Perf: Improve gkr-mimc memory use

[Tabaie]

Improves the amount of heap allocations in the benchmark of a 2^16 BLS12-377 element long hash down to 1798.62 MB on an hpc6a.48xlarge machine. This constitutes a 20% improvement over the linea-monorepo baseline (2267.45 MB.)

Most of the improvement was achieved by introducing a reusable pool / stack for temporary field element variables, and is generic to any use of the GKR API.
A further reduction was due to a hard-coded implementation of the most commonly used MiMC gate in BLS12-377, which is (state + msg + key)^17.

Log Instance Size	computeGJ	Solve	Total
14	51.05 MB	1102.33 MB	1153.38 MB
15	103.09 MB	1244.49 MB	1347.58 MB
16	228.72 MB	1569.90 MB	1798.62 MB
17	388.39 MB	2943.39 MB	3331.78 MB
18	871.35 MB	4127.38 MB	4998.73 MB
19	1657.63 MB	6413.27 MB	8070.9 MB
20	3352.88 MB	12711.18 MB	16064.06 MB
21	6.63 GB	21.47 GB	28.1 GB
22	13.01 GB	42.69 GB	55.7 GB
23	26.06 GB	83.92 GB	109.98 GB

I believe that for small instance sizes (< 2^16) the cost is dominated by the GKR verifier and the PLONK prover itself. From that point on, the slope of the fitted line (<1) suggests an at most linear rate of growth.

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Note

Introduce a pooled, pointer-based GateAPI (with SumExp17) and plumb it through GKR/MiMC paths to cut heap allocations; update engine hints, templates, SNARK wrapper, and tests/benchmarks.

• GKR backend/runtime:
  • Add stateful gateAPI with a synchronous memory pool (allocated, nbUsed), pointer receivers, newElement, freeElements, and method cast refactor.
  • Introduce SumExp17 in GateAPI; add FrontendAPIWrapper.SumExp17 for in-circuit use; update interface in std/gkrapi/gkr/types.go.
  • Replace global api usage with local gateAPI instances and pass by pointer in evaluation paths (computeGJ, degree checks, equality tests, hints, Complete).
  • Update SNARK-side calls to wire.Gate.Evaluate to use FrontendAPIWrapper.
  • Engine hints: switch gateAPI to hold mod *big.Int; fix modular reductions.
• MiMC permutation:
  • Convert round constants to frontend.Variable per curve; register gates using new types.
  • Use SumExp17 path for degree-17 S-box; keep pow5/pow7 forms.
• Generators/templates and curve backends:
  • Regenerate GKR files across fields to adopt pooled gateAPI and pointer API.
  • Add freeElements() calls in loops hot paths.
• Tests/benchmarks:
  • Update MiMC tests to new backend APIs; broaden curves/backends; rename hash tree bench to Merkle tree and modernize runner.

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[Copilot]

Pull Request Overview

This PR optimizes memory usage in the GKR-MiMC implementation by introducing memory pooling for field element allocations and adding a specialized SumExp17 operation. The changes result in a 20% reduction in heap allocation (from 2267.45 MB to 1798.62 MB) for BLS12-377 benchmarks.

• Memory pool implementation in gateAPI to reduce heap allocations
• New SumExp17 method for optimized computation of (a+b+c)^17 operations
• Refactoring from global to instance-based API usage patterns

Reviewed Changes

Copilot reviewed 33 out of 33 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
std/gkrapi/gkr/types.go	Adds SumExp17 method to GateAPI interface
std/gkrapi/compile.go	Wraps API with FrontendAPIWrapper for gate evaluation
internal/gkr/gkr.go	Adds FrontendAPIWrapper with SumExp17 implementation
std/permutation/gkr-mimc/gkr-mimc.go	Optimizes addPow17 function with BLS12-377 specific caching
Multiple internal/gkr/*/gkr.go	Implements memory pooling in gateAPI across all curve implementations
Multiple internal/gkr/*/solver_hints.go	Updates to use instance-based gateAPI
Test files	Renames hashTreeCircuit to merkleTreeCircuit and improves test configuration

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