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At present, the built-in constants Ellipsis (...) and NotImplemented cannot be pickled. Perhaps there is a good reason for this, but the only discussion I can find is at msg<108957>, where it is stated that these values (along with their types, and type(None)) cannot be pickled.
I ran across this in a class that keeps track of numpy-style slicing operations, and so sometimes stores references to Ellipsis. While this is easy to work around, it does seem a little surprising that ... cannot be pickled, when slice objects can be. I don't know if there is a likely use for pickling NotImplemented.
If this is not changed, perhaps it could be explicitly stated in the documentation that these objects cannot be pickled?

I think it's a reasonable feature request. Now someone has to write a patch for it.

We will need to bump the protocol number to add support for None, Ellipsis, and NotImplemented. Antoine, can you add this to PEP 3154?

> We will need to bump the protocol number to add support for None,
> Ellipsis, and NotImplemented. Antoine, can you add this to PEP 3154?
I don't think this needs a protocol bump. These are global singletons,
they can be pickled as such, and they will be unpickleable on any
Python.

I've submitted a patch that just uses save_global to pickle Ellipsis and NotImplemented, so the resulting pickle should be unpicklable anywhere. I'm completely new to the C API so not sure if the way I am building python strings (to pass to save_global) is correct, but it seems to work.

I haven't taken a look at the patch in detail, but it lacks some tests.
Pickling tests are generally in Lib/test/pickletester.py, they are invoked by test_pickle and test_pickletools.

> I'm completely new to the C API so not sure if the way I am building
> python strings (to pass to save_global) is correct
It's correct but it's probably less efficient than calling a more specialized function, such as PyUnicode_FromString():
http://docs.python.org/dev/c-api/unicode.html#PyUnicode_FromString
You also have to check the return value (for non-NULL, NULL meaning an error occurred) before calling save_global with it.

There is indeed a 5% performance gain from using PyUnicode_FromString instead of the generic Py_BuildValue function.

New changeset 5832d3622473 by Łukasz Langa in branch 'default':
Fixes #13842: cannot pickle Ellipsis or NotImplemented.
http://hg.python.org/cpython/rev/5832d3622473 

New changeset 5353357382e2 by Łukasz Langa in branch 'default':
#13842: check whether PyUnicode_FromString succeeded
http://hg.python.org/cpython/rev/5353357382e2