feat: support bberg lookups

[Maddiaa0]

see AztecProtocol/aztec-packages#3880 for implementation example

Lookups allow us to assert that values in a set of columns equal some values in another set of columns.

This approach uses the log derivative method to perform lookups, where the lookup relation requires four extra columns ( as well as the read and write columns ) to function.

• One selector column to initiate adding a value into the READ side of the lookup table ( lhs in pil )
• One selector column to initiate adding a value into the WRITE side of the lookup table ( rhs in pil ) - { adding to the table }
• One selector column to compute inverses - ( helper column )
• One column to store the number of times a WRITE term is read - ( helper column )

The selector columns will need to be defined manually - as in the ToyAvm example.
The inverse column and the counts columns are automatically included by the code gen. ( this means there are two extra columns per lookup ( which is a little bit inefficient; but will do for now ).

The name of the inverse column is decided by the attribute tag #[attribute] above the lookup - which is required.
The name of the counts column is ${attribute}_counts.

Note: that in the circuit builder you are currently required to set the counts column value manually.

syntax:

  #[lookup_xor] // attribute
    q_xor { xor_a, xor_b, xor_c } in q_xor_table { table_xor_a, table_xor_b, table_xor_c };
    // lhs selector, lhs columns        // rhs selector, rhs columns

[jeanmon]

Very nice work! Please address/look at my feedback before merging.

[jeanmon]

nitpick: I would prefer two different identifiers, unless this is Rust standard practice.

[Maddiaa0]

This can just be replaced with the single identifier, as it is just for string templating - will edit

[jeanmon]

Copy-paste leftover? Probably should be "LookupSide"

[Maddiaa0]

Actually good point here- they are more or less the same i can unify the type

[Maddiaa0]

Actually i probably wont, even though it is repeated it is much more readable when they are defined beside each other

[jeanmon]

In this function and subsequent ones, replace variables like "perm", "perm_settings" by "lookup", "lookup_settings".

[jeanmon]

Suggested change

	* 2) Update all the values with the ones needed for your permutation
	* 2) Update all the values with the ones needed for your lookup

[jeanmon]

Suggested change

	* @brief They type of WRITE_TERM used for each write index
	* @brief The type of WRITE_TERM used for each write index

[jeanmon]

Rename function to "get_lookup_side"

[Maddiaa0]

I shall unify these

[jeanmon]

Suggested change

	* @brief Get all the entities for the lookup when need to update them
	* @brief Get all the entities for the lookup when we need to update them