Add GKR implementation of Grand Product lookups

[andrewmilson]

This change is 

[andrewmilson]

• 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 92.72727% with 16 lines in your changes missing coverage. Please review.

Project coverage is 92.56%. Comparing base (778d86c) to head (9883b66).

Files	Patch %	Lines
crates/prover/src/core/lookups/gkr_prover.rs	91.57%	8 Missing ⚠️
crates/prover/src/core/lookups/gkr_verifier.rs	92.64%	2 Missing and 3 partials ⚠️
crates/prover/src/core/backend/cpu/lookups/gkr.rs	94.64%	2 Missing and 1 partial ⚠️

Additional details and impacted files

@@                            Coverage Diff                             @@
##           05-08-Implement_GkrOps_for_CPU_backend     #620      +/-   ##
==========================================================================
+ Coverage                                   89.77%   92.56%   +2.78%     
==========================================================================
  Files                                          72       72              
  Lines                                        9379     9589     +210     
  Branches                                     9379     9589     +210     
==========================================================================
+ Hits                                         8420     8876     +456     
+ Misses                                        887      634     -253     
- Partials                                       72       79       +7     

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[spapinistarkware]

Reviewed 1 of 8 files at r1, all commit messages.
Reviewable status: 1 of 11 files reviewed, 4 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 32 at r3 (raw file):

        claim: SecureField,
    ) -> UnivariatePoly<SecureField> {
        let k = h.n_variables();

n_variables or n_vars

Suggestion:

n_variables

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 35 at r3 (raw file):

        let n_terms = 1 << (k - 1);
        let eq_evals = h.eq_evals;
        let y = eq_evals.y();

What's this? Rename or doc.

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 51 at r3 (raw file):

                    let rhs0 = input_layer[(n_terms + i) * 2];
                    let rhs1 = input_layer[(n_terms + i) * 2 + 1];

Suggestion:

                    // Input polynomial at points (r,0,bits(i),1), ...
                    let inp_at_r0i0 = input_layer[i * 2];
                    let inp_at_r0i1 = input_layer[i * 2 + 1];

                    let inp_at_r1i0 = input_layer[(n_terms + i) * 2];
                    let inp_at_r1i1 = input_layer[(n_terms + i) * 2 + 1];
                    
                    let inp_at_r2i0 = (inp_at_r1i0.double() - inp_at_r0i0);
                    let inp_at_r2i1 = (inp_at_r0i1.double() - inp_at_r0i1);

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 54 at r3 (raw file):

                    let product2 = (rhs0.double() - lhs0) * (rhs1.double() - lhs1);
                    let product0 = lhs0 * lhs1;

Suggestion:

                    // Product polynomial prod(x) = inp(x,0)*inp(x,1)
                    //   at points (r,0,bits(i)), ...
                    let prod_at_r0i = inp_at_r0i0 * inp_at_r0i1;
                    let prod_t_r2i = inp_at_r2i0 * inp_at_r2i1;