Ark-ff Small Field Support

[z-tech]

Description

Arkworks Prime fields are instantiated using procedural macros (e.g. #[derive(MontConfig)]) that rely on the num_bigint::BigInt library. While the flexibility of this approach allows for arbitrary-length prime moduli, it is slower than using system native arithmetic for small moduli.

To capture this optimization, in the linked PR we introduce a new procedural macro, SmallFp, which targets primes < 128 bits. It generates field arithmetic using the smallest appropriate integer primitive (u8, u16, u32, u64, u128).

For multiplication workloads, we observe a > 30% improvement across all primes < 2^127 bits. For Goldilocks specifically, we observe multiplication heavy performance within 5% of https://github.com/succinctlabs/plonky3/blob/main/goldilocks/src/lib.rs#L29 (in serial)

Note: We have prioritized correctness in this PR. We have not yet added prime-specific tricks or SIMD/vectorized optimizations. We will do this immediately upon acceptance of the linked PR.

TL;DR: SmallFp is designed as a drop-in replacement for the existing prime field implementation whenever p < 128 bits. It also lays the groundwork for SIMD optimizations, which we plan to contribute next