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Make random module PEP-384 compatible

I'm curious what this does for us. _randommodule.c isn't public. Internally, we get to use our full ABI, not just the stable public ABI.
I'm unclear on why this needs to change at all. Is code like this deemed broken in some way?

I have the same questions. The new code looks more complex and cumbersome. What is the benefit of all these changes?
I see you have created many similar issues. Would be nice to discuss first on the Python-Dev list what they do and why they are needed.

There's several different reasons why these changes are beneficial. It'll help make the modules more compatible with PEP 554 in the future, enable more code re-use across Python VMs, reduce code maintenance going forward, and may also help with performance oriented changes in the future. 
On the PEP 554 front it is necessary to remove the static state that is used in the modules as we can't have sharing across the interpreters. The modules that are loaded into the different interpreter will need to not share any state on so all of their state needs to be per-instance state (there's also just an argument that static global state is just kind of ugly).
On the re-use across VMs front it'll mean that alternative VMs will only need to stick to the stable API and well be able to use these modules as-is without having to re-implement them. It may not even be strictly necessary that these modules stick to 100% of the stable API if the places where they go outside dramatically help the implementation (for example PR 15805 uses _PyBytesWriter still). 
Sticking to the stable API will also naturally make it somewhat easier to make changes that impact the non-stable API. By it's very nature the stable API is going to change less (theoretically never) and therefore these modules will be less impacted by updates which are attempting to improve performance on the core. One example of that is the recent vector call support where many of the types needed to be updated (although trivially). 
So the final, and probably most speculative area, is the possibility of unlocking performance in the core runtime per Victor's stable API work: https://pythoncapi.readthedocs.io/. By having less dependencies on the core implementation details it should be easier to evolve those going forward an making it easier to unlock future performance gains in the core.

New changeset 04f0bbfbedf8d2bb69b012f853de6648b1a9f27f by T. Wouters (Dino Viehland) in branch 'master':
bpo-38075: Port _randommodule.c to PEP-384 (GH-15798)
https://github.com/python/cpython/commit/04f0bbfbedf8d2bb69b012f853de6648b1a9f27f

> bpo-38075: Port _randommodule.c to PEP-384 (GH-15798)
It seems like this change introduced a reference leak: bpo-38176.

commit 09dc2c672f937cbe53300cb680fca1f9c78ff976
Author: Dino Viehland <dinoviehland@gmail.com>
Date: Sun Sep 15 15:51:44 2019 +0100
 Fix missing dec ref (#16158)
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index 8b0a0244bf..1ea2bf28ab 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -572,6 +572,7 @@ static int
 _random_clear(PyObject *module)
 {
 Py_CLEAR(_randomstate(module)->Random_Type);
+ Py_CLEAR(_randomstate(module)->Long___abs__);
 return 0;
 }

Commit 04f0bbfbedf8d2bb69b012f853de6648b1a9f27f introduced a regression: bpo-39918.
I proposed PR 18897 to fix it.

New changeset 00d7cd8ab8db2c1e1f591ade828f88a1a973d70f by Victor Stinner in branch 'master':
bpo-38075: Fix random_seed(): use PyObject_CallOneArg() (GH-18897)
https://github.com/python/cpython/commit/00d7cd8ab8db2c1e1f591ade828f88a1a973d70f