The numbers.Real ABC requires the __ceil__ and __floor__ methods (https://github.com/python/cpython/blob/v3.8.0/Lib/numbers.py#L178-L186), however, the float type does not have them.

In regular Python, this is not a problem, because math.ceil() and math.floor() special-case float and work on it directly, and numbers.Real is implemented on float by explicitly registering it (so it's not checked that all required methods are implemented).

Where it becomes a (minor) problem is in typeshed, where the type checker *does* check that all abstract methods are implemented. So, because float is missing these two, typeshed cannot have float implement numbers.Real.

Refs: https://github.com/python/typeshed/issues/3195

Ran, do you want to work on this or can i take it?

You can take it - thanks!

If float.__ceil__ is only needed for typeshed, maybe add a special case for typeshed?

I have doubts about adding a C code which is never even executed.

> I have doubts about adding a C code which is never even executed.

My reading of the PR is that it *would* be executed: the math module first looks for the __floor__ special method, then falls back to using the libm floor if that doesn't exist. Am I missing something?

Oh, you are right. I misunderstood the original issue and thought that the code first checks PyFloat_Check() or PyFloat_CheckExact().

If float.__ceil__ will be executed it will add significant overhead for creating and executing the method object.

> If float.__ceil__ will be executed it will add significant overhead for creating and executing the method object.

Yes, I'd definitely like to see timings; I think Victor already asked for those on the PR.

$ ./python -m pyperf timeit -s "from math import floor" --duplicate 100 "floor(12345.6)"
Before:  Mean +- std dev: 52.5 ns +- 2.6 ns
After:  Mean +- std dev: 71.0 ns +- 1.7 ns

$ ./python -m pyperf timeit -s "from math import ceil" --duplicate 100 "ceil(12345.6)"
Before:  Mean +- std dev: 51.2 ns +- 1.5 ns
After:  Mean +- std dev: 74.4 ns +- 2.2 ns

However, this is an instance of a general problem: whenever we want to strongly type (via dunders) protocols that specialcase builtin types, we will have to choose between three options:

* special case them also in typing engine, complicating the typing engine
* implement dummy dunders, puzzling readers of the code
* implement dunders that do the right thing but never actually execute, puzzling Serhiy (and probably others)
* implement dunders that are actually called (un-specialcasing builtin types), slowing down the common path

Do we have a preference for a "default" position when we encounter such problems in the future? Of course, we can override it on a case-by-case basis in the presence of good arguments, but still, a default would be nice to have.

I don't know much about static typing (which is why I loved Python until this typing craze happened:), but it seems to me that we might have another option: we can currently say that a type might be a virtual subclass of an abstract class in more than one way, right? For example, we still support old-style iterators (via __getitem__ and IndexError), IIRC. So, can we say that a type can implement numbers.Real also in two ways: by having some dunders, or by being (a literal or a subtype of) float?

New changeset cb8b946ac10386e6cab1376945f64f683b5b16d3 by Victor Stinner (Batuhan Taşkaya) in branch 'master':
bpo-38629: implement __floor__ and __ceil__ for float type (GH-16985)
https://github.com/python/cpython/commit/cb8b946ac10386e6cab1376945f64f683b5b16d3

Thanks Batuhan Taşkaya for the implementation, and thanks Ran Benita for the feature request :-)