Logup - rename claimed_sum to total_sum

[shaharsamocha7]

Rename claimed_sum to total_sum
Take total_sum from cum_sum column

---

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

This stack of pull requests is managed by Graphite. Learn more about stacking.

Join @shaharsamocha7 and the rest of your teammates on Graphite

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.95%. Comparing base (e9c6ba2) to head (62932c1).
Report is 2 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #825      +/-   ##
==========================================
- Coverage   91.98%   91.95%   -0.03%     
==========================================
  Files          90       90              
  Lines       12198    12195       -3     
  Branches    12198    12195       -3     
==========================================
- Hits        11220    11214       -6     
- Misses        872      875       +3     
  Partials      106      106              

Flag	Coverage Δ
	91.95% <100.00%> (-0.03%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[Alon-Ti]

Reviewed 3 of 7 files at r1, 4 of 4 files at r2, all commit messages.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @shaharsamocha7)

---

crates/prover/src/constraint_framework/logup.rs line 173 at r2 (raw file):

        };

        // The last element in bit-reversed order of the the circle order is at index 1.

We should come up with a name for this order, and maybe constants like %sOrder::Last, etc.

[shaharsamocha7]

Reviewable status: 6 of 7 files reviewed, 1 unresolved discussion (waiting on @Alon-Ti)

---

crates/prover/src/constraint_framework/logup.rs line 173 at r2 (raw file):

Previously, Alon-Ti wrote…

We should come up with a name for this order, and maybe constants like %sOrder::Last, etc.

For now I called it bit-reversed circle domain order
Maybe in the future we will want an Order Struct but I think it is a premature now.

[Alon-Ti]

Reviewed 1 of 1 files at r3, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @shaharsamocha7)