Add static analysis to find bugs earlier

There are a number of options for finding issues via static analysis, whether via self-run tooling or via SaaS, e.g.,

Specific tools

Collections, lists, reviews, etc.

I think we should start with enabling Coverity Scan and integrating Clang analyzers (since we're going to use Clang for building our code anyway).

Adding CppCheck and FlawFinders are also a good idea, but if they don't support C++11 (or C++14, if/when we upgrade this repo's minimum C++ requirements), that might become an issue.