It Is Better to Run Iterative Resynthesis on Parts of the Circuit

1. It Is Better to Run Iterative Resynthesis on Parts of the Circuit Petr Fišer, Jan Schmidt Faculty of Information TechnologyCzech Technical University in Prague fiserp@fit.cvut.cz, schmidt@fit.cvut.cz

2. Outline • Preliminaries • Iterative resynthesis • Motivation • Circuit resynthesis by parts • Experiments • Conclusions IWLS’10

3. Preliminaries • Synthesis (optimization) of circuits (networks) will be discussed • Just for simplicity: • Combinational circuits are assumed • Mapping into arbitrary 2-input gates • Cost (optimality criterion, quality) = # of gates IWLS’10

4. Iterative Resynthesis • Iterative resynthesis = improving the result quality by repetitive application of a single synthesis process, in order to improve the result quality • Possible assumption: the synthesis process cannot make the circuit worse • Needs not be always true IWLS’10

5. Iterative Resynthesis in ABC • ABC naturally supports iterative resynthesis • Emphasized by “choices” • Many possible processes • Suggested: repeating {choice; map} • Superchoice: fraig_store; resyn fraig_store; resyn2 fraig_store; resyn2rs fraig_store; share fraig_store; fraig_restore IWLS’10

6. Iterative Resynthesis in ABC IWLS’10

7. How Many Iterations suffice? • 228 of IWLS’93 benchmarks examined IWLS’10

8. Motivation Imagine: e64 IWLS’93 circuit (65 inputs, 65 outputs, 649 2-input gates) Case 1 – synthesis of the circuit, as it is: • 530 gates • 2.33s runtime Case 2 – split the circuit into two halves, synthesize them separately, then merge the results • 522 gates • 1.73s total runtime Where is the problem? What’s wrong? IWLS’10

9. Circuit Resynthesis by Parts Resynthesize(Network N, opt) { do { (W, NR) = Extract_Window(N, opt); W’ = resynthesize_by_ABC(W); N’ = NRW’; if (cost(N’) ≤ cost(N)) N = N’; } while (!end()); } IWLS’10

10. Window Extraction IWLS’10

11. Window Extraction Connected circuits are always extracted Method 0 – Random selection • Randomly select one “pivot” gate • Incrementally add randomly selected adjoining gates Method 1 – Minimize_fanin • Randomly select one “pivot” gate • Incrementally add adjoining gates, so that the number of window primary inputs is minimized (in a greedy way) Method 2 – Minimize_fanout • Randomly select one “pivot” gate • Incrementally add adjoining gates, so that the number of window primary outputs is minimized (in a greedy way) Method 3 – Minimize_fanin+fanout • Randomly select one “pivot” gate • Incrementally add adjoining gates, so that the sum of numbers of window primary inputs and outputs is minimized (in a greedy way) • These methods allow for arbitrary window size scaling IWLS’10

12. Window Extraction Method 4 – RadiusSelect • Randomly select one “pivot” gate • Add all adjoining gates (i.e., all fan-in and fan-out gates) • For each gate in the window, do (2.), up to the given radius Method 5 – Windowing-like selection Similar to the window selection algorithm in the resubstitution process in ABC • Randomly select one “pivot” gate • Find the minimum level of its transitive fan-in to a given depth • Generate transitive fan-out of the pivot, to a given depth • For these fan-out nodes, include all transitive fan-in nodes up to the computed level into the window • The window size is partially determined by the circuit structure IWLS’10

13. Experimental Setup • 228 of IWLS’93 benchmarks processed • Resynthesis using ABC, using the “superchoice” script, followed by technology mapping into 2-input gates • Iterated 1000-times (recall – this should be more than enough) • 100% circuit resynthesis yielded 19.97% improvement in the average IWLS’10

14. Comparison of Methods Gates (size 20%) Time (size 20%) IWLS’10

15. Comparison of Methods IWLS’10

16. Results Method 0 (Random select), improvement vs. ABC iterated 1000-times IWLS’10

17. Results Method 4 (Radius select), improvement vs. ABC iterated 1000-times IWLS’10

18. Why This Happens - Example Cases Behavior of one of the “good for us” circuits (e64) Method 0 (random selection) IWLS’10

19. Why This Happens - Example Cases Behavior of one of the “bad for us” circuits (clip) Method 0 (random selection) IWLS’10

20. Convergence, Maybe? IWLS’10

21. Convergence, Maybe? IWLS’10

22. Conclusions • Sometimes it is better to resynthesize circuits by parts, rather than as whole • In cases where not, probably it is due to random fluctuations caused by random part selections • Resynthesis by parts converges slower, but yields better results • Why? IWLS’10

23. Questions Discussion Stoning to death… IWLS’10