Git chokes on large file

I've discovered a problem using Git. It's not clear to me what the "correct" behavior should be, but it seems to me that Git is failing in an undesirable way.

The problem arises when trying to handle a very large file. For example:

    $ git --version
    git version 1.8.3.1
    $ mkdir $$
    $ cd $$
    $ git init
    Initialized empty Git repository in /common/not-replicated/worley/temp/5627/.git/
    $ truncate --size=20G big_file
    $ ls -l
    total 0
    -rw-rw-r--. 1 worley worley 21474836480 May 27 11:59 big_file
    $ time git add big_file

    real	4m48.752s
    user	4m31.295s
    sys	0m16.747s
    $

At this point, either 'git fsck' or 'git commit' fails:

    $ git fsck --full --strict
    notice: HEAD points to an unborn branch (master)
    Checking object directories: 100% (256/256), done.
    fatal: Out of memory, malloc failed (tried to allocate 21474836481 bytes)

    $ git commit -m Test.
    [master (root-commit) 3df3655] Test.
    fatal: Out of memory, malloc failed (tried to allocate 21474836481 bytes)

The central problem is that one can accidentally add a file that leaves the repository in a "broken" state, where various normal commands simply don't work. The most worrying aspect is that "git fsck" fails -- of all the commands, the one that verifies the validity of the repository (and diagnoses errors) should be the most robust!

Even doing a 'git reset' does not put the repository in a state where 'git fsck' will complete:

    $ git reset
    $ git fsck --full --strict
    notice: HEAD points to an unborn branch (master)
    Checking object directories: 100% (256/256), done.
    fatal: Out of memory, malloc failed (tried to allocate 21474836481 bytes)

Dale