First version of logaritmic derivative lookup Hab22 argument is implemented as an halo2 gate. In short, we can observe ~25% gain for batch lookups. This gate is defined with ConstraintSystem API and it is not comfortable to work with in practice since the argument requires some specific witness generation procedures. While here we implement logup argument as a gate using frontend API, scroll/halo2/49 implements the same argument in more convenient way that replaces existing lookup in constraint system backend. However with this example we also want to show that precompiles such as copy constraints, subset and shuffle arguments may be better implemented in expressive way. So that pluging-in new precompiles into halo2 constraint system backend would be relatively easier.
| Argument | k | # of columns | table size | prover time |
|---|---|---|---|---|
| Subset | 17 |
8 |
2^16 |
8.214s |
| Logup | 17 |
8 |
2^16 |
6.142s |