Add constraint for Logup claimed cumsum

[shaharsamocha7]

Add optional constraint for logup claimed sum
The constraint applies only in case that the claimed_sum is not the total sum
Uses for padding components with default rows

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This change is 

[shaharsamocha7]

• trace in bit reverse order #857
• State machine prover #845
• State machine AIR #841
• Add constraint for Logup claimed cumsum #830 👈
• Logup generator returns multiple prefix sums #829
• Logup - rename claimed_sum to total_sum #825
• Revert logup without is_first #818
• dev

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[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.21%. Comparing base (69bcf5e) to head (8ba2299).
Report is 3 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #830      +/-   ##
==========================================
+ Coverage   92.15%   92.21%   +0.06%     
==========================================
  Files          90       90              
  Lines       12306    12322      +16     
  Branches    12306    12322      +16     
==========================================
+ Hits        11340    11363      +23     
+ Misses        860      853       -7     
  Partials      106      106              

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[andrewmilson]

Reviewable status: 0 of 6 files reviewed, 1 unresolved discussion (waiting on @Alon-Ti and @shaharsamocha7)

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crates/prover/src/constraint_framework/logup.rs line 84 at r2 (raw file):

            Some((claimed_sum, claimed_row_index)) => {
                let [cur_cumsum, prev_row_cumsum, claimed_cumsum] = eval
                    .next_extension_interaction_mask(self.interaction, [0, -1, claimed_row_index]);

It's more efficient using is_first column and doing the constraint with cur_cumsum and a row selector

[Alon-Ti]

Reviewed 3 of 6 files at r1, 3 of 3 files at r2, all commit messages.
Reviewable status: all files reviewed, 2 unresolved discussions (waiting on @shaharsamocha7)

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crates/prover/src/constraint_framework/logup.rs line 104 at r2 (raw file):

        // Constrain that the claimed_sum in case that it is not equal to the total_sum.
        if let Some((claimed_cumsum, claimed_sum)) = claimed_cumsum {

Move this to the match above.

[shaharsamocha7]

Reviewable status: 5 of 6 files reviewed, 2 unresolved discussions (waiting on @Alon-Ti and @andrewmilson)

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crates/prover/src/constraint_framework/logup.rs line 84 at r2 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

It's more efficient using is_first column and doing the constraint with cur_cumsum and a row selector

Added a TODO.

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crates/prover/src/constraint_framework/logup.rs line 104 at r2 (raw file):

Previously, Alon-Ti wrote…

Move this to the match above.

Done.

[andrewmilson]

Reviewable status: 5 of 6 files reviewed, 3 unresolved discussions (waiting on @Alon-Ti and @shaharsamocha7)

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crates/prover/src/constraint_framework/logup.rs line 26 at r3 (raw file):

/// Represents the value of the prefix sum column at some index.
/// Should be used to eliminate padded rows for the logup sum.
pub type ClaimedPrefixSum = (SecureField, isize);

Would there ever be a negative index?

Suggestion:

usize

[shaharsamocha7]

Reviewable status: 5 of 6 files reviewed, 3 unresolved discussions (waiting on @Alon-Ti and @andrewmilson)

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crates/prover/src/constraint_framework/logup.rs line 26 at r3 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Would there ever be a negative index?

You can also feed negative numbers if you want (as the domain is cyclic)
I can change it to usize, but there would be a cast afterwords because next_extension_interaction_mask gets a list of isize.
Should I make the change?

[andrewmilson]

Reviewable status: 5 of 6 files reviewed, 2 unresolved discussions (waiting on @Alon-Ti and @shaharsamocha7)

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crates/prover/src/constraint_framework/logup.rs line 26 at r3 (raw file):

Previously, shaharsamocha7 wrote…

You can also feed negative numbers if you want (as the domain is cyclic)
I can change it to usize, but there would be a cast afterwords because next_extension_interaction_mask gets a list of isize.
Should I make the change?

Given it's an index I think it should be usize. Offsets make sense as isize so I think it's better to be usize here and to cast to isize when it's needed as an offset

[Alon-Ti]

Reviewed 3 of 3 files at r4, all commit messages.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @shaharsamocha7)

[shaharsamocha7]

Reviewable status: 4 of 6 files reviewed, 1 unresolved discussion (waiting on @Alon-Ti and @andrewmilson)

---

crates/prover/src/constraint_framework/logup.rs line 26 at r3 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Given it's an index I think it should be usize. Offsets make sense as isize so I think it's better to be usize here and to cast to isize when it's needed as an offset

Done.

[andrewmilson]

Reviewable status: 3 of 6 files reviewed, 1 unresolved discussion (waiting on @Alon-Ti)