1 Integrating Logic Retiming and Register Placement Tzu-Chieh Tien, Hsiao-Pin Su, Yu-Wen Tsay Yih-Chih Chou, and Youn-Long Lin Department of Computer Science Tsing Hua University Hsin-Chu, Taiwan, R.O.C.

2 Outline Motivation Key problems Proposed System flow Retiming algorithm Interconnection delay estimation Register placement Experimental results Conclusion and future work

3 Motivation Wiring delay dominance in VDSM era. Retiming cannot ignore wiring delay. Wiring delay is layout dependent. retiming layout ? ?

4 Key Problems Post-Layout Retiming incorporating interconnection delay Interconnection delay estimation –delay change due to register insertion or removal –tree topology dependence Post-retiming (register) placement

5 Retiming Incorporating Interconnection Delay Given estimated interconnection delay, find a legal retiming such that the clock period of the circuit is optimal. Delays a, b, and c must be estimated before retiming. a bc

6 Previous Work Soyata and Friedman (ICCAD’94): –branch-and-bound method –optimal solution in the first time –time consuming Lalgudi and Papaefthymiou (DAC’95): –integer linear programming method optimal solution –polynomial time algorithm if the circuit is one-way extendible

7 Interconnection Delay Estimation Given layout –Estimate wiring delay change due to register insertion or removal –Tree-topology dependence of wiring delay

8 Effect of Register Insertion or Removal on Wiring Delay (a) adding a register (b) deleting a register (c) an unchanged wire

9 Tree-Topology-Dependence of Wiring Delay

10 Post-Retiming (Register) Placement Post-retiming layout refinement to meet timing goal Need specific technique

11 Proposed System Flow

12 Retiming Incorporating Wiring Delay Extend a previous algorithm (proposed in pp , SASIMI’93) to incorporate the interconnection delay. Efficient, optimal for circuits satisfy the path monotonicity constraints.

13 Interconnection Delay Estimation (a) adding a register (b) deleting a register (c) an unchanged wire

14 Predicting Location for the Inserted Register In the slot nearest the geometric center among its fan-in and fan-out cells. G40392 G42709 G42767

15 Tree-Topology Selection Choosing the one with the most delay.

16 Post-Retiming (Register) Placement Freeze all combinational cells Relocate all registers in 3 steps –Slack assignment –Placement range calculation –Simultaneous register to slot assignment

17 Slack Assignment

18 Placement Range G40391 G42612 G

19 Simultaneous Register Place- ment by Bipartite Matching G161 G164 G167 G170 G173 G176 G180 G183 G188 G191 G194 G170 G173 G176 G180 G183 G188 G191 G218 register slot

20 Experimental Results

21 Conclusion Retiming and layout are combined for the first time. Three sub-problems: retiming incorporating interconnection delay, delay estimation, and post-retiming (register) placement.

22 Future Work Tightly coupled simultaneous placement and retiming Retiming considering wire delay and number of registers Using more advanced delay model and considering more VDSM effects