Check for changes to the public API

We would like to get to a stage where we can commit to the public API.
To help us achieve this add a script that generates the public API and
checks it against three committed files, one for each feature set: no
features, alloc, std.

The idea is that with this applied any PR that changes the public API
should include a final patch that is just the changes to the api/*.txt
files, that way reviewers can discuss the changes without even needing
to look at the code, quickly giving concept ACK/NACKs. We also run the
script in CI to make sure we have not accidentally changed the public
API so that we can be confident that don't break semver during releases.
The script can also be used to diff between two release versions to get
a complete list of API changes, useful for writing release notes and for
users upgrading.

There is a development burden involved if we apply this patch.