## Summary
The deposit cache now has the ability to finalize deposits. This will cause it to drop unneeded deposit logs and hashes in the deposit Merkle tree that are no longer required to construct deposit proofs. The cache is finalized whenever the latest finalized checkpoint has a new `Eth1Data` with all deposits imported.
This has three benefits:
1. Improves the speed of constructing Merkle proofs for deposits as we can just replay deposits since the last finalized checkpoint instead of all historical deposits when re-constructing the Merkle tree.
2. Significantly faster weak subjectivity sync as the deposit cache can be transferred to the newly syncing node in compressed form. The Merkle tree that stores `N` finalized deposits requires a maximum of `log2(N)` hashes. The newly syncing node then only needs to download deposits since the last finalized checkpoint to have a full tree.
3. Future proofing in preparation for [EIP-4444](https://eips.ethereum.org/EIPS/eip-4444) as execution nodes will no longer be required to store logs permanently so we won't always have all historical logs available to us.
## More Details
Image to illustrate how the deposit contract merkle tree evolves and finalizes along with the resulting `DepositTreeSnapshot`
## Other Considerations
I've changed the structure of the `SszDepositCache` so once you load & save your database from this version of lighthouse, you will no longer be able to load it from older versions.
Co-authored-by: ethDreamer <37123614+ethDreamer@users.noreply.github.com>
## Issue Addressed
Resolves#1100
## Proposed Changes
* Implement the `SafeArith` trait for `Slot` and `Epoch`, so that methods like `safe_add` become available.
* Tweak the `SafeArith` trait to allow a different `Rhs` type (analagous to `std::ops::Add`, etc).
* Add a `legacy-arith` feature to `types` and `state_processing` that conditionally enables implementations of
the `std` ops with saturating semantics.
* Check compilation of `types` and `state_processing` _without_ `legacy-arith` on CI,
thus guaranteeing that they only use the `SafeArith` primitives 🎉
## Additional Info
The `legacy-arith` feature gets turned on by all higher-level crates that depend on `state_processing` or `types`, thus allowing the beacon chain, networking, and other components to continue to rely on the availability of ops like `+`, `-`, `*`, etc.
**This is a consensus-breaking change**, but brings us in line with the spec, and our incompatibilities shouldn't have been reachable with any valid configuration of Eth2 parameters.
