If e.g. the root tree is invalidated, we still want to write out
its children, since those may still have valid cache entries.

Keeping the cache around after read-tree is only one part of the
optimisation opportunities. In order to share the cache between program
instances, we need to write the TREE extension to the index.

Do so, taking the opportunity to rename 'entries' to 'entry_count' to
match the name given in the format description. The included test is
rather trivial, but works as a sanity check.

This wasn't used. We invalidate based on the full path, so we always go
down the tree, never up.

When reading from a tree, we know what every tree is going to look like,
so we can fill in the tree cache completely, making use of the index for
modification of trees a lot quicker.

This simplifies freeing the entries quite a bit; though there aren't
that many failure paths right now, introducing filling the cache from a
tree will introduce more. This makes sure not to leak memory on errors.

While I was looking at the conflict cleanup code, I looked over at
the tree cache code, since we clear the tree cache for each entry
that gets removed and there is some redundancy there.  I made some
small tweaks to avoid extra calls to strchr and strlen in a few
circumstances.