ispd 2001, sonoma county, april 3rd, 20011 consistent floorplanning with super hierarchical...

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ISPD 2001, Sonoma County, April 3rd, 2001 1 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI Information and Media Sciences, The University of Kitakyushu, Japan

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Page 1: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 1

Consistent Floorplanning with Super Hierarchical Constraints

Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

Information and Media Sciences,

The University of Kitakyushu, Japan

Page 2: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 2

Contents Our Concept: Consistent Floorplanning Dilemma about Partitioning and Block-

Placement Super-Constraint under the Sequence-

Pair Consistency with Clock-Tree Synthesis Experiments Conclusions

Page 3: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 3

Our Concept: Consistent Floorplanning Conventionally, block placement (BP) is

executed independently of partitioning (PT) In PT, we consider

Minimization of wire-density Timing closure

In BP, because of lack of consistency with PT, we lose the low wire-density or the timing closureWe need consistency between PT and BP!

Page 4: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 4

Dilemma about PT and BP Slicing structure   [Wong et.al.,DAC, 1986]

Consistent with bi-PT Larger chip size

General structure SP [Murata et.al.,ICCAD,1995] BSG [Nakatake et.al., ICCAD, 1996] O-tree [Guo et.al., DAC, 1999]

Inconsistent with bi-PT Smaller chip size

We propose consistent techniques applicable tofloorplan of general structure

Page 5: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 5

From PT to Sequence-Pair (1) The Sequence-Pair based BP For example,

Apply bi-PT twice and get 4 clusters How do you construct a sequence-pair

consisting of 4 clusters?

Page 6: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 6

From PT to Sequence-Pair (2)

a, b

c, d

a b

c d

a b

c d

(acbd,cdab)

(abcd,cadb)

?

Vertical bi-PT

a

c

b

d

Horizontal bi-PT

Page 7: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 7

Ambiguous Sequence Expression

ambiguous sequence possible sequence a+b ab or ba (commutative) ab ab (non-commutative)

a

b

c

dEach edge corresponds to a non-commutative relation

For example,a(b+cd) abcd, acbd, acdb

Page 8: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 8

Super-Constraint (1)

a b

c d

a b

c d

Correspond to (a(b+c)d, c(a+d)b)

Super-constraint on the sequence-pair

(acbd,cdab) (abcd,cadb)

We need only sequence-pairs that correspond to (a(b+c),c(a+d)b)

Page 9: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 9

Super-Constraint (2)

If each cluster consists of one block, then(a(b+c)d, c(a+d)b) corresponds to :

(abcd,cadb) (acbd,cadb) (acbd,cdab) (abcd,cdab)

a b

c d

a b

c d

a b

c d

ab

cd

Page 10: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 10

Super-Constraint (3)

If each cluster consists of two or more blocks, then(a(b+c)d, c(a+d)b) corresponds to :

a1

d1

c

b a

d

c1

b1

a2

d2 c2

b2

(a1a2bcd1d2,ca2d2a1d1b) (ab1c1b2c2d,c1c2adb1b2)

Page 11: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 11

How to Construct Super-Constraint (1)

1

2

34

5 6

78

9 ab

c

d

e

fg

circuit

1

2

34

5 6

78

9a

bc

d

e

fg

Vertical bi-PT

Page 12: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 12

How to Construct Super-Constraint (2)

1

2

34

5 6

78

9a

bcd

e

fg

1 2

3

4

5 67

8

9

a

b

cd

e f

g

Horizontal bi-PT

Horizontal bi-PT

Page 13: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 13

How to Construct Super-Constraint (3)

=(1+2+5+6)(9+a+d+e+3+4+7+8)(b+c+f+g)=(d+9+e+a)(5+1+6+2+f+b+g+c)(7+3+8+4)),(

Sequence-pair:

1 2

3

45 6

78

9a

bcd

e fg

Cluster positioning according to PT processes

1. A pair of bi-PTs : once 4 clusters

Page 14: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 14

How to Construct Super-Constraint (4)

1 2 3 4

5 6 7 8

9 a b c

d e f g

=1(2+5)6(9(a+d)e+3(4+7)8)b(c+f)g=d(9+e)a(5(1+6)2+f(b+g)c)7(3+8)4

),( Sequence-pair:

2. A pair of bi-PTs: twice 16 clusters

Page 15: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 15

How to Optimizationunder Super-Constraint Simulated annealing

Full-exchange: Take a pair of blocks such that they are not ordered relation in both sequences, and interchange them in both sequences

Half-exchange: Take a pair of blocks such that they are not any ordered relation in either of sequences, and interchange them in the focused sequence

Rotation: Take a block and rotate it 90 degree

Page 16: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 16

Consistency with Clock-Tree Synthesis (1) MMM-algorithm [Jackson et.al., DAC, 1990]

Consistent with bi-PT

Partition the region into two by a slice line(dot-line) such that the center of the mass lies on the line.

Connect the centers of masses by the line (solid-line).

Page 17: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 17

Consistency with Clock-Tree Synthesis (2) PT: optimize ratio-cut R

: #cut-nets Ci : cluster Hi : the number of flip-flop’s terminals inclu

ded in Ci

|||||||| HjHiCjCiR

Page 18: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 18

Experiments Algorithm

SPa: BP by the Sequence-Pair SPa-super: BP by the Sequence-Pair under

super-constraints Data: MCNC benchmark Size of the space each algorithm

searches SPa : SPa-super:

2)!(n2)!)!2(!( kkk n=4k

Page 19: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 19

Experimental Results

dataalgorithm SPa SPa- super SPa SPa- superMST(μ m) 604,814 579,071 644,889 593,803

Calc.Time(Sec.) 68.73 67.76 265.26 168.08

apte xerox

SPa SPa- super SPa SPa- super104,832 97,538 776,482 722,526278.47 215.82 423.42 433.91

ami33 ami49

The results by SPa-super are of shorter MST !

Page 20: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 20

PT Aware BP

BLK[0]

BLK[1]

BLK[2]

BLK[3]

BLK[4]

BLK[5]

BLK[6]

BLK[7]

BLK[8]

BLK[9]

BLK[10]

BLK[11]

BLK[12]

BLK[13]

BLK[14]

BLK[15]BLK[16]

BLK[17]

BLK[18]

BLK[19]BLK[20]

BLK[21]

BLK[22]

BLK[23]

BLK[24]

BLK[25]

BLK[26]

BLK[27]

BLK[28]

BLK[29] BLK[30]

BLK[31] BLK[32]

BLK[0]

BLK[1]

BLK[2]BLK[3]

BLK[4]

BLK[5]

BLK[6]BLK[7]

BLK[8]

BLK[9]

BLK[10]

BLK[11]

BLK[12]BLK[13]

BLK[14]

BLK[15]

BLK[16]

BLK[17]

BLK[18]

BLK[19]

BLK[20]

BLK[21]

BLK[22]

BLK[23]

BLK[24] BLK[25] BLK[26]

BLK[27]

BLK[28]

BLK[29]

BLK[30]

BLK[31]

BLK[32]

By SPa-Super By SPa

•Almost keeping positions of clusters•Non-slicing structure•Overcome the dilemma about PT and BP!

Page 21: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 21

Distribution Map of Wire-Density

20- 25

15- 20

10- 15

5- 10

0- 5

20- 25

15- 20

10- 15

5- 10

0- 5

•The result by SPa-super is of lower wire-density !•Super-constraint can convey PT feature to BP

By SPa-super By SPa

Page 22: ISPD 2001, Sonoma County, April 3rd, 20011 Consistent Floorplanning with Super Hierarchical Constraints Yukiko KUBO, Shigetoshi NAKATAKE, and Yoji KAJITANI

ISPD 2001, Sonoma County, April 3rd, 2001 22

Conclusions We introduced “consistent floorplanning” on the Sequ

ence-Pair. We discussed a dilemma about PT and BP by demons

trating some features in slicing- and general- structure.

The idea is to convey the partitioning feature into the Sequence-Pair as a constraint.

By this idea, the solution space is drastically reduced, and experiments showed the effect.

We convince that if we adopt timing-driven PT, we can control the block-level timing