Combine eq step constraints into single constraint

[andrewmilson]

This change is 

[andrewmilson]

• Create blake example that uses GKR for lookups #807
• Create MLE eval verifier component #805
• Create MLE eval prover component #804
• Add build trace functions for MLE eval component #803
• Remove InteractionElements and LookupValues #802
• Pass entire mask to components #801
• Add MleCollection for accumulating MLEs #800
• Combine eq step constraints into single constraint #799 👈
• Move all MLE eval related constraints into same module #798
• dev

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[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.35%. Comparing base (f16ba08) to head (c3af357).
Report is 4 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #799      +/-   ##
==========================================
+ Coverage   92.26%   92.35%   +0.09%     
==========================================
  Files          91       91              
  Lines       12442    12481      +39     
  Branches    12442    12481      +39     
==========================================
+ Hits        11479    11527      +48     
+ Misses        857      848       -9     
  Partials      106      106              

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[spapinistarkware]

Reviewed all commit messages.
Reviewable status: 0 of 1 files reviewed, 1 unresolved discussion (waiting on @andrewmilson)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 86 at r1 (raw file):

    // Check all variables except the last (last variable is handled by the constraint above).
    let step_constraints = (0..N_VARIABLES.saturating_sub(1)).map(|variable_i| {

Combine the constraints like we discussed

[andrewmilson]

Reviewable status: 0 of 2 files reviewed, 1 unresolved discussion (waiting on @spapinistarkware)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 86 at r1 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Combine the constraints like we discussed

Done.

[spapinistarkware]

Reviewed 1 of 2 files at r2, 1 of 2 files at r3, all commit messages.
Reviewable status: 2 of 3 files reviewed, 2 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 105 at r3 (raw file):

    // Check all the steps.
    eval.add_constraint(curr - next_next * carry_quotients_col_eval);

carry_quotients_col_eval can't be a constant column, right? I woudl imagine you need to evaluate it at a point, but eval_carry_quotient_col doesn't seem to accept EvalAtRow, so, how does carry_quotients_col_eval this get here?

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 213 at r3 (raw file):

    let step_coset = Coset::new(coset.initial_index, coset.log_size - 1);
    let mut res =
        (coset_vanishing(coset, p) / coset_vanishing(step_coset, p)).square() / BaseField::from(2);

Division is a bummer. Especially when you compute it log_step times!
I think you can compute all of these it in a better way.
The straight forward way is to do a batch inverse. But you canprobably save a bit more, if u do it wisely.

[andrewmilson]

Reviewable status: 2 of 3 files reviewed, 2 unresolved discussions (waiting on @shaharsamocha7 and @spapinistarkware)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 105 at r3 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

carry_quotients_col_eval can't be a constant column, right? I woudl imagine you need to evaluate it at a point, but eval_carry_quotient_col doesn't seem to accept EvalAtRow, so, how does carry_quotients_col_eval this get here?

Done. Discussed offline.

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 213 at r3 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Division is a bummer. Especially when you compute it log_step times!
I think you can compute all of these it in a better way.
The straight forward way is to do a batch inverse. But you canprobably save a bit more, if u do it wisely.

Done.

[spapinistarkware]

Reviewed all commit messages.
Reviewable status: 2 of 3 files reviewed, 2 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 217 at r4 (raw file):

    let mut numers = vec![coset_vanishing(coset, p).square()];
    let mut denoms = vec![coset_vanishing(step_coset, p).square().double()];
    for log_sub_step in 1..log_step {

Consider something like this:

let p_doublings = (0..log).scan(p,|(p,_)| (p.double(),p)).collect();
let initial_doublings = (0..log).scan(initial_point,|(p,_)| (p.double(),p)).collect();
let selectors = p_doublings.zip(initial_doublings).rev().scan(
  |(last_sel,(q,c))| (last_sel*(q.x-c.y))
);
  
}

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 219 at r4 (raw file):

    for log_sub_step in 1..log_step {
        let step_coset = Coset::new(coset.initial_index, coset.log_size - log_sub_step);
        numers.push(coset_vanishing(coset, p));

Isn't this the same expression at every iteration?

[spapinistarkware]

Reviewable status: 2 of 3 files reviewed, 3 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 182 at r4 (raw file):

        let log_step = variable_i as u32 + 2;
        let offset = (1 << (log_step - 1)) - 2;
        let half_coset0_selector = eval_step_selector_with_offset(coset, offset, log_step, p);

Now i'm not so sure why this works...
The selector you compute. Is it all 1s and 0s, or is it just 0s and non 0s?

[andrewmilson]

Reviewable status: 2 of 3 files reviewed, 3 unresolved discussions (waiting on @shaharsamocha7 and @spapinistarkware)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 182 at r4 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Now i'm not so sure why this works...
The selector you compute. Is it all 1s and 0s, or is it just 0s and non 0s?

All 1s and 0s

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 219 at r4 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Isn't this the same expression at every iteration?

Yes the num

[andrewmilson]

Reviewable status: 2 of 3 files reviewed, 3 unresolved discussions (waiting on @shaharsamocha7 and @spapinistarkware)

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 182 at r4 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

All 1s and 0s

start with coset_vanish(coset, p).square() / coset_vanish(half_coset, p) gives you all 1s on half coset0
Normalise and return there if we want step 2

Then add coset_vanish(coset, p)/coset_vanish(half_coset, p) which alternates 1, -1 on half coset0 and 0 on
Normalise and return there if we want step 4

Then add coset_vanish(coset, p)/coset_vanish(half_half_coset, p) which alternates 2, 0, -2, 0 on half coset0
Normalise and return there if we want step 8

etc.

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 217 at r4 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Consider something like this:

let p_doublings = (0..log).scan(p,|(p,_)| (p.double(),p)).collect();
let initial_doublings = (0..log).scan(initial_point,|(p,_)| (p.double(),p)).collect();
let selectors = p_doublings.zip(initial_doublings).rev().scan(
  |(last_sel,(q,c))| (last_sel*(q.x-c.y))
);
  
}

Think we need to do the quotienting to get 0 or 1 selectors on coset.
Maybe I don't fully understand the technique you're proposing.

I made some similarish modifications though WDYT?

---

crates/prover/src/examples/xor/gkr_lookups/mle_eval.rs line 219 at r4 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Yes the num

Done

[spapinistarkware]

Reviewed 1 of 1 files at r6, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @shaharsamocha7)