logging within shell scripts

["Gregory T. Norris" <haphazard@socket.net>]

This isn't really a Debian issue as such, but I thought that someone
here might be able to point me in the right direction... Hope I'm not
too far off base here :-)

I've got a shell script that I want to have log it's actions on a
selective basis (dependent upon run-time settings).  I know it could
re-exec itself with appropriate redirection, but I don't want to rely on
commandline parameters or environment settings which might inadvertently
be set.  Is there any way for a shell script to determine where it's
stdout/stderr is going, and to redirect it "from this point on"?
Preferably something which works with a generic /bin/sh, rather than
specific to bash, but I'll work with whatever I can get...

Thanx!