vlsi/cad laboratory department of computer science national tsing hua university th eda estimation...
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VLSI/CAD LaboratoryVLSI/CAD LaboratoryDepartment of Computer ScienceDepartment of Computer ScienceNational Tsing Hua UniversityNational Tsing Hua University
TH EDATH EDA
Estimation of Estimation of Maximum Instantaneous Current for Maximum Instantaneous Current for
Sequential CircuitsSequential Circuits
Cheng-Tao Hsieh and Shih-Chieh Chang
National Tsing Hua University
Hsinchu, Taiwan
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Maximum Instantaneous Current (MIC)Maximum Instantaneous Current (MIC)
To calculate the MIC, must decide which input vectors and at which time.
0
0
MIC=3 at time t=3 MIC=4 at time t=1.t=1t=2t=3
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Two Types of MethodsTwo Types of Methods
Vector dependent Deriving the worst case vectorsLower bound estimation
Vectorless No vector searchUpper bound estimation
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Two Types of MethodsTwo Types of Methods
Vector dependent Deriving the worst case vectorsLower bound estimation
Vectorless No vector searchUpper bound estimation
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Vectorless MethodsVectorless Methods
Definition: Two gates are Mutually Exclusive Switching (MES) at time t1 if they cannot switch simultaneously at t1.
[C.T. Hsieh, J.C. Lin, and S.C. Chang, accepted by TCAD]
The two transitions cannot occur simultaneously
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Combinational CorrelationCombinational Correlation
Signal correlation in a combinational circuit.
The two transitions cannot occur simultaneously
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Sequential CorrelationSequential Correlation
Correlation across sequential elements.
(f1, f2)= (0, 0)
(0, 1)
(1, 0)
(1, 1)f2
f1
t=0t=1
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Impact from Sequential CorrelationsImpact from Sequential Correlations
Accuracy loss if ignore sequential correlations.
0%
20%
40%
60%
80%
S38
2
S40
0
S44
4
S52
6
S83
8
S14
23
S53
78
S92
34
S15
850
S13
207
S38
584
S38
417
S35
932
Avg
.
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The Use of Real Delay ModelThe Use of Real Delay Model
Do not impact on accuracy but impact on efficiency.
The number of transitions on a gate may be exponential to the circuit size.
[H. Kriplani, et al., TCAD’95]
Large memory and run time to detect MES among many transitions.
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Solution for Efficiency ProblemSolution for Efficiency Problem
Detect MES in a time interval instead of at an exact time instant.
timet1 t2 t3
Time interval t1 to t3
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Trade-off Between Accuracy and EfficiencyTrade-off Between Accuracy and Efficiency
Larger time interval more efficient but less accurate.
0
1000
2000
3000
4000
iMax 0.5 0.2 0.1 0.05M
IC
0
500
1000
1500
iMax 0.5 0.2 0.1 0.05
Run
tim
e (s
)
Circuit C7552
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Accuracy of MIC EstimationAccuracy of MIC Estimation
circuit Delay iMaxOur approach
0.5 0.2 0.1 0.05 0.01
C432 4.9280 206 201 161 141 117 107
C499 3.1495 640 472 302 280 224 220
C880 3.6301 471 467 383 294 265 244
C1355 3.1706 686 546 316 278 272 236
C1908 4.6940 793 751 531 451 424 401
C2670 5.6569 963 897 630 476 427 401
C3540 6.9914 1348 1291 979 829 763 716
C5315 6.0240 2796 2738 1915 1631 1496 1378
C6288 15.1046 3746 3723 3130 2820 2701 2680
C7552 5.5335 3490 3415 2602 2277 2149 1982
Avg. 1 0.93 0.68 0.58 0.53 0.50
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Two Types of MethodsTwo Types of Methods
Vector dependent Deriving the worst case vectorsLower bound estimation
Vectorless No vector searchUpper bound estimation
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Vector Dependent MethodsVector Dependent Methods
GA-based, probability-based, ILP-based, and modified timed ATPG algorithm.[Y.M. Jiang, A. Krstic, and K.-T. Cheng,
TVLSI, ’00].
Modified timed ATPG algorithm can derive better results than other methods.
Timed ATPG is not scalable.
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A Timed ATPG ProblemA Timed ATPG Problem
A transition:
A logic change v v’ at a certain time t1.
Find a vector pair satisfying both functional and temporal conditions.
Temporal condition
Functional condition
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An Example of Timed ATPGAn Example of Timed ATPG
(a1,b1,c1), (a2,b2,c2) =(0,0,1), (1,1,0)
ab
c
gg=01 at t=2
ab
c
g
1
1 t=2
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Transition Characteristic FunctionTransition Characteristic Function
Definition:
A transition characteristic function (TCF),
g=01, t=t1(v1, v2),
characterizes all vector pairs v1 and v2 which causes gate g to have a rising transition at time t=t1.
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An Example of TCFAn Example of TCF
(a1,b1,c1), (a2,b2,c2) =(0,0,1), (1,1,0)(0,0,1), (1,1,1)(1,0,1), (1,1,0)(1,0,1), (1,1,1)(0,1,0), (1,1,0)(0,1,0), (1,1,1)(0,1,1), (1,1,0)(0,1,1), (1,1,1)
g=01, t=2 = a1’b1’c
1a2b2c2’ + a1’b1’c1a2b2c2 +a1b1’c1a2b2c2’ + a1b1’c1a2b2c2 +
a1’b1c1’a2b2c2’ + a1’b1c1’a2b2c2 +a1’b1c1a2b2c2’ + a1’b1c1a2b2c2 +
ab
c
gg=01 at t=2
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Construction of TCFConstruction of TCF
Construct a TCF by extracting information from circuit structure.
A TCF is represented in the multi-level form, more compact than the two-level form.
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An ExampleAn Example
g=01, t=2 = (a1b1+b1’c1’)’(a2b2+b1’c1’)
ab
c
g
a1
b1
c1
a2b2
g=01, t=2
g=01 at t=2
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Sequential CorrelationSequential Correlation
a
bc
Flip-flop
b1
c1
b2g=01, t=2
a1
b1
c1
a2
The second vector on input b depends on the first vector.
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Initial Experimental ResultsInitial Experimental Resultscircuit #PIs #gates
Random Ours MES
MIC MIC time (s) MIC
s444 3 234 14 17 1.4 28
s510 19 262 16 20 1.5 23
s526 3 313 16 21 2.3 34
s641 35 234 28 31 2.0 42
s713 35 252 26 31 2.4 45
s820 18 524 28 34 2.3 39
s1196 14 574 39 41 6.5 49
s1238 14 668 21 26 7.2 52
s1423 17 714 53 75 14 81
s5378 35 1888 80 176 174 252
s9234 36 1692 60 151 112 176
Avg. 1 1.43 1.96
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ConclusionConclusion
Propose vectorless and vector dependent estimation for the MIC.
Consider sequential correlations, which can significantly impact the MIC estimation.
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AcknowledgeAcknowledge
Prof. Shih-Chieh Chang Jian-Cheng Lin Yu-Min Kuo Yue-Lung Chang
Download: http://nthucad.cs.nthu.edu.tw/~sclab/