1. Optimality Study of Logic Synthesis for LUT-Based FPGAs Jason Cong and Kirill Minkovich

2. Outline Terms Purpose How the Examples were constructed Compare their structure to existing benchmarks Look at the results 2

3. Terms LEKO – Logic Synthesis examples with Known Optimal LEKU – Logic Synthesis examples with Known Upper bounds MCNC – Microelectronics Center of North Carolina MFFC – Maximum Fanout Free Cone (a method of measuring the structure of the circuit) 3

4. Purpose To develop an algorithm for generating synthetic benchmarks (LEKO and LEKU) with known optimal technology mapping solutions Allow us to construct arbitrarily large test circuits for Synthesis software To show that these benchmarks are structurally similar the MCNC benchmark Show results 4

5. LEKO Construction Basic Building Block – Core Graph (C n ): ◦It has n inputs and n outputs ◦Every output is a function of all n inputs ◦Each internal node of C n has exactly 2 inputs ◦There exists an optimal mapping (area/depth) of C n into a 4-LUT mapping solution These *same* building blocks are put together on several layers so that there exist a path from every Basic block on the bottom layer to the top layer. 5

6. 6 5 input core Graph – C 5

7. Additional Notes To construct a core graph from a pre- existing benchmark, all you have to do is extract a piece of logic from that has an equal number of inputs and outputs LEKU circuits are derived from the LEKO circuits by collapsing and gate decomposition 7

8. Structure Comparison 8

9. Important notes about the results Only performed the logic synthesis step of the tools and did not go through the final placement and routing The actual depths are not report because Xilinx uses two 4-LUTS in their logic blocks 9

10. Examples Used 10

11. Results Mapping Results (LEKO) Synthesis Results (LEKU) 11

12. Results (2) This suggests that there may be significant opportunity for improvement in the logic-synthesis algorithms. They must have a more global view of synthesis including duplication removal. 12

13. Conclusions The problems with the MCNC is that almost every logic-synthesis tool is specifically tuned to perform well on these benchmarks. LEKO allows the designer to combine multiple ‘hard to map’ cares into one design with a known optimal Knowing the optimal solution, the designer can see exactly where the algorithm made the mistake and why 13

14. Conclusions (2) LEKU circuits are meant to test how the existing algorithms perform and how much room is left for improvement when handling each type of inefficiency and/or redundancy. This is basically a platform to create new benchmarks that can test every part of a synthesis tool 14