Timing Optimization by IRredundancy Removal and Addition

1. Timing Optimization by IRredundancy Removal and Addition Speaker : Guo-Jhu Huang Advisor : Chun-Yao Wang 2009.08.14

2. Outline • Introduction • Our idea • Future work

3. Introduction • Timing optimization have been an important goal in IC design • Given a timing constraint (usually the clock period) • the combinational circuit must meet its timing constraint to work correctly

4. Introduction • In different phases, different techniques are used to improve circuit speed • Logic level: structure of circuit • Topological level: placement and routing • Physical level: sizing and buffering

5. Introduction • IRRA is a rewiring technique • Our goal is using IRRA to restructure the circuit for timing improvement

6. Our idea • First stage • Greedy approach • Second stage • Add stimulus to SIS, use sis timing engine to optimize the timing

7. Greedy approach • Define the timing model, • Gate delay = 1+ α．(# of fanout) original after removing the target wire • If choosing a dominator as a destination • gn.arrival_time <= gd.arrival_time • ga.slack > 0

8. Greedy approach original after removing the target wire • If choosing a forced MA as a destination • gn.arrival_time <= gd.required_time • ga.slack> 0

9. Greedy approach • 1. compute arrival, required and slack • 2. select candidate removed nodes • 3. choose candidate nodes’ fanin as wt to compute alternative wires • 4. choose the alternative wire with the largest weight • weight=number of removed critical wires • 5. add the alternative wire to remove many wires

10. Example 1.Compute arrival time, required time and slack a:0.2 i1 r:2.0 g1 s:1.8 a:1.6 r:3.2 g5 a:0.2 o1 s:1.6 i2 a:4.2 r:1.8 r:4.2 g3 s:1.6 s:0 i3 a:3.2 a:0.4 r:3.2 r:0.4 g2 g6 s:0 s:0 o2 a:4.2 i4 a:1.8 a:0.2 r:4.2 r:1.8 r:0.4 s:0 g4 s:0 s:0.2 a:3.0 i5 r:3.2 a:0.2 s:0.2 r:2.0 s:1.8

11. Example 2. Select candidate removed nodes a:0.2 i1 r:2.0 g1 s:1.8 a:1.6 r:3.2 g5 a:0.2 o1 s:1.6 i2 a:4.2 r:1.8 r:4.2 g3 s:1.6 s:0 i3 a:3.2 a:0.4 r:3.2 r:0.4 g2 g6 s:0 s:0 o2 a:4.2 i4 a:1.8 a:0.2 r:4.2 r:1.8 r:0.4 s:0 g4 s:0 s:0.2 a:3.0 i5 r:3.2 a:0.2 s:0.2 r:2.0 s:1.8

12. Example 3. For each candidate nodes, choose its critical fanin as wt to compute alternative wires i1 g1 g5 o1 i2 wt g3 ga:g3 gd:g5 wt i3 wt wt g2 g6 o2 i4 g4 ga:i2 gd:i5 ga:g3 gd:i5 ga:g3 gd:g6 i5

13. Example • Greedy condition: • gn.arrival_time:1.6 <= original i5.required_time:2.0 • i2.slack:1.4 > 0 a:0.2 i1 r:1.8 g1 a:1.6 s:1.6 r:3.0 g5 o1 a:0.4 s:1.4 i2 a:4.0 r:1.8 r:4.0 g3 a:3.0 s:1.4 s:0 r:3.0 s:0 i3 a:0.4 wt g2 a:1.8 r:0.4 g6 a:4.0 s:0 r:1.8 o2 r:4.0 s:0 i4 a:0.2 s:0 r:0.4 g4 ga:i2 gd:i5 s:0.2 a:3.0 Original i5 gn r:3.0 a:0.2 a:0.2 a:1.6 s:0 r:2.0 r:0.6 r:1.8 s:1.8 s:0.4 s:0.2

14. Example i1 g1 g5 o1 i2 wt g3 gd:g5 ga:g3 wt i3 wt wt g2 g6 o2 i4 g4 gd:i5 ga:i2 gd:i5 ga:g3 gd:g6 ga:g3 i5

15. Example 4. Choose the alternative wire with largest weight target wire: g3-g6 alternative wire: gd:i5 ga:i2

16. SIS: Speed-up • 1. compute the slacks to find the critical nodes • 2. compute the weight of every critical node • weight=Wt+α*Wa • 3. use maxflow-mincut algorithm to find resynthesis cutset • 4. do partial collapse with depth d to resynthesis node • 5. decompose the resynthesis region

17. Stimulus to SIS • We take the resynthesis node as a dominator, and remove a wire to create a network

18. Stimulus to SIS • Which wire to remove? • The wire is on the critical paths • Weight=α．|slack|+β．Wn • 1) If the resynthesis node has D or D’ value • Wn=|P|, P={x| x is PI of SMA} • 2) If the resynthesis node has no value • Wn=Max(|P|, |Q|-|P|), Q={x| x is PI of gd and x is not PI of SMA}

19. Example Assume mincut node={g5,g6} g5 has no dominated critical wire to remove i1 g1 g5 o1 i2 g3 i3 g2 g6 o2 i4 g4 i5

20. Example Assume mincut node={g5,g6} i1 g1 g5 o1 i2 g3 i3 g2 g6 o2 i4 g6 has no dominated critical wire to remove g4 i5

21. Flow chart

22. Future work • Find some ideas to improve • Programming