builtins: preparation for having the number types derive from the numbers ABCs

[bluetech]

This should make e.g. this work: (See comment #3108 (comment)).

from decimal import Decimal
from numbers import Real

x: Real = 1.2
x = Decimal('1.2')
if isinstance(x, Real):
    # Not dead to mypy

This PR has some preparation commits before making the change. Should be easier to review each one separately.

[bluetech]

Hmm, this causes mypy with the new semantic analyzer to crash:

RuntimeError: Internal error: unresolved placeholder type builtins.int

[srittau]

I like the first three commits. I am a bit wary of deriving the built-in number types from the ABCs, though. The real classes are not derived from the ABCs and probably use ABCMeta.register() or a similar mechanism. While I'm not totally opposed to this for practicability reasons and since this about Python's built-in numeric tower, I'd prefer to see another, more general solution, either involving protocols or some kind of typing support to registering ABCs.

[bluetech]

@srittau Thanks for taking a look, I'll remove the last commit from this PR and open an issue to discuss it.

[bluetech]

@srittau Updated. Will open the issue a bit later.

[srittau]

The last two don't seem to exist (which surprised me):

Python 3.7.3 (default, Jun  3 2019, 18:27:33) 
[GCC 6.3.0 20170516] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> x = 3.0
>>> x.__trunc__()
3
>>> x.__floor__()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'float' object has no attribute '__floor__'
>>> x.__ceil__()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'float' object has no attribute '__ceil__'

[bluetech]

Hmm, should have checked all of them.

I looked into cpython code, and what I understand is that math.floor (same for math.ceil) has a special case for floats, or rather types that can be converted to float (implement __float__()). In these cases, if __floor__ is not defined, it converts to float and does the operation directly.

import math

class X:
    def __float__(self):
        return 5.4

    #def __floor__(self):
    #    return 10

print(math.floor(X()))

Commented it prints 5, uncommented it prints 10.

So I think that, given numbers.Real already requires __float__, we can just diverge from the actual definition of numbers.Real and remove __floor__ and __ceil__ from it in typeshed. WDYT? The numbers.Real doc only requires math.floor to work.

[JelleZijlstra]

Not sure why this needs overloads.

[bluetech]

The idea is to have the same form as float above. Once this stub is filled the return types of the two overloads will be different, I think.

[JelleZijlstra]

The arguments are actually positional-only

[bluetech]

Is there some special way to encode this?

[JelleZijlstra]

Start the names with two underscores, like __modulo.

[bluetech]

I stripped the useful parts of this PR to separate PRs and opened an issue about the __ceil__/__floor__ situation.