A Stable Fixed-outline Floorplanning Method Song Chen and Takeshi Yoshimura Graduate School of IPS, Waseda University March, 2007

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Problem Given –A set of rectangular blocks among which connections (nets) exist –Specified width w i and height h i for each block b i –Specified rectangular region: W 0, H 0. (Fixed-outline) The fixed-outline floorplanning is to determine coordinates for each block such that –There is no overlapping between any two blocks. –All the blocks are placed inside the specified region (fixed-outline) –Some objectives, such as wire-length, etc., are optimal. W0W0 H0H0

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Previous Work S. Adya and I. Markov, ICCD’01 TCAD’03 (Parquet) –New objective functions; New types of move. C. Lin, et al., ASPDAC’04 –Evolutionary search-based robust fixed-outline floorplanning; Fixed-outline constraint only. R. Liu et al., ISCAS’05. –Instance augmentation; Fixed-outline constraint only. T.C. Chen and Y.W. Chang, ISPD’05. –Adaptive Fast-SA; Weights in the cost function changed Dynamically.

Previous Work (Cont’) The existing fixed-floorplanning methods work well when fixed-outline constraint is the only objective. –Poor success rates when optimizing wire and other objectives. –And when the aspect ratios are far away from one (W=H).

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Overview of Floorplanning Sequence Pair is used for floorplan representation Objective function Solution perturbation –Remove a block randomly –Compute the floorplan of the blocks except the removed one –Select fixed number of candidate insertion points for the removed block by enumerating insertion points –Choose for the removed block one of the candidate insertion points randomly

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Objective Function Objective functions used in the existing fixed- outline floorplanners. –Low success rate when given larger aspect ratios. –Low success rate when other objectives exist. since the function values hardly reach zero when competitions from other objectives exist. –A trade-off between area and aspect ratios. EwEw EhEh H0H0 W0W0 Fixed-outline

Objective Functions (Cont’) Calculate chip area costs for fixed-outline floorplanning (assume λ>1 ) –E W = max(W −W 0, 0) –E H = max(H − H 0, 0) –C 1 and C 2 are user-defined constants –λ is the aspect ratio. High success rates for large aspect ratios High success rate when combined with other objectives EwEw EHEH H0H0 W0W0

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Solution Perturbation –Enhanced Remove and Insertion Remove a block randomly Insert the block –Select some candidate insertion points (CIP, totally 100 here) by Enumerating Insertion Points (EIP) (rough estimation) –Select from the CIPs the insertion point for the removed block

Enumerate Insertion Points (EIP) Sequence Pair (P, M) –(…b i …b j …, …b i …b j …)  b j is left to b i –(…b i …b j …, …b j …b i …)  b j is below b i –An insertion point means one position in P and one position M -- (p, m) In order to evaluate an insertion point, we need to know how much inserting a block into the insertion point will contribute to the chip width and height

EIP – Computing x-coordinates Given a Sequence Pair (P, M) –Coordinates (with origin at the bottom-left corner of the chip) of a block b i only depend on the blocks that are left to b i in the sequence M –Coordinates of the blocks that are right to b i in both P and M are larger than that of b i ( a b c e d f g, a c b d e g f ) ( a b c e d f g, a c b d e g f )

EIP— Computing x-coordinates (Cont’) Based on the previous observations, we can compute the x-coordinates of all insertion points –Given a sequence pair (P, M) = (f c e d b a, c b f a d e) ( f c e d b a, c b f a d e ) Distance of CIPs (p, c + ) to the left boundary: p is before c in P, 0; p is after c in P: 2. Distance of CIPs (p, b + ) to the left boundary: p is before c in P, 0; p is between b and c in P, 2; p is after b: 4.

Enumerating Insertion Points Following pairs of sequences are scanned to compute the distance of an insertion point to the chip boundaries –(P, M): Distance to the left boundary –(P r, M): Distance to the bottom boundary –(P r, M r ): Distance to the right boundary –(P, M r ): Distance to the top boundary P M MrMr PrPr top left bottom right

Enumerating Insertion Points (Cont’) The enumerating is similar to the computation of x- coordinates, but, for each time, we have to scan four lists simultaneously. Without consideration of wire length, the complexity of enumerating is O(n 2 ), which is linear with the number of insertion points. During the enumerating, we take into account only the nets that have connections to the removed block. –a linear piecewise function is used for wire-length calculation.

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

Experimental Results-Success Rate white space percent 10%, all blocks are hard, and the aspect ratios are chosen from the range [1,3] with interval 0.5. Success rate: Parquet (SP) 60%, Parquet (BTree) 100%, NTU-FOFP 94%, IARFP 100%. Runtime: IARFP is the least one. (a tenth part)

Experimental results-Wire White space 10%, 50 runs for n100, 10 runs for n200 and n300. Success rate: IARFP 100%, NTU-FOFP 45%, and Parquet (SP) 34% Wire: IARFP achieved 12% and 7% improvement Runtime: IARFP spent much less time.

Experimental Results-Objective Function Embed objective function into the existing fixed- outline floorplanner NTU-FP –White space: 10% –Aspect ratios: From the range [1,3] with interval 0.5

Outline Problem Previous Work Fixed-outline Floorplanning –Overview –Objective Function –Solution Perturbation Experimental Results Conclusions

We developed a stable fixed-outline floorplanner –A new method for calculating area costs in fixed-outline floorplanning is proposed. –An enhanced remove and insertion solution perturbation method is implemented based on enumerating insertion points. Compared with the existing method, the proposed method is very effective and efficient.

Thanks for your attentions!