1. Fuzzy Logic Placement Emily Blem ECE556 Final Project December 14, 2004 Reference: E. Kang, R.B. Lin, and E. Shragowitz. “Fuzzy Logic Approach to VLSI Placement.” IEEE Trans. On VLSI Systems. V. 2, No. 4. December 1994.

2. Objectives Multiple placement objectives: timing, chip size, interconnection length, etc. Need a framework in which to resolve multiple objectives Not well addressed by most algorithms

3. Methods(1) Fuzzy set: a group of objects with different levels of membership Objects may partially belong to a set Operations:  1 and  2 = max(  1,  2 )  1 or  2 = min(  1,  2 ) (image from Kang et. al. 1994)

4. Methods (2) Can be applied to iterative or constructive design In an iterative design, reduce number of criteria for each objective to 1 or 2 due to time constraints Constructive algorithm:  Top level: place cells in feasible regions based on timing requirements  Middle level: assign cells to feasible intervals  Bottom level: assign each cell to a position within its feasible interval  Assignment completed row by row based on fuzzy logic decision maker (FZDM)

5. Methods(3) Small chip area rules:  If a candidate cell provides good utilization of existing feed through pins and a small # of rows is used for each net connected to it, then a small # of feed through cells will be added  If a candidate cell adds a small # of feed through cells and produces almost equal row length, then small chip area will be generated  For large designs, criterion 1/2/1 has a not so strong preference over criterion 1/2/2  In early stages of placement, criterion 1/2/1/1 has a strong preference over criterion 1/2/1/2  In middle stages of placement, criterion 1/2/1/2 has a mild preference over criterion 1/2/1/1

6. Results Ability to tune solution a key feature of fuzzy placement In paper, (balanced) fuzzy placement consistently outperformed TimberWolf6.1 and OASIS using same routers after placement design nameFractStructBiomed placerTW6.1FuzzyTW6.1FuzzyTW6.1Fuzzy propagation delay (ns)1.120.656.155.3213.3210.9 chip area (mm 2 )0.53 6.896.8051.3451.40 (data from Kang et. al. 1994)

7. Conclusions FZDM avoids issues of greedy placer in constructive placement In iterative placement, CPU time issues make FZDM into a weighted cost function According to paper, achieves impressive results Fuzzy logic structure makes it easy to tune solution for different goals and achieve multiple objectives