Do we have tests for the various cases ...

It occurs to me that I don't know how a subclass of float that implements its own __float__ should behave.

>>> class MyFloat(float):
...     def __float__(self):
...         return 9.0
... 
>>> x = MyFloat(16)
>>> math.sqrt(x)
4.0
>>> float(x)
9.0

I think that it would be better to not call __float__ for float subclasses, __int__ and __index__ for int subclasses, __complex__ for complex subclasses, __str__ for str subclasses, etc. We already have a content of corresponding class and can convert it to a C value or to a new Python instance.

Thank you for your review @mdickinson, I addressed your comments and added tests. Could you please take another look?