verkle: remove allocations for storage slot tree calculation

[jsign]

This PR eliminates the usage of big.Int when calculating the tree-hash for a storage slot.
It does some careful calculations using u256.Int to avoid any potential overflow.

[jsign]

I was quite explicit in the comments, but adding a note here.

The TL;DR for this case is that we need to do (MAIN_STORAGE_OFFSET + storage_key)/VERKLE_NODE_WIDTH
The detail is that we avoid doing MAIN_STORAGE_OFFSET + storage_key, since that would overflow in a uint256; so we do it in parts.

First we do storage_key/VERKLE_NODE_WIDTH, and then we add mainStorageOffsetLshVerkleNodeWidth which is a constant literally MAIN_STORAGE_OFFSET/VERKLE_NODE_WIDTH.

Note doing this in part is correct since MAIN_STORAGE_OFFSET is a multiple of VERKLE_NODE_WIDTH, we we aren't "loosing precision" in the VERKLE_NODE_WIDTH lower bits having "carries".

This is similar to doing something like: (100 + 12) / 10 which should be 11. In this case it's correct doing 100/10+12/10 since also yields 11.

But note that if we had to do something like (109+12)/10 it yields 12. But if we try doing 109/10+12/10 that is incorrect since it yields 11!

[gballet]

Looks like this PR no longer applies as this function no longer exists after merging the new access witness.

[gballet]

That function no longer exists after the shapella rebase/your new access witness, would it make sense to try to adapt GetTreeKeyWithEvaluatedAddess with this technique?

[jsign]

Uhm, not sure I follow. GetTreeKeyStorageSlotTreeIndexes is used by GetTreeKeyStorageSlotWithEvaluatedAddress (L272 in this file; prev function); and this last function is used every time we need to get the key for a storage slot in the trie.

And that is called in:

• In our VKT overlay tree migration logic
• (*VerkleTrie) methods GetStorage(...), UpdateStorage(...) and DeleteStorage.

Also note that this is targeting a branch that this already rebased on top of the (merged) new access witness.

[gballet]

that was a rebase error, I tried and it works, showing some slight speed improvement (and less allocations)