performance optimization global routing with rlc crosstalk constraints

Performance Optimization Performance Optimization Global Routing with RLC Global Routing with RLC

Crosstalk Constraints Crosstalk Constraints

Ling Zhang,Ling Zhang, Tong Jing, Tong Jing, Xianlong Hong, Jingyu Xu Jinjun Xiong, Lei HeXianlong Hong, Jingyu Xu Jinjun Xiong, Lei He

Dept. of CST, Tsinghua Univ Dept. of EE, UC, Los AngelesDept. of CST, Tsinghua Univ Dept. of EE, UC, Los Angeles

2023 4 19年月日2023 4 19年月日 ASICON2003, BeijingASICON2003, Beijing 22

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IntroductionIntroductionPrevious WorkPrevious WorkOur Algorithm: CEE-GrOur Algorithm: CEE-GrExperimental Results & DiscussionsExperimental Results & DiscussionsConclusionsConclusions


IntroductionIntroduction

Device size shrinking and clock frequency Device size shrinking and clock frequency increasingincreasing

Coupling capacitance and inductance Coupling capacitance and inductance could not be ignoredcould not be ignored

Longer delay and crosstalk caused by Longer delay and crosstalk caused by coupling effectscoupling effects

Global routing with performance Global routing with performance optimization becomes more important.optimization becomes more important.


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Previous Work (1)Previous Work (1)Noise minimizationNoise minimization

Spacing in detailed routingSpacing in detailed routing (K. Chaudhary, A. Onozawa et al, 1993)

Track permutation in detailed routingTrack permutation in detailed routing (T. Gao, C. L. Liu, 1996)

WWire perturbationire perturbation in detailed routing in detailed routing (P. Saxena, C. L. Liu, 1999)

Crosstalk reduction after global routingCrosstalk reduction after global routing (T. X. Xue, E. S. Kuh, D. F. Wang, 1997) (J. J. Xiong, J. Chen, J. Ma, L. He, 2002)


Previous Work (2)Previous Work (2)

Noise modelingNoise modelingSakurai model Sakurai model (T. Sakurai, C. Kobayashi, M. Node, 1993)

LSK model for calculating coupling inductanceLSK model for calculating coupling inductance (L. He, K. M. Lepak, 2000)

Model for calculating noise voltageModel for calculating noise voltage (K. M. Lepak, I. Luwandi, L. He, 2001)


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Our Algorithm: CEE-GrOur Algorithm: CEE-Gr

The major contribution of this workThe major contribution of this work We present a performance optimization We present a performance optimization

global routing algorithm, named CEE-Gr, global routing algorithm, named CEE-Gr, with RLC crosstalk constraints.with RLC crosstalk constraints.

To our knowledge, it is the first to study To our knowledge, it is the first to study RLC coupling noise, timing performance, RLC coupling noise, timing performance, and routability simultaneously at global and routability simultaneously at global routing level.routing level.


Problem FormulationProblem Formulation

1GRC

Fig.1 Global Routing Graph(GRG)

GRG1v

e

v2

GRCi

Cells


The CEE-Gr Algorithm (1)The CEE-Gr Algorithm (1)

Gr: Timing and congestion optimization Gr: Timing and congestion optimization CEE: Crosstalk estimation and elimination CEE: Crosstalk estimation and elimination

Gr firstly generates an initial routing solution considering congestion and timing optimization

Then, CEE eliminates the crosstalk from the solution by inserting shields and gets a mid-result

Finally, regard the mid-result as input and send it to Gr for iterations


The CEE-Gr Algorithm (2)The CEE-Gr Algorithm (2)

Fig.2 CEE-Gr flow chart

eliminates the crosstalk

from the solution by inserting

shields and gets a mid-

result

generate initial routing solution considering congestion and timing optimization

do iterate again

regarding the mid-result as

input

Gr (without crosstalk consideration)

CEE

Gr (subtract tracks used by shields)


(1) Gr(1) Gr

Congestion and timing optimization Congestion and timing optimization

Based on our previous methodsBased on our previous methods SSTT (search space traversing technology) and RINO SSTT (search space traversing technology) and RINO

(considering independent of net ordering)(considering independent of net ordering) (T. Jing, X. L. Hong, H. Y. Bao, Y. C. Cai, J. Y. Xu, 2001)

Critical-network-based technologyCritical-network-based technology (T. Jing, X. L. Hong, H. Y. Bao, Y. C. Cai, J. Y. Xu et al, 2002)


(2) CEE (1)(2) CEE (1) Eliminate crosstalk in each GRG:Eliminate crosstalk in each GRG:

According to each , this step applies According to each , this step applies simulated annealing method in each region to simulated annealing method in each region to insert shields, so that all region’s crosstalk is insert shields, so that all region’s crosstalk is within bound value. within bound value.

Local Refinement: Local Refinement: Check each net to eliminate possible remnant Check each net to eliminate possible remnant

crosstalk and delete unnecessary shields to crosstalk and delete unnecessary shields to minimize the area. minimize the area.

itK


(2) CEE (2)(2) CEE (2)

LSK bound

Get global routing solution from Gr and

Crosstalk bound budgeting

Eliminate crosstalk in each region

Local refinement

CEE

Insert shield with

simulated annealing method

partition the LSK bound at each sink of a net into the GRG edges belonging to the source-sink paths. Check each net

to eliminate possible remnant

crosstalk and delete

unnecessary shields to

minimize total area.

Flow chart:Flow chart:


Crosstalk Bound Budgeting (1)Crosstalk Bound Budgeting (1)CBUD (uniform distributed crosstalk CBUD (uniform distributed crosstalk

budgeting) strategy budgeting) strategy

len

LSKK ij

it

ijLSK

itK

The crosstalk bound at sink pij for net Ni

Crosstalk sub-bound assigned to each GRG region t

len The total length from the source pio to sink pij

(1)


Crosstalk Bound Budgeting (2)Crosstalk Bound Budgeting (2)

CBLP (linear programmed crosstalk budgeting) CBLP (linear programmed crosstalk budgeting) strategystrategy

Consider different congestion situation in Consider different congestion situation in different GRG region in partitioning. Thus, different GRG region in partitioning. Thus, introduce a linear programming problem. introduce a linear programming problem.

The objective is to minimize the number of The objective is to minimize the number of used tracks in most congested GRG region.used tracks in most congested GRG region.


CBLP (1)CBLP (1)

One dimensional GRG--horizontal wires One dimensional GRG--horizontal wires routing in one row: routing in one row:

……

R1 R2 Rt

Fig.4 One dimensional GRG


CBLP (2)CBLP (2)

tit GN

titit K

Minimize maxhSubject to

tit GN

tttitt hOGK max RSETRt (2)

ijt HR

ijitt LSKKl NSETNandPp iiij (3)

tit GN

titit K 0 RSETRandRN ttit (4)

ht: Number of tracks used by nets, shields or obstacles in region Rt

Gt: Number of nets in region Rt

Ot: Number of obstacles in region Rt

: Estimated number of shields in region Rt


CBLP (3)CBLP (3)Two dimensional GRG:Two dimensional GRG:

……

……

……

……

CLMSET ROWSET

Fig.5 Two dimensionsal GRG


CBLP (4)CBLP (4) Minimize

Subject to

(5)

(6)

(7)

(8)

ROWSETRww tt |maxmax

CLMSETRhh tt |maxmax

tit GN

titit K 0

ijt HR

ijitt LSKKl

RSETRandRN ttit

NSETNandPp iiij

maxwOGKROWR GN

tttitt

t tit

ROWSETROW

maxhOGKCLMR GN

tttitt

t tit

CLMSETCLM

maxmax wh


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Experimental Results (1)Experimental Results (1)

Circuits Number of nets Grids

C2

745 9 11

C5

1764 16 18

C7

2356 16 18

Technology: 0.2um

Sensitivity rate: 0.5 for all nets and sensitivity matrix is random.

LSK bound:1000 at each sink


Experimental Results (2)Experimental Results (2)Circuits C2 C5 C7

W mode

(Gr) Wire length (um) 459786 1297814 1545454

(CEE-Gr) Wire length (um) 473588 1336102 1564408

Increase in wire length 3.00% 2.95% 1.23%

Overflow edge number 0 1 0

T mode

(Gr) Wire length (um) 466288 1298210 1569038

(CEE-Gr) Wire length (um) 468836 1326670 1570882


(Gr) Min-R -0.007417 0.006431 0.000910

(CEE-Gr) Min-R -0.006042 0.010355 0.003196


COMPARISON BETWEEN Gr AND CEE-Gr WITH CBUD


Experimental Results (3)Experimental Results (3)Circuits C2 C5 C7

Wire length of Gr in W mode (um) 459786 1297814 1545454

Sink number that violates the crosstalk bound

583 1570 1845

CEE-Gr (CBUD)

Shield number 158 483 595

Area 154 200 273 298 346 380

Wire length (um) 473588 1336102 1564408



CEE-Gr(CBLP)

Shield number 422 1315 1769

Area 150 229 267 343 344 448

Wire length (um) 478240 1330950 1580938



COMPARISON BETWEEN CBUD AND CBLP IN CEE-Gr


DiscussionsDiscussions CEE-Gr can eliminate all crosstalk by adding shields, CEE-Gr can eliminate all crosstalk by adding shields,

while the initial solution has serious crosstalk.while the initial solution has serious crosstalk. The increase in wire length of CEE-Gr is quite small The increase in wire length of CEE-Gr is quite small

compared to Gr.compared to Gr. The minimum redundancy of delay (The minimum redundancy of delay (requiredDelay-requiredDelay-

currentDelaycurrentDelay) is almost unaffected. ) is almost unaffected. CBUD strategy consumes less shields and small area CBUD strategy consumes less shields and small area

than than CBLP strategy.CBLP strategy. CBLP reduces the maximal used tracks in GRG, which CBLP reduces the maximal used tracks in GRG, which

is helpful for optimization with other constraints and low is helpful for optimization with other constraints and low power design.power design.

Simulated annealing method increases the running Simulated annealing method increases the running time of CEE-Gr.(40 mins for C2)time of CEE-Gr.(40 mins for C2)


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ConclusionsConclusions

Tackle coupling noise, timing performance and routability simultaneously

Take coupling inductance into consideration

Obtain good routing results

Efficiently eliminate crosstalk throughout the global routing phase by inserting shields and has little influence on wire length and timing performance.


THANK YOUTHANK YOU

Ling ZhangLing Zhang

Dept. of CST, Tsinghua Univ

Email: [email protected]

performance optimization global routing with rlc crosstalk constraints

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