Unified Quadratic Programming Unified Quadratic Programming Approach Approach for Mixed Mode for Mixed Mode Placement Placement Bo Yao, Hongyu Chen, Chung-Kuan Bo Yao, Hongyu Chen, Chung-Kuan Cheng, Nan-Chi Chou*, Lung-Tien Liu*, Cheng, Nan-Chi Chou*, Lung-Tien Liu*, Peter Suaris* Peter Suaris* CSE Department CSE Department University of California, San Diego University of California, San Diego *Mentor Graphics Corporation *Mentor Graphics Corporation
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Unified Quadratic Programming Approach for Mixed Mode Placement Bo Yao, Hongyu Chen, Chung-Kuan Cheng, Nan-Chi Chou*, Lung-Tien Liu*, Peter Suaris* CSE.
Mixed Mode Placement Common design needs Mixed signal designs (analog and RF parts are macros) Mixed signal designs (analog and RF parts are macros) Hierarchical design style Hierarchical design style IP blocks IP blocks Memory blocks Memory blocks Challenges for placement Huge amount of components Huge amount of components Heterogeneous module sizes/shapes Heterogeneous module sizes/shapes Memory IP Analog
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OutlineOutlineIntroduction to the mixed mode placementIntroduction to the mixed mode placementUnified cost functionUnified cost functionDCT based cell density costDCT based cell density costExperimental resultsExperimental resultsConclusions Conclusions
Mixed Mode PlacementMixed Mode Placement
Common design needsCommon design needs Mixed signal designs Mixed signal designs
(analog and RF parts are (analog and RF parts are macros)macros)
WL = WL = 1/2x1/2xTTQx+px +1/2yQx+px +1/2yTTQy+pyQy+py Bounding box wire length for discrete optimizationBounding box wire length for discrete optimization
DPghtDensityWeiWLWLWeight **
Cell Density Cell Density Common strategyCommon strategy Partition the placement area into Partition the placement area into NN
by by NN rooms roomsCell density matrix Cell density matrix D D = = {{ddijij} } ddijij is the total cell area in room (i,j) is the total cell area in room (i,j)
A
00000.250.50.2500.510.500.250.50.250
D
DCT: Cell Density in Frequency DCT: Cell Density in Frequency DomainDomain
2-D Discrete Cosine Transform (DCT)2-D Discrete Cosine Transform (DCT)Cell density matrixCell density matrix D D => Frequency matrix => Frequency matrix FF = { = {ffijij}}where where ffij ij is the weight of density pattern (i,j)is the weight of density pattern (i,j)
Njv
NiudjCiC
Nf
N
u
N
vuvij 2
)12(cos2)12(cos)()(2 1
0
1
0
Otherwise
iiC
1
02/1)(
Properties of Frequency MatrixProperties of Frequency Matrix
Each Each ffuvuv is the weight of is the weight of frequency (frequency (u,vu,v))
Inverse DCT recovers the Inverse DCT recovers the cell densitycell density
Nvj
NuifvCuC
Nd
N
u
N
vuvij 2
)12(cos2)12(cos)()(2 1
0
1
0
…
…
…
(0,0) (1,0) (3,0)
(0,1) (1,1)
(0,3) (3,3)
…
0001000000000000
D
0.070.140.180.140.140.250.330.250.180.330.430.33
0.140.250.330.25
F
…
…
…
(0,0) (1,0) (3,0)
(0,1) (1,1)
(0,3) (3,3)
…
Frequency Matrix: An ExampleFrequency Matrix: An ExampleDensity matrix D and frequency matrix FDensity matrix D and frequency matrix F
Properties of DCTProperties of DCTCell density energy Cell density energy ddijij
22 = = ffijij22
Cell perturbation and frequency matrixCell perturbation and frequency matrix
We propose a unified cost function for global We propose a unified cost function for global optimization, which provides good trade-offs optimization, which provides good trade-offs between wire length minimization and cell between wire length minimization and cell spreading.spreading.We introduce a DCT based cell density We introduce a DCT based cell density calculation method, and a quadratic calculation method, and a quadratic approximation.approximation.The unified placement approach The unified placement approach generates promising results on mixed generates promising results on mixed mode designs.mode designs.