Embed Size (px)
Citation preview
1
Ryan Kastner
ASIC/SOC, September 2000
Coupling Aware RoutingCoupling Aware RoutingCoupling Aware RoutingCoupling Aware Routing
Ryan Kastner, Elaheh Bozorgzadeh and Majid Sarrafzadeh
Department of Electrical and Computer Engineering
Northwestern University
Ryan Kastner, Elaheh Bozorgzadeh and Majid Sarrafzadeh
Department of Electrical and Computer Engineering
Northwestern University
2
Ryan Kastner
ASIC/SOC, September 2000
OutlineOutlineOutlineOutline
Coupling Definition Effects
Coupling-Free Routing Definition Uses
Algorithms for Coupling-Free Routing Greedy Forcing
Results Conclusion
Coupling Definition Effects
Coupling-Free Routing Definition Uses
Algorithms for Coupling-Free Routing Greedy Forcing
Results Conclusion
3
Ryan Kastner
ASIC/SOC, September 2000
CouplingCouplingCouplingCoupling
Definition - capacitance between adjacent wires Deep submicron trends:
Interconnect has more dominant role Scale wire height at slow rate compared to width
Definition - capacitance between adjacent wires Deep submicron trends:
Interconnect has more dominant role Scale wire height at slow rate compared to width
Coupling can account for up to 70% of interconnect capacitance even in .25 micron designsCoupling can account for up to 70% of interconnect capacitance even in .25 micron designs
4
Ryan Kastner
ASIC/SOC, September 2000
Effects of couplingEffects of couplingEffects of couplingEffects of coupling Delay deterioration
Total capacitance seen by a gate is no longer a constant value Causes uncertainty in delay calculation
Crosstalk Noise caused by coupling Leads to circuit failure and increased delay
Delay deterioration Total capacitance seen by a gate is no longer a constant value Causes uncertainty in delay calculation
Crosstalk Noise caused by coupling Leads to circuit failure and increased delay
Ce= 0Ce= 0 Ce= 2Cc Ce= 2Cc
aggressor
victim
5
Ryan Kastner
ASIC/SOC, September 2000
Interconnect delayInterconnect delayInterconnect delayInterconnect delay
resistivity of the conductor = insulator dielectric constantw,t,h = conductor’s width, thickness and separationl, s = coupled length and spacing of interconnect
During routing, we can control l and s
resistivity of the conductor = insulator dielectric constantw,t,h = conductor’s width, thickness and separationl, s = coupled length and spacing of interconnect
During routing, we can control l and s
6
Ryan Kastner
ASIC/SOC, September 2000
How can we avoid coupling?How can we avoid coupling?How can we avoid coupling?How can we avoid coupling?
Interconnect spacing Increasing the spacing between wires can reduce coupling Much work on this subject (Wong @ U. Texas, Cong @ UCLA)
Coupled interconnect length Coupling directly depends on the parallel length of adjacent
wires Route wires to avoid long parallel overlaps
Interconnect spacing Increasing the spacing between wires can reduce coupling Much work on this subject (Wong @ U. Texas, Cong @ UCLA)
Coupled interconnect length Coupling directly depends on the parallel length of adjacent
wires Route wires to avoid long parallel overlaps
HighlycoupledHighlycoupled No couplingNo coupling
7
Ryan Kastner
ASIC/SOC, September 2000
Simplify definition of couplingSimplify definition of couplingSimplify definition of couplingSimplify definition of coupling
Two wires couple if the segments forming them are closer than d units for more than l units
Two wires couple if the segments forming them are closer than d units for more than l units
distance < ddistance < dlength > llength > l
Two wires couple if distance < d AND length > l
Otherwise, they do not couple
Two wires couple if distance < d AND length > l
Otherwise, they do not couple
8
Ryan Kastner
ASIC/SOC, September 2000
Coupling-Free Routing (CFR)Coupling-Free Routing (CFR)Coupling-Free Routing (CFR)Coupling-Free Routing (CFR)
Given a set of nets S={Ni={(x1i,y1i),(x2i,y2i)} | 1 i n} S is coupling-free if there is a single bend layout for
every net such that no two routes couple
Given a set of nets S={Ni={(x1i,y1i),(x2i,y2i)} | 1 i n} S is coupling-free if there is a single bend layout for
every net such that no two routes couple
Coupled layoutCoupled layout Coupling-free layoutCoupling-free layout
9
Ryan Kastner
ASIC/SOC, September 2000
Usefulness of CFRUsefulness of CFRUsefulness of CFRUsefulness of CFR
Minimum interconnect delay Single bend routing insures minimum wirelength Introduces only one via Coupling between nets is minimized
Increases predictability of routes Allows accurate prediction of wirelength, congestion, etc Predictable Routing, ICCAD 2000
Speeds up single net routing process
Minimum interconnect delay Single bend routing insures minimum wirelength Introduces only one via Coupling between nets is minimized
Increases predictability of routes Allows accurate prediction of wirelength, congestion, etc Predictable Routing, ICCAD 2000
Speeds up single net routing process
10
Ryan Kastner
ASIC/SOC, September 2000
Usefulness of CFR-Detailed RoutingUsefulness of CFR-Detailed RoutingUsefulness of CFR-Detailed RoutingUsefulness of CFR-Detailed Routing
As fabrication technology progresses, routing layers become more plentiful
Reserving layers for critical nets is common Power, ground and clock are already routed on preferred layers
Use preferred layers for critical nets Layer can be used for timing critical nets Critical nets have little “slack” - need minimum delay CFR insures that nets have minimum delay
minimum wirelength minimum number of vias minimum coupling
As fabrication technology progresses, routing layers become more plentiful
Reserving layers for critical nets is common Power, ground and clock are already routed on preferred layers
Use preferred layers for critical nets Layer can be used for timing critical nets Critical nets have little “slack” - need minimum delay CFR insures that nets have minimum delay
minimum wirelength minimum number of vias minimum coupling
11
Ryan Kastner
ASIC/SOC, September 2000
Usefulness of CFR-Single Layer Usefulness of CFR-Single Layer Usefulness of CFR-Single Layer Usefulness of CFR-Single Layer
Single layer routing is a important problem for routing Area routers often use single layer routing for each layer Printed Circuit Board (PCB) use single layer algorithms
Best known academic single layer router (developed by Lin and Ro) uses two step process
Find a maximum planar set of one-bend nets Use rubberband equivalent to route remaining nets
CFR can be easily be incorporated into in first step to
produce a planar set of nets with minimum coupling
Single layer routing is a important problem for routing Area routers often use single layer routing for each layer Printed Circuit Board (PCB) use single layer algorithms
Best known academic single layer router (developed by Lin and Ro) uses two step process
Find a maximum planar set of one-bend nets Use rubberband equivalent to route remaining nets
CFR can be easily be incorporated into in first step to
produce a planar set of nets with minimum coupling
12
Ryan Kastner
ASIC/SOC, September 2000
Usefulness of CFR-Global routingUsefulness of CFR-Global routingUsefulness of CFR-Global routingUsefulness of CFR-Global routing
Coupling at global routing is hard to determine Routes are not exact, makes it difficult to know adjacency
relations of nets Detailed router will often make local changes
Global routing allows global changes, it is next to impossible to make global changes at the detailed stage
A coupling-free global layout will produce a coupling-free detailed layout
Coupling at global routing is hard to determine Routes are not exact, makes it difficult to know adjacency
relations of nets Detailed router will often make local changes
Global routing allows global changes, it is next to impossible to make global changes at the detailed stage
A coupling-free global layout will produce a coupling-free detailed layout
13
Ryan Kastner
ASIC/SOC, September 2000
MAX-CFL DefinitionMAX-CFL DefinitionMAX-CFL DefinitionMAX-CFL Definition
Given a set of two-terminal nets S and a positive integer K |S|. Is there a single bend routing for at least K nets such that no two routings couple?
Additional routing constraints can easily be added Routed nets must be planar Routed nets must be routed on two layers
MAX-CFL for planar layouts is NP-Complete General MAX-CFL NP-Complete?
Given a set of two-terminal nets S and a positive integer K |S|. Is there a single bend routing for at least K nets such that no two routings couple?
Additional routing constraints can easily be added Routed nets must be planar Routed nets must be routed on two layers
MAX-CFL for planar layouts is NP-Complete General MAX-CFL NP-Complete?
14
Ryan Kastner
ASIC/SOC, September 2000
AlgorithmsAlgorithmsAlgorithmsAlgorithms
We developed two algorithms Greedy Forcing
Algorithms try to maximize number of nets routed and/or criticality of routed nets
We developed two algorithms Greedy Forcing
Algorithms try to maximize number of nets routed and/or criticality of routed nets
15
Ryan Kastner
ASIC/SOC, September 2000
CriticalityCriticalityCriticalityCriticality
Most often defined as the amount of timing slack available for the net
Slack values given gates, nets during logic synthesis stage Delay through a network of gates and wires must not exceed
clock frequency
Most often defined as the amount of timing slack available for the net
Slack values given gates, nets during logic synthesis stage Delay through a network of gates and wires must not exceed
clock frequency
Flip Flop
gate
gate
gateFlip Flop
networknetwork
DSM increases for need interconnect timing slack DSM increases for need interconnect timing slack
16
Ryan Kastner
ASIC/SOC, September 2000
Results in terms of criticalityResults in terms of criticalityResults in terms of criticalityResults in terms of criticality
Benchmarks do not have criticality data
We used wire length for criticality Delay increases at rate:
O(l2) without wiresizing O(ll) with optimal wiresizing O(l) with proper buffer insertion
We ran experiments using each function as criticality
Benchmarks do not have criticality data
We used wire length for criticality Delay increases at rate:
O(l2) without wiresizing O(ll) with optimal wiresizing O(l) with proper buffer insertion
We ran experiments using each function as criticality
Criticality functions: Quadratic (l2), l-root-l (l l) and linear (l) functions
Criticality functions: Quadratic (l2), l-root-l (l l) and linear (l) functions
17
Ryan Kastner
ASIC/SOC, September 2000
Greedy AlgorithmGreedy AlgorithmGreedy AlgorithmGreedy Algorithm
1 Given a set of nets N
2 Sort N by criticality (largest smallest)
3 for each net n N
4 do route n in upper-L or lower-L, if possible
Simple and fast; Running time is O(n log n)
1 Given a set of nets N
2 Sort N by criticality (largest smallest)
3 for each net n N
4 do route n in upper-L or lower-L, if possible
Simple and fast; Running time is O(n log n)
18
Ryan Kastner
ASIC/SOC, September 2000
Forcing algorithmForcing algorithmForcing algorithmForcing algorithm
In order to avoid coupling, a routing of a net forces another net into a particular route
In order to avoid coupling, a routing of a net forces another net into a particular route
Net 1Net 1
Net 2Net 2 To avoid coupling
Net 2 must be lower-L
To avoid coupling
Net 2 must be lower-L
Net 1Net 1
Net 2Net 2
An lower-L routing of Net 1 forces a lower-L routing of Net 2An lower-L routing of Net 1 forces a lower-L routing of Net 2
19
Ryan Kastner
ASIC/SOC, September 2000
Forcing AlgorithmForcing AlgorithmForcing AlgorithmForcing Algorithm
1 Given a set of net N2 Determine the forcing interactions between the nets N3 R NULL4 for each net n N5 do R R U n.upper-L U n.lower-L6 Sort R by number of forcings (smallest largest)7 for each routing r R8 do if net associated with r is unrouted and r is
routable9 then route r
1 Given a set of net N2 Determine the forcing interactions between the nets N3 R NULL4 for each net n N5 do R R U n.upper-L U n.lower-L6 Sort R by number of forcings (smallest largest)7 for each routing r R8 do if net associated with r is unrouted and r is
routable9 then route r
Running time is O(n2)Running time is O(n2)
20
Ryan Kastner
ASIC/SOC, September 2000
EvaluationEvaluationEvaluationEvaluation
Find the x “most critical” nets in each circuit Vary x from 25 to 250 Perform algorithms on the x nets Gathered statistics from each layout
Percentage of nets laid out Criticality of nets laid out
Find the x “most critical” nets in each circuit Vary x from 25 to 250 Perform algorithms on the x nets Gathered statistics from each layout
Percentage of nets laid out Criticality of nets laid out
21
Ryan Kastner
ASIC/SOC, September 2000
Circuit BenchmarksCircuit BenchmarksCircuit BenchmarksCircuit BenchmarksData file Num Cells Num Nets Num Pins MCNC Benchmarksprimary1 833 1156 3303primary2 3014 3671 12914avqs 21584 30038 84081biomed 6417 7052 22253struct 1888 1920 5407 ISPD98 Benchmarksibm01 12036 13056 45815ibm05 28146 29647 127509ibm10 68685 29647 127509ibm15 161187 186991 716206ibm18 210341 202192 819969
22
Ryan Kastner
ASIC/SOC, September 2000
Fraction of nets placedFraction of nets placedFraction of nets placedFraction of nets placed
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
25 50 75 100 125 150 175 200 225 250
total nets considered
fra
cti
on
ro
ute
d
greedy
forcing
Algorithm Avg. routes laid outgreedy 30.28%direct forcing 35.30%
Forcing algorithm outperforms greedy algorithmForcing algorithm outperforms greedy algorithm
23
Ryan Kastner
ASIC/SOC, September 2000
Forcing vs. GreedyForcing vs. GreedyForcing vs. GreedyForcing vs. Greedy
forcing vs greedy
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
25 50 75 100 125 150 175 200 225 250
total nets considered
rela
tiv
e c
riti
ca
lity
quadratic
linear
l root l
relative criticality = (greedy criticality)/(forcing criticality)relative criticality = (greedy criticality)/(forcing criticality)
24
Ryan Kastner
ASIC/SOC, September 2000
Criticality resultsCriticality resultsCriticality resultsCriticality results
Greedy algorithm outperforms every other function
Using linear function: 20% better than forcing algorithm
l-root-l and quadratic functions have similar trends
Greedy algorithm outperforms every other function
Using linear function: 20% better than forcing algorithm
l-root-l and quadratic functions have similar trends
Greedy algorithm best for criticalityGreedy algorithm best for criticality
25
Ryan Kastner
ASIC/SOC, September 2000
ConclusionConclusionConclusionConclusion
Coupling-free routing useful for many routing algorithms Detailed routing Global routing Single layer routing
Allows early prediction of routing metrics Congestion Wire length Interconnect delay
Implication algorithm maximizes routes placed Greedy algorithm maximizes criticality placed
Coupling-free routing useful for many routing algorithms Detailed routing Global routing Single layer routing
Allows early prediction of routing metrics Congestion Wire length Interconnect delay
Implication algorithm maximizes routes placed Greedy algorithm maximizes criticality placed
