CellE: Automated Standard Cell Library Extension via Equality Saturation

Context

This note summarizes how standard cell library extension (SCLX) can more systematically discover composite cells that post-mapping netlist mining tends to miss.
The main focus is the phase-ordering problem caused by expanding a library from one structural implementation, and the alternative of searching through semantic equivalence.

This paper argues that CellE can find more useful composite standard cells than conventional SCLX by using equality saturation to semantically explore a space of functionally equivalent implementations.
The key idea is to avoid mining only one post-mapping structure. Instead, CellE extracts subcircuit candidates while considering many equivalent implementations inside an e-graph.
In the reported results, EPFL + FreePDK45 shows an average 15.41% area reduction over the original library, while a commercial ASAP7 flow reports an average 8.00% delay reduction and 1.27% area reduction.

Conventional SCLX depends on a single post-mapping netlist, so it can easily miss useful cell patterns that only appear in other structures implementing the same function.
This paper is therefore a useful example of why semantic exploration can improve library extension quality compared with purely structural mining.

First, a post-mapping netlist is converted into an e-graph that compactly represents many logically equivalent implementations.
Equality saturation is then performed with rewrite rules such as commutativity, De Morgan transformations, simplification, and involution.
The saturated e-graph is converted into a bipartite graph, and candidate cells are found with a modified gSpan-style frequent subgraph mining method that respects subcircuit constraints.
Finally, only useful cells are kept after SAT-based equivalence filtering, layout/netlist generation, and technology-mapping QoR validation.

The method only targets single-output subcircuits/cells, so multi-output cell extension is outside its scope.
The experiments manage search complexity by limiting new cells to at most 5 original cells and at most 3 inputs.
As the paper notes in future work, the current search does not directly include physical cell properties, so physical awareness remains limited compared with the richness of the semantic search.

It would be useful to collect more cases showing whether equality-saturation-based semantic exploration is repeatedly effective in other SCLX or logic optimization flows.
CellE's limits should be compared more clearly with follow-up work that includes physical properties directly in the search process.