* Refactor GMiMC code
Adds a sub-trait of `Field` called `GMiMCInterface`, which is similar to `PoseidonInterface`.
This lets us have different fields with different GMiMC constants in a type-safe way.
* Remove `Interface`
* Const generic for width
* Move some Field members to a Field64 subtrait
I.e. move anything specific to 64-bit fields.
Also, relatedly,
- Tweak a bunch of prover code to require `Field64`, since 64-bit stuff is used in a couple places, like the FRI proof-of-work
- Remove `bits()`, which was unused and assumed a 64-bit field
- Rename a couple methods to reflect that they're u64 variants
There are no functional changes.
* Field64 -> PrimeField
* Remove `exp_u32`, `kth_root_u32`
* PrimeField: PrimeField
* Move `to_canonical_biguint` as well
* Add back from_noncanonical_u128
Mainly storing pending generators in a Vec rather than a HashMap. Requires an extra check to make sure we don't run one twice after adding it to the Vec twice.
No functional changes here. The biggest change was moving certain files into new directories like `plonk` and `iop` (for things like `Challenger` that could be used in STARKs or other IOPs). I also split a few files, renames, etc, but again nothing functional, so I don't think a careful review is necessary (just a sanity check).
* Have add_gate take a generic type instead of GateRef
There are a couple advantages
- Users writing their own gates won't need to know about the `GateRef` wrapper; it's more of an internal thing now.
- Easier access to gate methods requiring `self` -- for example, `split_le_base` can just call `gate_type.limbs()` now.
* Update comment
* Always insert
With this approach, we don't need `Target::PublicInput`; any routable `Target` can be marked as a public input via `register_public_input`. The circuit itself hashes these targets, and routes the hash output to the first four wires of a `PublicInputGate`, which is placed at an arbitrary location in the circuit.
All gates have direct access to the purported hash of public inputs. We could think of them as accessing `PI_hash_i(x)` (as in Plonk), but these are now (four) constant functions, so they effectively have direct access to the hash itself.
`PublicInputGate` checks that its first four wires match this purported public input hash. The other gates ignore the hash.
Resolves#64.
* Draw challenge points from the extension field
* Now building
* Misc
* Default eval_unfiltered_base
* fmt
* A few field settings
* Add to Sage
* Display tweak
* eval_filtered_base
* Quartic in bench
* Missing methods
* Fix tests
* PR feedback
