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: m1andm2 = max(m1, m2) m1orm2 = min(m1, m2) (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 (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