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Floorplan Sizing 1. Floorplanning Algorithms Common Goals  To minimize the total length of interconnect, subject to an upper bound on the floorplan area.

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Presentation on theme: "Floorplan Sizing 1. Floorplanning Algorithms Common Goals  To minimize the total length of interconnect, subject to an upper bound on the floorplan area."— Presentation transcript:

1 Floorplan Sizing 1

2 Floorplanning Algorithms Common Goals  To minimize the total length of interconnect, subject to an upper bound on the floorplan area or  To simultaneously optimize both wire length and area 2

3 3 3.5.1Floorplan Sizing Shape functions Legal shapes w h w h Block with minimum width and height restrictions ha*aw  Aha*aw  A Otten, R.: Efficient Floorplan Optimization. Int. Conf. on Computer Design, 499-502, 1983 Legal shapes

4 4 3.5.1Floorplan Sizing Shape functions w h Hard library block Otten, R.: Efficient Floorplan Optimization. Int. Conf. on Computer Design, 499-502, 1983 w h Discrete (h,w) values

5 5 3.5.1Floorplan Sizing Corner points 5 2 2 5 25 2 5 w h

6 مرتضي صاحب الزماني 6 Slicing Floorplan Sizing

7 Floorplan Sizing Algorithm:  finds the minimum floorplan area for a given slicing floorplan in polynomial time.  For non-slicing floorplans, the problem is NP-hard.  Construct the shape functions of all individual blocks Bottom up:  Determine the shape function of the top-level floorplan from the shape functions of the individual blocks Top down:  From the corner point (minimum top-level floorplan area), trace back to each block’s shape function −Find that block’s dimensions and location 7

8 8 4 2 2 4 Block B: Block A: 5 5 3 3 Step 1: Construct the shape functions of the blocks 3.5.1Floorplan Sizing – Example

9 9 4 2 2 4 Block B: Block A: 5 5 3 3 3.5.1Floorplan Sizing – Example 2 4 h 6 w 26 4 5 3 Step 1: Construct the shape functions of the blocks

10 10 4 2 2 4 Block B: Block A: 5 5 3 3 3.5.1Floorplan Sizing – Example 2 4 h w 26 4 6 3 5 Step 1: Construct the shape functions of the blocks

11 11 4 2 2 4 Block B: Block A: 5 5 3 3 w 26 2 4 h 4 6 hA(w)hA(w) 3.5.1Floorplan Sizing – Example Step 1: Construct the shape functions of the blocks

12 12 4 2 2 4 Block B: Block A: 5 5 3 3 hB(w)hB(w) w 26 2 4 h 4 6 hA(w)hA(w) 3.5.1Floorplan Sizing – Example Step 1: Construct the shape functions of the blocks

13 13 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) 8 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

14 14 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) 8 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

15 15 w 26 2 4 h 4 6 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) hB(w)hB(w) hA(w)hA(w) hC(w)hC(w) 88 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

16 16 w 26 2 4 h 4 6 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) hB(w)hB(w) hA(w)hA(w) hC(w)hC(w) 5 x 5 88 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

17 17 w 26 2 4 h 4 6 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) hB(w)hB(w) hA(w)hA(w) hC(w)hC(w) 3 x 9 4 x 7 5 x 5 88 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

18 18 w 26 2 4 h 4 6 w 26 2 4 h 4 6 hB(w)hB(w) hA(w)hA(w) hB(w)hB(w) hA(w)hA(w) hC(w)hC(w) 3 x 9 4 x 7 5 x 5 88 Minimimum top-level floorplan with vertical composition 3.5.1Floorplan Sizing – Example Step 2: Determine the shape function of the top- level floorplan (vertical)

19 19 w 26 2 4 h 4 6 w 26 2 4 h 4 6 hA(w)hA(w) hB(w)hB(w)hC(w)hC(w) hA(w)hA(w) hB(w)hB(w) 9 x 3 7 x 4 5 x 5 8 8 3.5.1Floorplan Sizing – Example Minimimum top-level floorplan with horizontal composition Step 2: Determine the shape function of the top- level floorplan (vertical)

20 20 3.5.1Floorplan Sizing – Example Step 3: Find the individual blocks’ dimensions and locations w 26 2 4 h 4 6 8 (1) Minimum area floorplan: 5 x 5 Horizontal composition

21 21 w 26 2 4 h 4 6 (1) Minimum area floorplan: 5 x 5 (2) Derived block dimensions : 2 x 4 and 3 x 5 8 3.5.1Floorplan Sizing – Example Step 3: Find the individual blocks’ dimensions and locations Horizontal composition

22 22 2 x 43 x 5 5 x 5 3.5.1Floorplan Sizing – Example Step 3: Find the individual blocks’ dimensions and locations w 26 2 4 h 4 6 (1) Minimum area floorplan: 5 x 5 (2) Derived block dimensions : 2 x 4 and 3 x 5 8 Horizontal composition

23 23 2 x 43 x 5 5 x 5 Resulting slicing tree B V A BA 3.5.1Floorplan Sizing – Example

24 24 DeFer: Deferred Decision Making Enabled Fixed-Outline Floorplanner DAC 2008 Jackey Z. Yan Chris Chu

25 25 Fixed-Outline Floorplanning

26 26 Constraints of Ordinary Slicing Tree A B C ED H H V BA C V D E Block orientation Slice line direction (H/V) Left-right or top-bottom relative order

27 27 DDM in Shape/Orientation  Defer the decision for subfloorplan (i.e., block) orientation until the end H H V BA CV D E Pick any point! Fixed-outline region A B C E D H W A A

28 28 DDM in Relative Order  The relative order (left-right / top-down) between subfloorplans does not affect the shape curves AB V BA A V AB B Same shape curve  Decision on subfloorplan relative order will be made at the end to minimize HPWL H W ABV H W BAV V BA V BA V BA and

29 29 DDM in Slice Line Direction  Two combine operators in ordinary slicing tree A B H BA AB V BA A B H BA AB V BA BA and  Generalized combine operator

30 30 Floorplans by Generalized Slicing Tree AB Block orientation Slice line direction Left-right or top-bottom relative order Deferred Decision Making (DDM)

31 31 Shape Curve Operation for H W A B ( i ) Addition C h C v ( iii ) Merging H W W=H C v C AB C ABC C h ( ii ) Flipping H W W=H C h

32 DeFer  Binary and source code in −http://www.public.iastate.edu/~zijunyan/ 32

33 Cluster Growth Cluster growth:  Iteratively add blocks to the cluster until all blocks are assigned −Merged either horizontally, vertically, or diagonally with the cluster.  Only the different orientations of the blocks (instead of the shape/aspect ratio) are taken into account 33 w h w h w h aaa b b c Growth direction 2 4 6 4 6 4 © 2011 Springer Verlag

34 Cluster Growth Cluster growth:  Blocks b and c are placed so that the increase to the floorplan’s dimensions is minimum. Linear ordering  to minimize total wirelength of connections between blocks 34 w h w h w h aaa b b c Growth direction 2 4 6 4 6 4 © 2011 Springer Verlag

35 Linear Ordering Linear-ordering algorithms  often invoked to produce initial placement solutions for iterative-improvement placement algorithms. Linear-ordering objective:  Arrange blocks in a single row so as to minimum total wirelength of connections  Initial block: −Either randomly −Or based on number of connections to others 35

36 Linear Ordering Categories of nets for a block:  Terminating nets: −have no other incident blocks that are unplaced.  New nets −have no pins on any block from the partially- constructed ordering.  Continuing nets −have at least one pin on a block from the partially-constructed ordering and at least one pin on an unordered block. 36

37 Linear Ordering 37 … Terminating netsNew nets Continuing nets

38 Cluster Growth Example cluster growth.ppt 38

39 Cluster Growth Example Given: (1)blocks a-e (2)linear ordering. a:  (w a = 2, h a = 3) or (w a = 3, h a = 2) b:  (w b = 2, h b = 1) or (w b = 1, h b = 2) c:  (w c = 2, h c = 4) or (w c = 4, h c = 2) d:  (w d = 3, h d = 3) e:  (w e = 6, h e = 1) or (w e = 1, h e = 6) Task:  find a floorplan with minimum global bounding box area. 39 Growth direction

40 Cluster Growth Example 40

41 Cluster Growth Example 41

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