Cython returns 0 for expression that should evaluate to 0.5?

It's because it's using C ints rather than Python integers so it matches C behaviour rather than Python behaviour. I'm relatively sure this used to be documented as a limitation somewhere but I can't find it now. If you want to report it as a bug then go to https://github.com/cython/cython/issues, but I suspect this is a deliberate trade-off of speed for compatibility.

The code gets translated to

__Pyx_pow_long(2, -1L)

where __Pyx_pow_long is a function of type static CYTHON_INLINE long __Pyx_pow_long(long b, long e).

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The easiest way to fix it is to change one/both of the numbers to be a floating point number

 print(2. ** (-1))

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As a general comment on the design choice: people from the C world generally expect int operator int to return an int, and this option will be fastest. Python had tried to do this in the past with the Python 2 division behaviour (but inconsistently - power always returned a floating point number).

Cython generally tries to follow Python behaviour. However, a lot of people are using it for speed so they also try to fall back to quick, C-like operations especially when people specify types (since those people want speed). I think what's happened here is that it's been able to infer the types automatically, and so defaulted to C behaviour. I suspect ideally it should distinguish between specified types and types that it's inferred. However, it's also probably too late to start changing that.

It looks like Cython is incorrectly inferring the final data type as int rather than float when only numbers are involved

The following code works as expected:

print(2.0 ** (-1))

See this link for a related discussion: https://groups.google.com/forum/#!topic/cython-users/goVpote2ScY