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Large Scale Circuit Partitioning With Loose/Stable Net Removal

And Signal Flow Based Clustering

Support : DARPA/ITO, NSF, Fujitsu MICRO

Jason CongHonching Li

Sung-Kyu LimDongmin Xu

UCLA VLSI CAD Lab

Toshiyuki Shibuya

Fujitsu Lab, LTD

Outline

• Loose and Stable net Removal Partitioning Algorithm

• Maximum Fanout Free Subgraph Clustering Algorithm

• Performance of LSR/MFFS

• Conclusion & Ongoing Work

LSR Partitioning

1. Background

2. Motivation

3. Implementation

Circuit Partitioning

• Formulation– minimize connection– satisfy area constraint

• Significance– fundamental for hierarchical layout– essential for future technology

• Iterative Improvement Partitioning– flexible, effective, and efficient

Evolution of IIP Algorithm

• Early Development– KL : Kernighan & Lin [Bell70]– FM : Fiduccia & Mattheyses [DAC82]– LA : Krishnamurthy [TCom84]

• Recent Development– CDIP/PROPf : Dutt & Deng [ICCAD96]– Strawman : Hauck & Borriello [TCAD96]– hMetis : Karypis & Kumar [DAC97]– MLc : Alpert, Huang & Kahng [DAC97]

FM Algorithm Basics

• Basic Operation : Cell Move– cost : gain (= reduction in cutsize)– constraint : area balance– cell status : free or locked

• Structurewhile (gain > 0)

while (∃ free cell)move cell

retrieve max-gain movespass run

Loose-net Removal (LR)

• New Gain Formulation

block 0 block 1

FREE net : only free cells



block 0 block 1

LOOSE net : locked cells in one block



block 0 block 1

-3 -2FM :

FREE cells of LOOSE net



block 0 block 1

IMMEDIATE ATTENTION, W > 0

W WLR :



block 0 block 1

WLR : +W



block 0 block 1

LOOSE net removed

more LOOSE net formed



block 0 block 1



block 0 block 1

Net Pulling Effect

block 0 block 1

LR Implementation

• Gain Increase of LR

favor shorter nets

LR Implementation

• Gain Increase of LR

block 0 block 1

incr(n) =k

size(n)

33 33

25 25 25

= 100

LR Implementation

• Gain Increase of LR : upper bound

k

Less Tie-Break

LR Implementation

• FM Enhancement

while (gain > 0)while (∃ free cell)

move max-gain cell c

retrieve max-gain moves

for (each loose net n incident on c)for (each free cell f of n)

if (f.gain < T)f.gain += incr(n)

Performance of LR

• Bipartitioning without Clustering

922

1023

1956

1761

500 700 900 1100 1300 1500 1700 1900 2100

LR

CDIP

LA3

FM

Stable Net Transition (SNT)

• Stable Net [Shibuya et al, FSTJ95]– remain cut during entire run– limit FM solution

• Stable Net Removal– at the end of each run– detect stable net and isolate– new initial partition– fast convergence

Enhancement of LR

• Benefit of LR + SNT– small loose + big stable net– dynamic + static– speedup LR

• How?– initial partition by SNT for next run of LR– Loose and Stable net Removal (LSR)

MFFS Clustering

1. Motivation

2. Algorithm

3. Speedup

Circuit Clustering

• Definition– group closely connected component in

circuits

• Significance– reduce problem size– speedup partitioning– improve partitioning solution– refinement through decomposition

Maximum Fanout Free Cone

• Significance [Cong & Ding, DAC93]– exploit signal flow during clustering– group logically dependant cells– linear time complexity

• Benefit– partitioning [Cong, Li, & Bagrodia DAC94]– placement [Cong & Xu, ASP-DAC95]

Definition of MFFC

• Cone Rooted at v : Cv– v and its predecessor s.t. if u in Cv, every

path from u to v resides entirely in Cv

• Fanout Free Cone at v : FFCv– Cv is fanout free if output(Cv) = output(v)

• Maximum FFCv : MFFCv– fanout free and maximum FFCv

Definition of MFFC

• Find All Single MFFC– complexity : O(|N|+|E|)

Limitation of MFFC

• Designed for Combinational Circuit– can’t handle cycles in sequential circuit

applyMFFC

algorithm

Limitation of MFFC

• Designed for Combinational Circuit– can’t handle cycles in sequential circuit

applyMFFS

algorithm

Definition of MFFS

• For a node v in a sequential circuit;

MFFSv = {u|for all FFSv, u ∈ FFCv } – Maximum Fanout Free Subgraph rooted at v

FFSv = {u|every path from u to somePO passes through v }

– Fanout Free Subgraph rooted at v

MFFS Construction

• For Single MFFSv

MFFS Construction

• For Single MFFSv– select root node v and cut its fanout

v

MFFS Construction

• For Single MFFSv– mark nodes reachable backwards from PO

v

MFFS Construction

• For Single MFFSv– MFFSv = {unmarked nodes}

v

MFFS Construction

• For Single MFFSv– complexity : O(|N|+|E|)

v

MFFS Clustering

• For Clustering Entire Circuit

MFFS Clustering

• For Clustering Entire Circuit– find MFFSv and remove

v

MFFS Clustering

• For Clustering Entire Circuit– output to removed nodes is new PO

v

MFFS Clustering

• For Clustering Entire Circuit– repeat until all nodes are clustered

vv

MFFS Clustering


v v

MFFS Clustering


v v

v

MFFS Clustering

• For Clustering Entire Circuit– complexity : O(|N|• (|N|+|E|))

Speedup of MFFS Clustering

• Single MFFSv Construction– slow : O(|N|+|E|)

v


• Subset of MFFSv– search on subcircuit

v


• Subset of MFFSv

circuit

h

v

SC (v, h)

– internal node : depth h-BFS at node v

pseudo PIs

pseudo POs

– pseudo PI/PO : I/O to/from subcircuit

LSR/MFFS Algorithm

• Overview– cluster circuit with MFFS approximation

algorithm– partition clustered circuit with LSR

algorithm– decompose clusters completely– refine cutline with LSR algorithm on

declustered circuit

Experimental Result

1. Experiment Setting

2. MFFS Clustering

3. LSR/MFFS Partitioning

Experimental Setting

• Benchmark– 16 MCNC circuits with signal flow info– SPARC 5-85 with gcc v2.4– bipartitioning under 45-55% skew– real cell area

Area Variation Ratio = min cell areamax cell area

• Metric– cutsize : min of 20 runs– runtime : total of 10 runs

MFFS Clustering Result

Exact Approxckt size AVR # clst time # clst time

s1423 619 1.0 193 0.9 168 1.9

sioo 664 4.6 442 2.3 442 2.6

………

s35932 18148 1.0 5562 420.8 2943 32.1

s38584 20995 1.0 5139 565.1 4242 44.5

avq.sm 21918 4.5 8477 1287.3 8309 116.1

S38417 23949 1.0 5906 452.2 5295 45.1

avq.lg 25178 4.5 9103 1473.2 8658 90.2

Total 150379 48033 4543.9 42494 449.7

Cutsize Reduction Trend

500 700 900 1100 1300 1500 1700 1900

LSR

LR

SNT

FM

Cutsize Reduction Trend

500 700 900 1100 1300 1500 1700 1900

LSR

LR

SNT

FM

FLATMFFS

LR, SNT, MFFS are all effective

Runtime Reduction Trend

0 50 100 150

LSR

LR

SNT

FM

Runtime Reduction Trend

0 50 100 150

LSR

LR

SNT

FM

FLATMFFS

SNT and MFFS are both effective

Cutsizes Among IIPs

845

861

872

898

961

1023

700 750 800 850 900 950 1000 1050

LSR/MFFS

MLc

hMetis

Strawman

PROPf

CDIP

achieved BEST cutsize

Runtimes Among IIPs

1388

3455

1388

12577

5611

5817

0 1000 2000 3000 4000 5000 6000

LSR/MFFS

MLc

hMetis

Strawman

PROPf

CDIP

achieved BEST runtime

???

Cutsizes Among Non-IIPs

509

516

648

749

300 400 500 600 700

LSR/MFFS

PANZA

FBB

Paraboli


Runtimes Among Non-IIPs


1388

16024

24619

0 10000 20000

LSR/MFFS

PANZA

FBB

Paraboli

???

Conclusion & Ongoing Work

• LSR Partitioning– Loose and Stable net Removal

• MFFS Clustering– Maximum Fanout Free Subgraph

• Performance of LSR/MFFS

• Ongoing Work– LSR : multi-way partitioning– MFFS : multi-level cluster hierarchy– LSR/MFFS : mincut based placement

Thank You

For Your Attention

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