Implement GrandProductOps for SIMD backend

[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 76.68712% with 38 lines in your changes missing coverage. Please review.

Project coverage is 93.16%. Comparing base (be26562) to head (0dc6a31).

Files	Patch %	Lines
crates/prover/src/core/backend/simd/lookups/gkr.rs	81.81%	21 Missing and 1 partial ⚠️
crates/prover/src/core/lookups/gkr_prover.rs	56.75%	16 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #640      +/-   ##
==========================================
+ Coverage   93.05%   93.16%   +0.10%     
==========================================
  Files          86       86              
  Lines       11209    11364     +155     
  Branches    11209    11364     +155     
==========================================
+ Hits        10431    10587     +156     
+ Misses        685      682       -3     
- Partials       93       95       +2     

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[spapinistarkware]

Reviewed 5 of 7 files at r2, 3 of 3 files at r5, all commit messages.
Reviewable status: all files reviewed, 4 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 90 at r5 (raw file):

        // Note `inp(r, t, x) = eq(t, 0) * inp(r, 0, x) + eq(t, 1) * inp(r, 1, x)`
        //   => `inp(r, 2, x) = 2 * inp(r, 1, x) - inp(r, 0, x)`
        // TODO: Consider evaluation at `1/2` to save an addition operation since `inp(r, 1/2, x) =

Cool idea

Suggestion:

/ TODO(andrew): Consider e

---

crates/prover/src/core/backend/simd/lookups/gkr.rs line 120 at r5 (raw file):

// Can assume `len(layer) > N_LANES * 2`
fn next_grand_product_layer(layer: &Mle<SimdBackend, SecureField>) -> Layer<SimdBackend> {

Suggestion:

/// Assumpion: `len(layer) > N_LANES * 2`
fn next_grand_product_layer(layer: &Mle<SimdBackend, SecureField>) -> Layer<SimdBackend> {

---

crates/prover/src/core/backend/simd/lookups/mod.rs line 2 at r5 (raw file):

mod gkr;
// mod grandproduct;

Remove?

---

crates/prover/src/core/lookups/gkr_prover.rs line 6 at r5 (raw file):

use std::ops::Deref;

use educe::Educe;

What is this?

[andrewmilson]

Reviewable status: 6 of 10 files reviewed, 4 unresolved discussions (waiting on @shaharsamocha7 and @spapinistarkware)

---

crates/prover/src/core/backend/cpu/lookups/gkr.rs line 90 at r5 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Cool idea

Done.

---

crates/prover/src/core/backend/simd/lookups/gkr.rs line 120 at r5 (raw file):

// Can assume `len(layer) > N_LANES * 2`
fn next_grand_product_layer(layer: &Mle<SimdBackend, SecureField>) -> Layer<SimdBackend> {

Done.

---

crates/prover/src/core/backend/simd/lookups/mod.rs line 2 at r5 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

Remove?

Done.

---

crates/prover/src/core/lookups/gkr_prover.rs line 6 at r5 (raw file):

Previously, spapinistarkware (Shahar Papini) wrote…

What is this?

Gives us better derive macros for Clone Debug etc.
It gets around trait bound requirements of the default derive.

e.g.

#[derive(clone)]
struct Something<B: Backend> {
column: Col<B, SecureField>
}

This only implements Clone if B: Clone. But Col<B, SecureField> is Clone so B:Clone is a bad bound.

#[derive(Educe)]
#[educe(Clone)]
struct Something<B: Backend> {
column: Col<B, SecureField>
}

Understands that B doesn't have to be clone

[spapinistarkware]

Reviewed 6 of 6 files at r7, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @shaharsamocha7)