* Working "faster" inverse algo, using u128s.
* Faster inverse_2exp for large exp.
* More inverse tests.
* Make f, g u64.
* Comments.
* Unroll first two iterations.
* Fix bug and re-unroll first two iterations.
* Simplify loop.
* Refactoring and documentation.
* Clean up testing.
* Move inverse code to inversion.rs; use in GoldilocksField.
* Bench quartic Goldilocks extension too.
* cargo fmt
* Add more documentation.
* Address Jakub's comments.
For examlpe, if I change a test to use `ConstantArityBits(4, 5)`, I get
To efficiently perform FRI checks with an arity of 16, at least 152 wires are needed. Consider reducing arity.
* Refactor recursion tests
E.g. the main part of `test_recursive_recursive_verifier` is now
```rust
let (proof, vd, cd) = dummy_proof::<F, D>(&config, 8_000)?;
let (proof, vd, cd) = recursive_proof(proof, vd, cd, &config, &config, false)?;
let (proof, _vd, cd) = recursive_proof(proof, vd, cd, &config, &config, true)?;
```
Also adds a new `test_size_optimized_recursion` to see how small we can make the final proof in a recursion chain. The final proof is ~74kb (depending on compression luck) and takes ~20s to prove on my M1 (depending on PoW luck).
* Refactor serialization
* Don't log timestamps
* Automatically select FRI reduction arities
This way when a proof's degree changes, we won't need to manually update the `FriConfig`s of any recursive proofs on top of it.
For now I've added two methods of selecting arities. The first, `ConstantArityBits`, just applies a fixed reduciton arity until the degree has shrunk below a certain threshold. The second, `MinSize`, searches for the sequence of arities that minimizes proof size.
Note that this optimization is approximate -- e.g. it doesn't account for the effect of compression, and doesn't count some minor contributions to proof size, like the Merkle roots from the commit phase. It also assumes we're not using Merkle caps in serialized proofs, and that we're inferring one of the evaluations, even though we haven't made those changes yet.
I think we should generally use `ConstantArityBits` for proofs that we will recurse on, since using a single arity tends to be more recursion-friendly. We could use `MinSize` for generating final bridge proofs, since we won't do further recursion on top of those.
* Fix tests
* Feedback
