Optimize exact-scan MPC threshold primitives

[philsippl]

Summary

• add packed three-way MSB extraction matching the GPU threshold-ring circuit
• add a direct 18-bit circuit for the fixed anonymous-statistics FHD threshold instead of lifting every dense comparison into the 32-bit arithmetic ring
• fuse the independent mask-carry and threshold-expression adders into shared communication rounds
• refresh interleaved Galois-ring dot contributions directly into packed Rep3 components and materialize scalar code/mask shares only for public candidate indices
• preserve multi-flow session striping for batch-size-one workloads and stop clamping physical connections to the logical session count
• remove the benchmarked-but-inferior session-affine transport path

Why

The CPU linear scanner evaluates every first-eye candidate and needs threshold checks to remain parallel across an entire chunk. The generic lift/multiply/MSB path introduced unnecessary memory traffic and sequential MPC rounds. These primitives expose the GPU-equivalent threshold circuit to the CPU implementation while preserving the existing PRF use and wire semantics.

Consumed by worldcoin/iris-mpc#2347.

Correctness and validation

• cargo test -p ampc-actor-utils: 74 passed, 0 failed
• deterministic generic-vs-direct FHD threshold coverage
• randomized direct anonymous-threshold vs lifted-reference coverage
• fused Galois-to-Rep3 path checked against the dense path
• candidate selection checks preserve order and duplicate indices
• git diff --check origin/main...HEAD

End-to-end performance

Measured through the dependent Iris MPC implementation with batch size 1 on three AWS r8g.24xlarge instances:

• full TLS + MPC protocol, normal and mirror included: 5.17–5.20M logical comparisons/s
• measured traffic: 383.67 bytes/comparison/direction
• network demand at 5.2M/s: about 16.0 Gbit/s per direction

These are application-level results for the combined AMPC and Iris changes, not an isolated AMPC microbenchmark. Detailed benchmark context is recorded in worldcoin/iris-mpc#2347.