The assignments here were performing an implicit truncation from int to
s16. Make it explicit that this is desired behavior.

The current code inserts and deletes elements from the beginning of the audio buffer, which is very inefficient in an std::vector.

Profiling was done using VisualStudio2017's Performance Analyzer in Super Mario 3D Land.

Before this change: AudioInterp::Linear had 14.14% of the runtime (inclusive) and most of that time was spent in std::vector's insert implementation.
After this change: AudioInterp::Linear has 0.36% of the runtime (inclusive)

This makes clang-format useful on those.

Also add a bunch of forgotten transitive includes, which otherwise
prevented compilation.

Closes #2049.

Signed-off-by: MerryMage <MerryMage@users.noreply.github.com>