Use packed field operations for better performance in hash functions

[huitseeker]

Several places in the hash function implementations could benefit from using Plonky3's packed field operations for better SIMD performance.

Locations

1. Poseidon2 external rounds (miden-crypto/src/hash/algebraic_sponge/poseidon2/mod.rs:148)

   • Reference: Plonky3-rebased (alternate) #720 (comment)
   • Could use packing for the external round operations

2. AlgebraicSponge trait implementation (miden-crypto/src/hash/algebraic_sponge/mod.rs)

   • Reference: Plonky3-rebased (alternate) #720 (comment)
   • Note: If we implement Permutation for AlgebraicSponge, and with the upcoming new StatefulHasher from lifted FRI, we should be able to delegate to plonky3. The issue is the state ordering.

Benefits

Using packed fields (SIMD operations) can significantly improve performance for hash computations, especially in proof generation where hashing is a major bottleneck.

Related

Part of #724

[adr1anh]

Note that WASM has a SIMD width of 128 and therefore doesn’t work for Goldilocks (and the same holds for ARM-based CPUs).