Consistent Floorplanning with Super Hierarchical Constraints

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


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

Placement Super-Constraint under the Sequence-

Pair Consistency with Clock-Tree Synthesis Experiments Conclusions


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!


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


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?


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


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


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)



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



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)


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



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



=(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



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


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


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).


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


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


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 !


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!


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


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

Consistent Floorplanning with Super Hierarchical Constraints

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