Theo error handling for round is different for float and int. 

Python 3.5.1 (default, Apr 18 2016, 11:46:32) 
[GCC 4.2.1 Compatible Apple LLVM 7.3.0 (clang-703.0.29)] on darwin
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>>> round(1.0, None)
1
>>> round(1, None)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: 'NoneType' object cannot be interpreted as an integer

The different data types make different choices:

>>> from decimal import Decimal
>>> from fractions import Fraction
>>> (1).__round__(None)
Traceback (most recent call last):
  File "<pyshell#39>", line 1, in <module>
    (1).__round__(None)
TypeError: 'NoneType' object cannot be interpreted as an integer
>>> (1.0).__round__(None)
1
>>> Decimal(1).__round__(None)
Traceback (most recent call last):
  File "<pyshell#41>", line 1, in <module>
    Decimal(1).__round__(None)
TypeError: optional arg must be an integer
>>> Fraction(1, 1).__round__(None)
1
>>> from _pydecimal import Decimal
>>> Decimal(1).__round__(None)
1

For Fraction and _pydecimal, the behavior comes from using None as a placeholder (which is common and normal in pure python code).  For float there is explicit code to test for the None case.   For int, the None test was omitted (perhaps a mistake) and the error is raised by PyNumber_Index.

Looking through tests, only Lib/test/test_float.py tests for None being allowable.  Elsewhere, it seems to be an implementation detail.

The old Python 2 version of the round() function never let None be passed in (because it used PyArg_ParseTupleAndKeywords(args, kwds, "d|i:round").  That logic seems to get lost in the Python 3 version when __round__ was introduced.

To resolve the differences, I think the round() function should explicitly check for None and replace it with zero before calling the underling __round__ functions where we would allow variable according the needs of the implementation.

> I think the round() function should explicitly check for None and replace it with zero

That would be a change in behaviour: `round(x)` is not the same as `round(x, 0)`. For most types, `round(x)` returns an `int`, while `round(x, 0)` returns something of the same type as `x`. Instead, I think we should add the check for `None` to `int`s `__round__` implementation.

>>> round(1.3, 0)
1.0
>>> round(1.3)
1
>>> round(1.3, None)
1

Ah, sorry; now that I've looked at the patch, I see I misunderstood. You're not replacing None with zero; you're replacing it with NULL.

Patch LGTM.

The test could be strengthened to add a check that the types of `round(x)` and `round(x, None)` match.

For the record, the float behaviour was changed (for Python 3.5) in http://bugs.python.org/issue19933. There didn't seem to be any particularly strong motivation for that change, but it's done now.

New changeset c3c4d8e4ca1a by Raymond Hettinger in branch '3.5':
Issue 27936: Fix inconsistent round() behavior between float and int
https://hg.python.org/cpython/rev/c3c4d8e4ca1a

New changeset 7108f2a708c9 by Raymond Hettinger in branch '3.5':
Issue 27936: Update doc for round() to indicate that None is an allowable argument.
https://hg.python.org/cpython/rev/7108f2a708c9