* 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
