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ISPD 2001, Sonoma County, April 3rd, 20011 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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ISPD 2001, Sonoma County, April 3rd, 20012 Contents Our Concept: Consistent Floorplanning Dilemma about Partitioning and Block- Placement Super-Constraint under the Sequence- Pair Consistency with Clock-Tree Synthesis Experiments Conclusions
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ISPD 2001, Sonoma County, April 3rd, 20013 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 closure We need consistency between PT and BP!
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ISPD 2001, Sonoma County, April 3rd, 20014 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 to floorplan of general structure
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ISPD 2001, Sonoma County, April 3rd, 20015 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?
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ISPD 2001, Sonoma County, April 3rd, 20016 From PT to Sequence-Pair (2) a, b c, d ab cd ab cd (acbd,cdab) (abcd,cadb) ? Vertical bi-PT a c b d Horizontal bi-PT
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ISPD 2001, Sonoma County, April 3rd, 20017 Ambiguous Sequence Expression ambiguous sequence possible sequence a+b ab or ba (commutative) ab ab (non-commutative) a b c d Each edge corresponds to a non-commutative relation For example, a(b+cd) abcd, acbd, acdb
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ISPD 2001, Sonoma County, April 3rd, 20018 Super-Constraint (1) ab cd ab cd 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)
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ISPD 2001, Sonoma County, April 3rd, 20019 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) ab cd a b c d a b c d a b c d
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ISPD 2001, Sonoma County, April 3rd, 200110 Super-Constraint (3) If each cluster consists of two or more blocks, then (a(b+c)d, c(a+d)b) corresponds to : a1a1 d1d1 c b a d c1c1 b1b1 a2a2 d2d2 c2c2 b2b2 (a 1 a 2 bcd 1 d 2,ca 2 d 2 a 1 d 1 b) (ab 1 c 1 b 2 c 2 d,c 1 c 2 adb 1 b 2 )
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ISPD 2001, Sonoma County, April 3rd, 200111 How to Construct Super- Constraint (1) 1 2 34 5 6 7 8 9 a b c d e f g circuit 1 2 3 4 5 6 7 8 9 a b c d e f g Vertical bi-PT
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ISPD 2001, Sonoma County, April 3rd, 200112 How to Construct Super- Constraint (2) 1 2 3 4 5 6 7 8 9 a b c d e f g 1 2 3 4 5 6 7 8 9 a b cd e f g Horizontal bi-PT
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ISPD 2001, Sonoma County, April 3rd, 200113 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 4 5 6 7 8 9 a b c d e f g Cluster positioning according to PT processes 1. A pair of bi-PTs : once 4 clusters
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ISPD 2001, Sonoma County, April 3rd, 200114 How to Construct Super- Constraint (4) =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
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ISPD 2001, Sonoma County, April 3rd, 200115 How to Optimization under 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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ISPD 2001, Sonoma County, April 3rd, 200116 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).
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ISPD 2001, Sonoma County, April 3rd, 200117 Consistency with Clock-Tree Synthesis (2) PT: optimize ratio-cut R : #cut-nets Ci : cluster Hi : the number of flip-flop ’ s terminals included in Ci
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ISPD 2001, Sonoma County, April 3rd, 200118 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: n=4k
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ISPD 2001, Sonoma County, April 3rd, 200119 Experimental Results The results by SPa-super are of shorter MST !
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ISPD 2001, Sonoma County, April 3rd, 200120 PT Aware BP By SPa-Super By SPa Almost keeping positions of clusters Non-slicing structure Overcome the dilemma about PT and BP!
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ISPD 2001, Sonoma County, April 3rd, 200121 Distribution Map of Wire-Density The result by SPa-super is of lower wire-density ! Super-constraint can convey PT feature to BP By SPa-super By SPa
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ISPD 2001, Sonoma County, April 3rd, 200122 Conclusions We introduced “ consistent floorplanning ” on the Sequence-Pair. We discussed a dilemma about PT and BP by demonstrating 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
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