Add GKR implementation of Logup lookups

[andrewmilson]

This change is 

[andrewmilson]

• Add eval order and interpolate to SecureEvaluation #794
• Add MLE eval constraints #742
• Add eq evals constraints #741
• Add benchmarks for GKR lookups #673
• Implement LogupOps for SIMD backend #641
• Implement GrandProductOps for SIMD backend #640
• Implement GkrOps for SIMD backend #630
• Implement MleOps for SIMD backend #629
• Add GKR implementation of Logup lookups #623 👈
• Add GKR implementation of Grand Product lookups #620
• Implement GkrOps for CPU backend #621
• Add batch GKR prover and verifier #581
• Rename CPU* structs to Cpu* to conform to Rust's naming convention #617
• Remove AVX backend #616
• Convert wide_fibbonacci AVX backend example to SIMD backend #615
• Update CI to test Wasm simd128, avx2 and aarch64 neon #614
• Fix CirclePointIndex bug in debug mode for 32-bit archs #613
• Change opt-level in benchmarks script #612
• Add benchmarks for SIMD m31 #611
• Add benchmarks for SIMD merkle #610
• dev

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[codecov-commenter]

Codecov Report

Attention: Patch coverage is 93.05556% with 25 lines in your changes missing coverage. Please review.

Please upload report for BASE (dev@437ea59). Learn more about missing BASE report.

Files	Patch %	Lines
crates/prover/src/core/lookups/gkr_prover.rs	82.53%	11 Missing ⚠️
crates/prover/src/core/lookups/utils.rs	61.53%	10 Missing ⚠️
crates/prover/src/core/backend/cpu/lookups/gkr.rs	98.84%	0 Missing and 3 partials ⚠️
crates/prover/src/core/lookups/gkr_verifier.rs	91.66%	1 Missing ⚠️

Additional details and impacted files

@@          Coverage Diff           @@
##             dev     #623   +/-   ##
======================================
  Coverage       ?   92.84%           
======================================
  Files          ?       82           
  Lines          ?    10933           
  Branches       ?    10933           
======================================
  Hits           ?    10151           
  Misses         ?      688           
  Partials       ?       94           

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[spapinistarkware]

Reviewed 5 of 8 files at r3, 2 of 2 files at r5, 1 of 1 files at r8, all commit messages.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 180 at r8 (raw file):

) -> (SecureField, SecureField) {
    /// Represents the fraction `1 / x`
    struct Reciprocal {

I wonder if this is needed, or we can use Fraction with a constant numerator, and the compiler will optimizes with constant propagation...

Code quote:

struct Reciprocal

[spapinistarkware]

Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @andrewmilson and @shaharsamocha7)

[spapinistarkware]

Reviewed 1 of 1 files at r9, all commit messages.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @andrewmilson and @shaharsamocha7)

[andrewmilson]

Reviewable status: 6 of 10 files reviewed, 1 unresolved discussion (waiting on @shaharsamocha7 and @spapinistarkware)

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 180 at r8 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

I wonder if this is needed, or we can use Fraction with a constant numerator, and the compiler will optimizes with constant propagation...

Does not make the optimisation: https://godbolt.org/z/Mvz1YvdfT.
I remove this in a later PR in favour of a more general Reciprocal type (supporting regular and packed field types)