* 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
* Tree of scopes
This is an extension of the context concept.
Earlier I was planning to store a simple stack of contexts, but I ended up storing the whole history, in a tree structure. This gives us more control over the output, i.e. we can print the gate count of a parent scope before those of its child scopes, which seems more user-friendly.
Sample gate count output:
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] 27829 gates to root
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | 2373 gates to evaluate the vanishing polynomial at our challenge point, zeta.
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | | 1284 gates to evaluate gate constraints
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | 25312 gates to verify FRI proof
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | | 650 gates to verify 0'th FRI query
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | | | 96 gates to check FRI initial proof
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | | | 65 gates to compute x from its index
[2021-07-19T18:09:24Z INFO plonky2::circuit_builder] | | | 233 gates to combine initial oracles
...
Sample copy constraint failure:
Error: Copy constraint 'root > verify FRI proof > verify 0'th FRI query > check FRI initial proof > verify 0'th initial Merkle proof > check Merkle root: 0-th hash element' between wire 12 of gate #2550 [...] and wire 0 of gate #0 [...] is not satisfied. Got values of 6861386743364621393 and 0 respectively.
* No min
* info -> debug
* Move to its own file
Using `serde_cbor` for now. It's probably far from optimal, as we have many `Vec`s which I assume it will prefix with their lengths, but it's a nice and easy method for now.
* 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
