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
Jan 11, 2016
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
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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
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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
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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 !
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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!
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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