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__'

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.

Not sure why this needs overloads.

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.

The arguments are actually positional-only

Is there some special way to encode this?

Start the names with two underscores, like __modulo.