I was thinking we could have two sets of shared columns:
- First, a set of "core" columns which would contain instruction decoding registers during an execution cycle, or some counter data during a kernel bootloading cycle.
- Second, a set of "general" columns which would be more general-purpose. For now it could contain "looking" columns for most CTLs (Keccak, arithmetic and logic; NOT memory since memory can be used simultaneously with the others). It could potentially be reused for other things too, such as the registers used for `EQ` and `IS_ZERO` (but I know it's nontrivial to share those since we would need to use lower-degree constraints, so I wouldn't bother for now).
This PR implements just the latter. If it looks good I'll proceed with the former afterward.
Ultimately they're encoded as `[F; 8]`s in the table, but I don't anticipate that we'll have any use cases where we want to store more than 256 bits. Might as well store `U256` until we actually build the table since they're more compact.
It's a bit more type-safe (can't mix up segment with context or virtual addr), and this way uniqueness of ordinals is enforced, partially addressing a concern raised in #591.
To avoid making `Segment` public (which I don't think would be appropriate), I had to make some other visibility changes, and had to move `generate_random_memory_ops` into the test module.
The kernel is hashed using a Keccak based sponge for now. We could switch to Poseidon later if our kernel grows too large.
Note that we use simple zero-padding (pad0*) instead of the standard pad10* rule. It's simpler, and we don't care that the prover can add extra 0s at the end of the code. The program counter can never reach those bytes, and even if it could, they'd be 0 anyway given the EVM's zero-initialization rule.
In one CPU row, we can do a whole Keccak hash (via the CTL), absorbing 136 bytes. But we can't actually bootstrap that many bytes of kernel code in one row, because we're also limited by memory bandwidth. Currently we can write 4 bytes of the kernel to memory in one row.
So we treat the `keccak_input_limbs` columns as a buffer. We gradually fill up this buffer, 4 bytes (one `u32` word) at a time. Every `136 / 4 = 34` rows, the buffer will be full, so at that point we activate the Keccak CTL to absorb the buffer.
