Fix: Simplify LT bus packing to 2 elements per operand

[MauroToscano]

Summary

• Change LT bus receiver from 3× Direct packing to Packing::DWordHHW (2 elements)

• Change CPU LT sender from 3 linear combinations to Packing::DWordBL (2 elements)

• Both produce the same [lo32, hi32] fingerprint, enabling interoperability with DWordWL senders

• Add constraints so everything is properly range checked

  Motivation

This change enables MEMW timestamps (DWordWL format) to send to the LT bus using Packing::DWordWL, which also produces [lo32, hi32]. Previously, LT expected 3 elements per operand which was incompatible.

Changes

• prover/src/tables/lt.rs: Use Packing::DWordHHW for lhs/rhs (reads 3 columns, produces 2 bus elements)
• prover/src/tables/cpu.rs: Use Packing::DWordBL for arg1/arg2 (reads 8 bytes, produces 2 bus elements)

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base binary_search	69.9 ± 11.2	62.3	89.8	1.05 ± 0.21
head binary_search	66.5 ± 8.2	62.2	89.3	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base bitwise_ops	65.4 ± 3.7	62.2	69.7	1.00 ± 0.08
head bitwise_ops	65.4 ± 3.8	62.3	69.9	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base fibonacci_26	67.6 ± 2.3	65.6	71.3	1.01 ± 0.05
head fibonacci_26	67.2 ± 2.2	65.6	71.2	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base hashmap	135.3 ± 2.3	132.8	139.7	1.00
head hashmap	135.7 ± 2.9	132.2	138.8	1.00 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base keccak	133.1 ± 8.3	123.4	154.6	1.04 ± 0.07
head keccak	128.0 ± 3.3	124.5	135.7	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base matrix_multiply	68.7 ± 1.4	67.5	71.4	1.00 ± 0.03
head matrix_multiply	68.6 ± 1.2	67.4	71.5	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base modular_exp	65.0 ± 3.7	61.8	69.5	1.04 ± 0.06
head modular_exp	62.4 ± 0.7	61.7	63.3	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base quicksort	67.0 ± 1.6	66.1	71.3	1.00
head quicksort	67.3 ± 2.3	65.6	71.5	1.01 ± 0.04

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base sieve	72.7 ± 3.3	69.6	79.6	1.02 ± 0.06
head sieve	71.2 ± 2.5	69.5	75.8	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base sum_array	87.7 ± 20.1	77.8	144.4	1.00 ± 0.33
head sum_array	87.3 ± 20.2	79.2	144.6	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base syscall_commit	101.1 ± 5.1	96.2	107.2	1.00
head syscall_commit	109.3 ± 28.3	96.1	188.6	1.08 ± 0.29

[RobinJadoul]

If I'm understanding this correctly; you're essentially casting a HHW to a WL? Which will probably introduce unsoundness on the LT side, because the range-check assumptions (LT-A1/LT-A2) no longer necessarily hold if they're not enforced by the logup.

[RobinJadoul]

Formally marking it as "request changes" to prevent accidental merging

[RobinJadoul]

I don't know enough about the rest of the code, but this specific unsoundness should now be addressed 👍