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NuC
AD
ELECTRICAL ENGINEERING AND COMPUTER SCIENCEMcCormick Northwestern UniversityRobert R. McCormick School of Engineering and Applied Science
FA-STAC : A framework for fast and accurate static timing analysis with
coupling
Debasish DasElectrical Engineering and Computer ScienceNorthwestern UniversityEvanston, IL 60208
International Conference on Computer Design, San Jose, CA
October 2nd , 2006
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April 18, 2023 (2)
Co-authors
• Ahmed Shebaita, EECS, Northwestern University
• Hai Zhou, EECS, Northwestern University
• Yehea Ismail, EECS, Northwestern University
• Kip Killpack, Strategic CAD Lab, Intel Corporation
Industry Support
Cell Library Provider
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April 18, 2023 (3)
Outline
• Previous Research
• Accurate Coupling Delay Computation
• Efficient Iteration Mechanism
• Experimental Setup
• Conclusions and future work
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April 18, 2023 (4)
Previous Research (Coupling Model)
• Coupling cap dominates interconnect parasitics
• Miller coupling factor (MCF): switching dependent Step transitions : (0,2) Sapatnekar et.al, ICCAD 2000
Ramp Models : (-1,3) Kahng et.al, DAC 2000 Chen et.al, ICCAD 2000
Exponetial Models : (-1.885,3.885) Ghoneima et.al, ISCAS 2005
• Coupling Model Issues: Models not extended to Timing Analysis
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April 18, 2023 (5)
Previous Research (Static Timing)
• Timing Analysis with x-cap iterative
• Iterative analysis with continous models: Chen et.al ICCAD 2000
• Iterative analysis with discrete models: Sapatnekar et.al ICCAD 2000, Chen et.al ICCAD 2000, Arunachalam et.al DAC 2000
• Iterative analysis issues Circuit/Coupling structure Ignored
No detailed study of convergence
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April 18, 2023 (6)
• Salient features Waveform based accurate coupling model
Efficient iteration scheme (Chaotic Iteration)
Circuit and Coupling structure exploration
Speeding up iteration scheme using structure
NuCAD Presents:
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April 18, 2023 (7)
Outline
• Previous Research
• Accurate Coupling Delay Computation
• Efficient Iteration Mechanism
• Experimental Setup
• Conclusions and future work
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April 18, 2023 (8)
Circuit Model
• Rise/Fall-Delay-Window : (rdl,rdh)/(fdl,fdh)
• Rise/Fall-Slew-Window : (rsl,rsh)/(fsl,fsh)
• Associated nodes with coupling edge : N1 and N2
NAND
NAND
NANDCC
N1
N2
N3
CCCC
N1
NANDI1
I2
Rise Arc
Fall Arc
Coupling Edge
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April 18, 2023 (9)
Motivational Example
• Input Delay Rise I1 : [2,4] I2: [3,5]
• Input Delay Fall I1 : [2.5,3.5] I2: [3.5,4.5]
• Input Slew Rise/Fall I1: [0.2,0.6] I2 : [0.4,0.8]
• Average input slew Rise/Fall I1 : 0.4 I2 : 0.6
• Compute initial switching windows: MCF = 1.0
Rise Window : [2.6,5.3]Rise Slew : [0.5,0.7]
Rise Window : [3.0,5.8]Rise Slew : [0.6,0.8]
MCF = 1.8
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April 18, 2023 (10)
Coupling Factor Computation
• Associated Nodes with coupling edge Victim Node (V)
Aggressor Node (A)
Static timing seeks for worst bounds
• Waveform generation on V and A Overlap ratio (k) computation
• Overlap ratio is defined as the ratio of aggressor output waveform that overlap with victim threshold voltage
Choose waveforms to generate worst possible k
Effective coupling cap : (1+/- 2k)xCC
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April 18, 2023 (11)
Waveform selection
Aggressor
Victim
Doa Do
a+tas
Dov Do
v+0.5tvs Do
v+tvs
t
t
K = 1.0
Victim
Doa Do
a+tas
Dov Do
v+0.5tvs Do
v+tvs
t
t
Aggressor
K = (Doa+ta
s-tvs)/ta
s
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April 18, 2023 (12)
Waveform selection
Aggressor
Victim
Doa Do
a+tas
Dov Do
v+0.5tvs Do
v+tvs
t
t
Victim
Doa Do
a+tas
Dov Do
v+0.5tvs Do
v+tvs
t
t
Aggressor
K = (0.5tvs)/ta
sK = (Doa+0.5tv
s-Dov)/ta
s
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April 18, 2023 (13)
Waveform Selection
Victim
Doa Do
a+tas t
tDov Do
v+0.5tvs Do
v+tvs
K = 0
Aggressor
Victim
Doa Do
a+tas t
t Dov Do
v+0.5tvs Do
v+tvs
Aggressor
K = 0
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April 18, 2023 (14)
Accurate Coupling Delay Computation
The idea is !
Compute D and ts from WindowsTo get bounds (best/worst) on K
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April 18, 2023 (15)
Parameter Selection for K computation: Examples
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April 18, 2023 (16)
Outline
• Previous Research
• Accurate Coupling Delay Computation
• Efficient Iteration Mechanism
• Experimental Setup
• Conclusions and future work
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April 18, 2023 (17)
Iteration basics
• Traditional static timing analysis Topological order of the circuit
• Static timing analysis with coupling is ITERATIVE
• Iterative timing analysis converges to FixPoint Under a given coupling model (Zhou, ICCAD 2003)
• Node ordering is important
• How to make Static Timing Analysis efficient ? Explore circuit structure for node ordering
Decrease iterations
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April 18, 2023 (18)
Clustering
• Problems in analysis based on topological order Any update at d Propagate to e, f, g, h If update at d not permanent Calculation wasted
• Solution: Clustering Local cluster (B) : Change in e Changes f Global cluster (A) : Two interacting local clusters Timing Analysis Convergence on clusters
• Clustering Issues: With coupling whole circuit can be one global cluster
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April 18, 2023 (19)
How to use Clustering ideas ?
• Coupling edges are bidirectional on Timing Graph
• Select coupling edges Timing Graph Acyclic
G1
G2
G3
G4
G5
G6
G7
G8
• Such coupling edges are called Feedback Edges Example : Coupling edge with fan-out relation
• Carry out iterations based on feedback edges
CC1
CC2
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April 18, 2023 (20)
Feedback Edge Identification
• Local Coupling Edge Any change on aggressor should be updated to victim Update does not occur by fan-out
• Observation: Choosing CC1 as local coupling edge
• Force CC2 to become feedback edge Choosing CC2 as feedback edge
• Force CC1 related by fan-out
• Metric to identify local coupling edge Coupling Weight = Overlap ratio (K) with 1xCC timing windows
G1
G2
G3
G4
G5
G6
G7
G8
CC2
Coupling Edges with no fan-out relation
(Local Coupling Edges)CC1
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April 18, 2023 (21)
Coupling Partitioning Algorithm
• Coupling edges are partitioned into: Feedback edges (Global Coupling Edges)
Local Coupling Edges
• Algorithm: Using BFS identify “Easy” Global Edges
Sort remaining coupling edges by coupling weight
Do
• Identify highest weighted edge (e) as local
• Find global edges generated by e (ge)
• Remove ge from sorted coupling edges
While (no more coupling edges left)
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April 18, 2023 (22)
Coupling Partitioning Algorithm (Illustration)
G1
G2
G3
G4
G5
G6
G7
G8
CC2
CC1
kCC1 = 0.6 , kCC2 = 0.8
G1
G2
G3
G4
G6
G7
G8
CC2
CC1
G5
Local Coupling Edge= CC2
G1
G2
G3
G4
G6
G7
G8CC1
G5
Super-Nodeformation
G1
G2
G3
G4
G6
G7
CC1
G5
G8
CC1 identified asGlobal Edge
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April 18, 2023 (23)
Coupling Structure Aware Iteration Algorithm
• Initialization Add topological sorted nodes in queue
Update coupling capacitance with MCF = 1.0
Update windows on each node
• Modified Chaotic Iterations While (queue is not empty)
• u Pop a node from queue
• Update coupling capacitance with new MCFs
• Update timing windows on u
• If ( | uold – unew | > ε )
Add fan-out nodes of u to queue Add nodes to queue coupled by local coupling edges
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April 18, 2023 (24)
Outline
• Previous Research
• Accurate Coupling Delay Computation
• Efficient Iteration Mechanism
• Experimental Setup
• Conclusions and future work
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April 18, 2023 (25)
Circuit Modeling
• Experiments done on ISCAS85 benchmarks
• Circuit modeled as DAG (Timing Graph)
• Nodes in Timing Graph are Gates
• Edges represent interconnect
• Nodes are mapped to ASIC logic gates Faraday 90 nm experimental tech library used Delay tables are used : f( output load, input slew )
• Coupling graph generation Extracted coupling capacitance values are used Coupling graph is superimposed on timing graph Each net is assumed to couple with 4 aggressors
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April 18, 2023 (26)
Model Accuracy Results
• CE denotes number of coupling edges
• RT : Runtime in seconds, TA : Cell Table Lookup
• (rdl,rdh) : Rise delay window
• 012 Model can be non-conservative !
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April 18, 2023 (27)
Performance Enhancement Results
• CI : Iterative algorithm proposed by Chen et.al
• Fast-CI : Coupling structure aware algorithm
• Global : Number of global edges identified
• P-RT : Coupling partitioning runtime
Max = 62.1%
Min = 5.7%
Average = 26.8%
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April 18, 2023 (28)
Outline
• Previous Research
• Accurate Coupling Delay Computation
• Efficient Iteration Mechanism
• Experimental Setup
• Conclusions and future work
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April 18, 2023 (29)
Conclusions and future work
• We present FA-STAC Accurate static timing analysis with coupling
Efficient iteration mechanism to converge faster
• Novel coupling delay model developed
• Coupling structure exploited for fast iterations
• Experimental results on ISCAS benchmarks Our algorithm give average speed-up of 26.8%
Negligible error in timing windows
• Future directions Complex coupling model for local coupling edges
• Submitted to DATE 2007
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April 18, 2023 (30)
THANK YOU
Q & A