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
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
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!
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
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?
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
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
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)
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
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)
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
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
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
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
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
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).
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
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
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 !
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!
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
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