compile and the current directory

[Kai Grossjohann]

I have a project which contains a Makefile at its root directory.
Running make for me means to change to that directory before running
make.

(Actually, I'm running another command, not make.)

The problem with "just" running make from the current directory is
that it is a different directory depending on the file I'm editing.

Has somebody made something that would allow me to just invoke M-x
compile RET from any directory and that makes sure that the command is
invoked from the right directory, and that Emacs knows about it?

(I could specify "make -C $HOME/work/foo" as the command if I was
using make.)

Kai