Random.seed() resets self.gauss_next attribute to None. Maybe BaseRandom.seed() should do it, since the attribute comes from BaseRandom not from Random. By the way, SystemRandom.seed() doesn't reset self.gauss_next to None: the method does nothing, as documented.

I'm not sure if BaseRandom.__init__subclass__() works as expected: it uses random() if it's implemented, but BaseRandom now implements random() from getrandbits().

cc @pitrou

I'm not sure if BaseRandom.init__subclass() works as expected: it uses random() if it's implemented, but BaseRandom now implements random() from getrandbits().

Ah, I checked: it works as expected :-) But it would be worth it to add tests on class inheritance, to check which method is called ;-)

TODO:

• Decide if BaseRandom seed(), getstate() and setstate() should handle gauss_next, or if each subclass is supposed to deal with it.
• Add unit tests.
• Maybe add an example in the documentation which implements seed(), getstate() and setstate().

Example of subclass (it doesn't handle gauss_next):

class LCG(random.Random):
    def _rand_uint32(self):
        # Numerical Recipes LCG: generate 32 bits of entropy
        self._lcg = (self._lcg * 1664525 + 1013904223) % (2 ** 32)
        return self._lcg

    def seed(self, a=None):
        if a is not None:
            a = int(a & (2 ** 32 - 1))
        else:
            a = random.randint(0, 2 ** 32 - 1)
        self._lcg = a

    def getstate(self):
        return self._lcg

    def setstate(self, state):
        self._lcg = state

    def getrandbits(self, n):
        nword = n // 32
        ignore = n % 32
        if ignore:
            nword += 1
            ignore = 32 - ignore

        x = self._rand_uint32()
        for _ in range(nword - 1):
            x <<= 32
            x += self._rand_uint32()
        x >>= ignore
        return x

Decide if BaseRandom seed(), getstate() and setstate() should handle gauss_next, or if each subclass is supposed to deal with it.

Oh, in fact gauss_next only looks like an optimization. I moved it from BaseRandom to Random. BaseRandom.gauss() is now thread state. Random getstate() and setstate() don't have to bother with an attribute which came from its parent class.

I rebased my PR and squashed commits to be able to edit the commit message.

New changes:

• Add tests on BaseRandom subclasses
• Remove BaseRandom.__init__() method: BaseRandom() no longer calls seed(). It's up to the subclass to decide what to do in the constructor.
• Documentation completed.

@serhiy-storchaka, @tim-one: Ok, the PR is now ready for a review. Sorry, earlier versions of the PR were not complete. It was more complex than expected to implement this new base class.

I abandon my this PR and my PR #19700 since there is no clear consensus on these changes: see https://bugs.python.org/issue40346

I wrote PR #19797 instead: "Remove C implementation of Random.randbytes()".