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The implementation of 'round' for Python integers uses a round-to-nearest form of divmod: a, b -> q, r, where q is the nearest integer to a / b and r = a - b*q.
This form of divmod would be useful elsewhere. In particular, it's currently needed for implementing multiplication and division of timedeltas by a float: see issue 1289118 .
This patch exposes the operation to Python C code as _PyLong_Divmod_Near, and refactors long_round to use this operation.

Just a few nitpicks on the patch (in increasing pickiness):
1. Any reason to prefer PyTuple_SetItem to PyTuple_SET_ITEM at the end of _PyLong_Divmod_Near? You are filling a brand new tuple, so PyTuple_SET_ITEM seems to be more appropriate.
2. temp = (quo_is_neg ? long_add : long_sub)(..) is clever, but IMO is less readable than 
if (quo_is_neg)
 temp = long_add(..)
else
 temp = long_sub(..)
The later form may also be more optimization friendly, particularly if compiler wants to inline static long_add or long_sub.
3. Given that arguments are named 'a' and 'b' it is a bit confusing to have local variable c of a different type. I think 'cmp' would be a better choice.
4. I see that you removed a comment that displays round() implemented in python. I think it would be helpful to preserve it for documentation and testing purposes even though the actual algorithm is slightly different. As long as the results are the same, it is helpful to have reference python code.
5. Similarly to #4, having python implementation of divmod_near() displayed somewhere will be helpful.

Thanks for reviewing!
Updated patch, that addresses points 1-3. For 4, there's no need for the old code, since "self - divmod_near(self, 10**-n)[1]" is enough. And I didn't like the old algorithm anyway; the new one is more straightforward. For 5, I've added a Python version of divmod_near to the comments.

Looking at
 Py_DECREF(one);
 
 result = PyTuple_New(2);
 if (result == NULL)
 goto error;
..
 error:
 Py_XDECREF(one);
If PyTuple_New fails, wouldn't it result in one being DECREF's twice?

Ah, good point. I knew there was a reason I didn't like Py_XDECREF.
I'll fix this and then apply this patch tonight.

Committed (with the DECREF(one) fix) in r81541.