Reorder the text such that every function is discussed only once

Reorder the text such that every function is discussed only once
instead of discussing some of them at two different places.
Also follow a more logical order: initialization first, then reading
and writing, then retrieving the digest and reinitialization.
Leave context handling and chain duplication at the end because
both are rarely needed.

While here, also tweak the wording of the shuffled text
and add some precision in a few places.