git hooks and environment variables

I've noticed that not all hooks have all of the environment variables
set when they are run, and it is not clear from the manual pages which
hooks have which variables set on the command line. Specifically, they
don't all have GIT_DIR set, I haven't taken the time to verify exactly
which variables are set and which are not yet, but..

Which would be preferred? documentation of the current behaviors, or a
fixup that ensures that all the relevant variables get set?

I intend to have complete details as to which hooks get one settings,
but I had this at work and don't have it here, so I can update this
thread with the information later.

Regards,
Jake