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When C code needs to compare Python object with int 0 or add int 1 it either use local reference to PyLong_FromLong(0) and PyLong_FromLong(1) which should be decrefed just after use or module level global variable initialized and cleared during initializing and finalizing the module.
Proposed patch adds global variables _PyLong_Zero and _PyLong_One for references to integer objects 0 and 1. This simplifies the code since no need to initialize local variables, check for error the result of PyLong_FromLong() and decref it after use. The patch decreases the total code size by 244 lines.
That variables are only for internal use. User code should use PyLong_FromLong(0) and PyLong_FromLong(1).

I like it.

+1. Please create a PR for it.

+1 for this idea. 
Also consider adding new function PyLong_Increment. This basic operation is small pain using the current API. It may also give a small speed benefit.

Other common values used in C functions: empty byte string, empty Unicode string, empty tuple. The problem is to make sure that singletons are created in the right order :-/
This issue reminded me an old idea of writing a generalization of the _Py_IDENTIFIER() API. I created an issue #29881: Add a new private API for "static C variables" (_PyStaticVar) to clear them at exit. To be clear: it's related but different to this issue, the two issues are exclusive.

Yet one idea that can make the code simpler is make PyLong_FromLong(0) and PyLong_FromLong(1) never failing. I.e. require NSMALLPOSINTS not less than 2.
> Also consider adding new function PyLong_Increment. This basic operation is small pain using the current API. It may also give a small speed benefit.
Smaller pain with using _PyLong_One and Py_SETREF().
 Py_SETREF(long_obj, PyNumber_Add(long_obj, _PyLong_One));
Agree that with _PyLong_Increment() it can look better and be faster. But I don't know whether incrementing by 1 is enough popular operation. I have counted 5 cases in the stdlib (not counting tests): for enumerate, range and Counter.
> The problem is to make sure that singletons are created in the right order :-/
Yes, I spent much time for making empty Unicode string singleton always be initialized. It can be accessed at very early stage.

New changeset ba85d69a3e3610bdd05f0dd372cf4ebca178c7fb by Serhiy Storchaka in branch 'master':
bpo-29878: Add global instances of int for 0 and 1. (#852)
https://github.com/python/cpython/commit/ba85d69a3e3610bdd05f0dd372cf4ebca178c7fb

New changeset bae6881b4215b2613ad08ef0dc7bed7743c2b8cc by Serhiy Storchaka in branch 'master':
Update Argument Clinic generated code for bpo-29878. (#1001)
https://github.com/python/cpython/commit/bae6881b4215b2613ad08ef0dc7bed7743c2b8cc