I'm OK with -1, but I don't get that or -0.0 on 32-bit Windows Py 3.4.1:

Python 3.4.1 (v3.4.1:c0e311e010fc, May 18 2014, 10:38:22) [MSC v.1600 32 bit (Intel)] on win32
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>>> -0.5 // float('inf')
nan

So maybe NaN is the best answer ;-)

In favor of -1.0:  that _is_ the limit of the mathematical floor(-0.5 / x) as x approaches +infinity.

In favor of -0.0:  it "should be" mathematically that floor_division(x/y) = floor(x / y), and floor(-0.5 / inf) = floor(-0.0) = ... well, not -0.0!  floor() in Py3 is defined to return an integer, and there is no -0 integer:


>>> floor(-0.0)
0

That's +0.  So I see no justification at all for -0.0 in Py3.  -1 seems the best that can be done.  The NaN I actually get doesn't make sense.