[Architecture explanation] MV Lookup PR

[mratsim]

cc @AlekseiVambol , you can ask your questions here in-line with the code

[AlekseiVambol]

What is happening at the lines 549-625? Why are the "a.append(&mut b);" lines provided instead of arithmetic operations?

[Brechtpd]

Oh it just collects all the data to print out the information as given in the example here:

halo2/halo2_proofs/src/dev/failure.rs

Lines 434 to 444 in a265b2c

	/// Lookup inputs:
	/// L0 = x1 * x0 + (1 - x1) * 0x2
	/// ^
	/// | Cell layout in region 'Faulty synthesis':
	/// | | Offset | A0 | F1 |
	/// | +--------+----+----+
	/// | | 1 | x0 | x1 | <--{ Lookup inputs queried here
	/// |
	/// | Assigned cell values:
	/// | x0 = 0x5
	/// | x1 = 1

.

So it parses the input expression to collect all the cell values that are used. So it doesn't actually try to calculate the input expression (so no arithmetic), it just prints all the used cell values for debugging purposes.

[AlekseiVambol]

Thanks! Just noticed that the data type of the value being appended is not a field element, but a key-value pair:

Thus, this makes sense for me now.

[AlekseiVambol]

Could you explain me the purpose of the "GraphEvaluator" data type (the line 200, if you already know the necessary details)? Perhaps, I will have to deal with it, though still not sure.

[Brechtpd]

It's a helper struct to do all the necessary evaluations in a more optimal way. So our circuits have lots of expressions, and most of them often overlap. So this tries to find sub expressions that are shared between all these expressions so it can optimize the calculation of all necessary expressions. Simple example: we have two expressions:

• a + b + c
• a + b + d

In a naive way, this requires 4 additions (two additions for each expression). However a + b is shared between the two expressions. So what the GraphEvaluator tries to do is calculate t := a + b once, and then calculate t + c and t + d to get the result of both expressions, but now only using 3 additions.

[AlekseiVambol]

Do I correctly understand that at the line 81 ("let instance: Vec<InstanceSingleScheme::Curve> = instances") the array describing the sets of the instance collumns for each circuit intsance is converted into the array of corresponding polynomials, each of which is given in two forms: coefficients of the powers of x and coefficients of the Lagrange basis polynomials? And what is the boolean variable "P::QUERY_INSTANCE"?

[Brechtpd]

I think so yes.

P::QUERY_INSTANCE seems related to the commitment scheme. It is true for IPA and false for KZG. Why or what it does however, I do not know because this also seems something new (or at least I can't remember).

[jonathanpwang]

Just FYI, I discovered that the direct cherry-pick of Scroll's PR will cause an error because there is an implicit assumption about the behavior of parallelize which changed after @mratsim 's optimization. See axiom-crypto@45e940c