Consistent Floorplanning with Super Hierarchical Constraints

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 closure We 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 to floorplan 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. a b a, b c d c, d (acbd,cdab) Horizontal bi-PT a b a b c d c d (abcd,cadb) From PT to Sequence-Pair (2) Vertical bi-PT ? ISPD 2001, Sonoma County, April 3rd, 2001

7. c a d b For example, • a(b+cd) abcd, acbd, acdb Each edge corresponds to a non-commutative relation Ambiguous Sequence Expression ambiguous sequence possible sequence • a+b ab or ba (commutative) • ab ab (non-commutative) ISPD 2001, Sonoma County, April 3rd, 2001

8. a b c d a b c d We need only sequence-pairs that correspond to (a(b+c),c(a+d)b) Super-Constraint (1) (acbd,cdab) (abcd,cadb) Correspond to (a(b+c)d, c(a+d)b) Super-constraint on the sequence-pair ISPD 2001, Sonoma County, April 3rd, 2001

9. (acbd,cadb) (acbd,cdab) (abcd,cdab) (abcd,cadb) a b a b a b a b d c c c d d c d Super-Constraint (2) If each cluster consists of one block, then (a(b+c)d, c(a+d)b) corresponds to : ISPD 2001, Sonoma County, April 3rd, 2001

10. (ab1c1b2c2d,c1c2adb1b2) (a1a2bcd1d2,ca2d2a1d1b) a1 b a b1 a2 b2 d1 c1 d2 c2 d c Super-Constraint (3) If each cluster consists of two or more blocks, then (a(b+c)d, c(a+d)b) corresponds to : ISPD 2001, Sonoma County, April 3rd, 2001

11. 2 5 1 6 4 8 3 7 Vertical bi-PT a 9 b e c g d f How to Construct Super-Constraint (1) 2 5 6 1 4 8 3 7 9 a b c e d g f circuit ISPD 2001, Sonoma County, April 3rd, 2001

12. 2 Horizontal bi-PT 1 4 8 6 5 3 7 Horizontal bi-PT f 9 e b d a g c How to Construct Super-Constraint (2) 2 5 1 6 4 8 3 7 a 9 b e c d g f ISPD 2001, Sonoma County, April 3rd, 2001

13. 2 1 4 8 1. A pair of bi-PTs : once 4 clusters 6 5 3 =(1+2+5+6)(9+a+d+e+3+4+7+8)(b+c+f+g) 7 f b 9 e g c =(d+9+e+a)(5+1+6+2+f+b+g+c)(7+3+8+4) a d How to Construct Super-Constraint (3) Cluster positioning according to PT processes Sequence-pair: ISPD 2001, Sonoma County, April 3rd, 2001

14. Sequence-pair: 2. A pair of bi-PTs: twice 16 clusters =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 How to Construct Super-Constraint (4) 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. 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 (1) • MMM-algorithm [Jackson et.al., DAC, 1990] • Consistent with bi-PT 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 included in Ci 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: n=4k ISPD 2001, Sonoma County, April 3rd, 2001

19. Experimental Results The results by SPa-super are of shorter MST ! ISPD 2001, Sonoma County, April 3rd, 2001

20. PT Aware BP 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 By SPa By SPa-super • The result by SPa-super is of lower wire-density ! • Super-constraint can convey PT feature to BP ISPD 2001, Sonoma County, April 3rd, 2001

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