A*:
Based on model ARouting resources can be different at different locations
Congestion Model B*:Based on model BRouting resources can be different at different locations
Congestion Model C:Based on model B*Routing resources can be different at different locationsEach net may be routed with detours
Congestion Model A*
1 1 1
1 1 1
1 0.5 1
s
T
1
1
The routes for wire k
0.50.5
0.50.5 4
41 2
2 2
2 1
2
The number of feasible routes forwire k passing through each grid
4/4
4/41/4 2/4
2/4 2/4
2/4 1/4
2/4
The probability of wire kpassing through each grid
Considering routing resources
Congestion Model A*Notations:
res(x,y): relative routing resources at the grid (x, y)Lk(x,y): the set of feasible routes for wire k passing through the grid
(x,y)Lk: the set of all feasible routes for wire kGk(l): the set of grids that the route l of wire k will pass throughwk(l): the weight of each feasible route l
Equations:
k
k
k
Llk
yxLlk
k
lGyxk
lw
lw
yxP
yxreslw
),(
)(),(
)(
)(
),(
),()(
Congestion Model B*
s
T 11
1 1
1
0.5
1
Division
2/5 1/2
1/2 1/5
1/2 2/5
1/2
The probability of wire kpassing through each grid
Considering routing resources
Congestion Model B*Notations:
res(x,y): relative routing resources at grid (x, y)
distk(x,y): the distance from the source of wire k to the grid (x,y)
divk(r): the set of grids that are r grids from the source of wire k
Equation
)),(()(
),(
),(),(
yxdistdivx,y
k
kk
yxres
yxresyxP
Congestion Model C
S
T
: Optional region
: Compulsory region
S
T
: SMD region
(0,0)Divisions
Considering routing resourcesEach net may be routed with detours
Congestion Model CNotations:
res(x,y): relative routing resources at the grid (x, y)dist(x,y): the distance from the the grid (0, 0) to the grid (x,y)divk(r): the set of grids that are r grids from the grid (0,0) of wire kCRk: the set of divisions located in the compulsory regionORk: the set of divisions located in the optional region: degrade factor for the grids outside the SMB region: degrade factor for the grids in the optional regiond(i, j, k, l): the distance between the grid (i, j) and (k, l)
Congestion Model C
Equation:
),,,(),,,(),,,(),( yxyxyxyxSMD ssttdttjidssjidjidk
Compulsory Region (divk(dist(x, y)) CRk):
Optional Region (divk(dist(x, y)) ORk):
)),(()(
),(
),(
)/),((
/),(),(
yxdistdivi,j
jid
yxd
k
k
kSMD
kSMD
jires
yxresyxP
),(
)),(()(
),(
),(1
)/),((
/),(),( jid
yxdistdivi,j
jid
yxd
kkSMD
k
kSMD
kSMD
jires
yxresyxP
Implementation
Floorplanning:Representations: SPHeuristics: Simulated AnnealingCost function: Weighted sum of wirelength
and number of over-congested grid
RoutingCadence’s WROUTE
Experimental Results
Test cases:
s298 188.0 162.0s344 241.0 222.0s349 242.0 223.0s382 238.0 215.0s386 227.0 195.0s400 246.0 222.0s444 263.0 238.0s510 293.0 271.0s526 281.0 250.0s641 517.0 514.0s713 532.0 527.0s820 395.0 357.0s832 395.0 355.0
CasesNo. ofcells
No. ofnets
Experimental Results
A* B* Cs298 0.00 0.00 0.00 0.00s344 0.00 0.00 0.00 0.00s349 0.00 0.00 0.00 0.00s382 0.00 0.00 0.00 0.00s386 0.00 0.00 0.00 0.00s400 0.00 0.00 0.00 0.00s444 0.00 0.00 0.00 0.00s510 0.00 0.00 0.00 0.00s526 0.00 0.00 0.00 0.00s641 226.00 0.50 1.00 0.00s713 460.50 110.00 4.25 0.00s820 0.00 0.25 0.00 0.00s832 46.50 0.00 0.00 0.00
No. of violationsCases
Experimental Results
A* B* Cs298 15964.50 15838.50 14910.25 15187.25s344 28627.75 26914.75 29472.25 27693.25s349 31799.25 27686.25 29381.75 28701.50s382 27686.25 25919.50 26026.25 23740.75s386 27836.00 27966.25 27079.25 25637.25s400 26460.00 26962.25 28128.50 25950.00s444 32160.75 30021.75 29796.25 28022.50s510 60940.50 58669.00 58806.00 56296.75s526 45291.00 39305.50 39569.25 36518.50s641 NA NA NA 152447.75s713 NA NA NA 174690.50s820 120262.75 NA 118631.50 117423.25s832 NA 115408.00 114526.00 111582.75
WirelengthCases
Experimental Results
A* B* Cs298 116.5 186.0 156.6 1028.2s344 235.0 318.6 277.9 3353.1s349 232.8 311.0 251.5 3209.9s382 232.8 333.6 288.8 3580.9s386 235.1 296.0 262.9 3768.9s400 197.9 312.6 263.2 1900.8s444 287.4 429.8 345.2 4347.5s510 255.3 387.6 338.2 2473.9s526 324.1 447.7 427.6 7373.4s641 811.4 1072.1 950.5 4340.0s713 881.3 1137.0 1014.0 4408.3s820 640.5 791.2 751.2 10984.7s832 523.7 728.6 654.5 4988.5
CasesRunning time
Future works
Limitations of congestion model CToo many parameters (, ) are usedLonger running time
Limitations of representationPacked closely together
Example
Example
Example 2
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