Store Pre-computed Lookup Tables in Memory

[suyash67]

Currently, our lookup tables (as a part of ultra-plonk) are pre-computed once for every execution. Ideally we should only ever pre-compute our lookup tables once. Note that even though lookup tables don't need to be static for UltraPlonk, pre-computing them on every run can become time-consuming if we support larger tables. Further, the way we avoid repeated pre-computation using the variable inited is error prone.

For example, with Pedersen hash using lookup tables, if we fill up the tables during compile-time (we don't disallow such cases), then the variable inited is true when we start the execution but the actual tables are empty. Such things can lead to subtle bugs and cost us a lot of programming time. It will be nice to implement static lookup tables instead.

[suyash67]

Since all of the lookup tables we use are relatively "small" (average size of cumulative lookup tables used in our circuits is $\le 2^{16}$), it is currently easier to just regenerate lookup tables while generating proof. We can revisit this if and when we use lookup tables in the range of $2^{20}$.

Further, the lookup tables we use in stdlib are prone to change (due to bug fixes, optimisations or specific circuit size targets). Using lookup tables in memory would have an overhead anyway when we need to regenerate lookup tables. So for now we keep using the same lookup table infrastructure.