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Optimality Study of Logic Synthesis for LUT-Based FPGAs
Jason Cong and Kirill Minkovich
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Outline
TermsPurposeHow the Examples were constructedCompare their structure to existing
benchmarksLook at the results
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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)
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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
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LEKO Construction
Basic Building Block – Core Graph (Cn):◦It has n inputs and n outputs◦Every output is a function of all n inputs◦Each internal node of Cn has exactly 2 inputs◦There exists an optimal mapping (area/depth) of Cn
into a 4-LUT mapping solutionThese *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.
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65 input core Graph – C5
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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
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Structure Comparison
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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
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Examples Used
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Results
Mapping Results (LEKO) Synthesis Results (LEKU)
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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.
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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
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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