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The int constructor can return an instance of int subclass.
>>> class BadTrunc:
... def __trunc__(self):
... return True
... 
>>> int(BadTrunc())
True
When __int__ returns non-exact int, at least a warning is emitted:
>>> class BadInt:
... def __int__(self):
... return True
... 
>>> int(BadInt())
__main__:1: DeprecationWarning: __int__ returned non-int (type bool). The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.
True
The constructor of int subclass always return an instance of correct type:
>>> class IntSubclass(int):
... pass
... 
>>> type(IntSubclass(BadTrunc()))
<class '__main__.IntSubclass'>
>>> type(IntSubclass(BadInt()))
__main__:1: DeprecationWarning: __int__ returned non-int (type bool). The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.
<class '__main__.IntSubclass'>
I don't know if it is worth to deprecate __trunc__ returning non-exact int, since this special method is used in math.trunc(). But I think that the int constructor should convert its result to exact int. If some preparatory period is needed, it can first start to emit FutureWarning.

> But I think that the int constructor should convert its result to exact int.
Agreed. See also issue 17576 and previous discussions on python-dev (thread started in March, but most of the messages in April):
- https://mail.python.org/pipermail/python-dev/2013-March/125022.html
- https://mail.python.org/pipermail/python-dev/2013-April/125042.html
I don't have strong feelings about `__trunc__` (or `__floor__` and `__ceil__`); it seems fine to me for those to be returning something other than a strict int.

Proposed patch makes int() always returning exact int.

Could you please make a review Mark?

> Could you please make a review Mark?
Sorry, Serhiy. I missed this. I've got some time off coming up, so I plan to look at this in the next few days.

The patch LGTM. I'm still in two minds about whether `__trunc__` should be required to return a strict `int`, but for now it's probably better to go with the status quo.

New changeset 81f229262921 by Serhiy Storchaka in branch 'default':
Issue #26984: int() now always returns an instance of exact int.
https://hg.python.org/cpython/rev/81f229262921