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See bpo-29708 meta issue and https://reproducible-builds.org/ for reproducible builds.
pyc files are not fully reproducible yet: frozenset items are not serialized in a deterministic order
One solution would be to modify marshal to sort frozenset items before serializing them. The issue is how to handle items which cannot be compared. Example:
>>> l=[float("nan"), b'bytes', 'unicode']
>>> l.sort()
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: '<' not supported between instances of 'bytes' and 'float'
One workaround for types which cannot be compared is to use the type name in the key used to compare items:
>>> l.sort(key=lambda x: (type(x).__name__, x))
>>> l
[b'bytes', nan, 'unicode']
Note: comparison between bytes and str raises a BytesWarning exception when using python3 -bb.
Second problem: how to handle exceptions when comparison raises an error anyway?
Another solution would be to use the PYTHONHASHSEED environment variable. For example, if SOURCE_DATE_EPOCH is set, PYTHONHASHSEED would be set to 0. This option is not my favorite because it disables a security fix against denial of service on dict and set:
https://python-security.readthedocs.io/vuln/hash-dos.html
--
Previous discussions on reproducible frozenset:
* https://mail.python.org/pipermail/python-dev/2018-July/154604.html
* https://bugs.python.org/issue34093#msg321523
See also bpo-34093: "Reproducible pyc: FLAG_REF is not stable" and PEP 552 "Deterministic pycs".

issue34722 also talks about frozenset, nondeterministic order and sorting. Maybe this ticket and that one are for the same issue?

Normal sets have the same issue, see bpo-43850.
Would it be reasonable to make it so that sets are always created with the definition order? Looking at the set implementation, this seems perfectly possible.

> Would it be reasonable to make it so that sets are 
> always created with the definition order?
No, it would not. We would also have to maintain order across set operations such as intersection which which would become dramatically more expensive if they had to maintain order. For example intersecting a million element set with a ten element set always takes ten steps regardless of the order of arguments, but to maintain order of the left hand operand could take a hundred times more work.

> No, it would not. We would also have to maintain order across set operations such as intersection which which would become dramatically more expensive if they had to maintain order. For example intersecting a million element set with a ten element set always takes ten steps regardless of the order of arguments, but to maintain order of the left hand operand could take a hundred times more work.
Can these operations happen during bytecode generation? I am fairly new to these internals so my understanding is not great. During bytecode generation is can code that performs such operations run?

s/hundred/hundred thousand/

s/is can/can/

Another idea, would it be possible to add a flag to turn on reproducibility, sacrificing performance? This flag could be set when generating bytecode, where the performance hit shouldn't be that relevant.

> Another idea, would it be possible to add a flag to turn on reproducibility, sacrificing performance?
The flag is the SOURCE_DATE_EPOCH env var, no?

I would not expect SOURCE_DATE_EPOCH to sacrifice performance. During packaging, SOURCE_DATE_EPOCH is always set, and sometimes we need to perform expensive operations. We only need this behavior during cache generation, making the solution not optimal.
Backtracking a bit to your proposal for sorting the elements. Is it possible to have two different types with the same name? We need a unique identifier for each type.
After that, we need the type to allow sorting/comparing items, which AFAIK is not something we can guarantee.
We could certainly do the sorting where we are able to, and bail out if impossible, which I feel should handle the majority of cases. This is not optimal, but reasonable.
Is there any way we could something like resetting the hash seed during cache generation?

Possible solution: add an ordered subtype of frozenset which would keep an array of items in the original order. The compiler only creates frozenset when optimizes "x in {1, 2}" or "for x in {1, 2}". It should now create an ordered frozenset from a list of constants (removing possible duplicates). The marshal module should save items in that order and restore ordered frozensets when load data. It should not increase memory consumption too much, because frozenset constants in code are rare and small.

What about normal sets? They also suffer from the same issue.

> What about normal sets?
pyc files don't contain a regular set. So it is out of scope of this issue.

Ah, my bad! Though, thinking about it, it does make sense. If that's the case, then the argument Raymond provided against preserving order does not seem that relevant, as we would only need to preserve the order in the creation operation. What do you think? Is there anything I may be missing here? :)

> If that's the case, then the argument Raymond provided against preserving order does not seem that relevant, as we would only need to preserve the order in the creation operation.
Note that PYC files are marshalled from code objects including frozenset instance, not from AST.
When marshaling, frozenset instance is created already and its creation order is lost .

I understand, the proposal would be to make frozensets keep the creation order.

> I understand, the proposal would be to make frozensets keep the creation order.
That would increase the memory consumption of all frozen set instances, which is likely not going to fly

The only way I can see here is to go with a similar strategy as Serhiy proposes, which seems that it has a non trivial complication (and a new type, which I am not very fond of) but is a bit cleaner than changing the semantics of the type, which affects much more than the storage.

Could this issue be fixed in marshal itself? Off the top of my head, one possible option could be to use the marshalled bytes of each elements as a sort key, rather than the elements themselves. So serialize, *then* sort?

No, it cannot be fixed in marshal itself.
s = {("string", 1), ("string", 2), ("string", 3)}
All tuples contain references to the same string. The first serialized tuple will contain serialization of the string, all other will contain references to it. So the binary representation of the tuple depends on whether it is serialized first on not first.

Ah, yeah.
Could we add a flag to disable the reference mechanism, just for frozenset elements? It would make marshalled frozensets a bit bigger (unless we re-marshalled each one after sorting)... but I still prefer that to adding more logic/subclasses to frozenset.

This rough proof-of-concept seems to have the desired effect:
diff --git a/Python/marshal.c b/Python/marshal.c
index 1260704c74..70f9c4b109 100644
--- a/Python/marshal.c
+++ b/Python/marshal.c
@@ -503,9 +503,23 @@ w_complex_object(PyObject *v, char flag, WFILE *p)
 W_TYPE(TYPE_SET, p);
 n = PySet_GET_SIZE(v);
 W_SIZE(n, p);
- while (_PySet_NextEntry(v, &pos, &value, &hash)) {
+ PyObject *pairs = PyList_New(0);
+ for (Py_ssize_t i = 0; _PySet_NextEntry(v, &pos, &value, &hash); i++) {
+ PyObject *pair = PyTuple_New(2);
+ PyObject *dump = PyMarshal_WriteObjectToString(value, p->version);
+ PyTuple_SET_ITEM(pair, 0, dump);
+ Py_INCREF(value);
+ PyTuple_SET_ITEM(pair, 1, value);
+ PyList_Append(pairs, pair);
+ Py_DECREF(pair);
+ }
+ PyList_Sort(pairs);
+ for (Py_ssize_t i = 0; i < n; i++) {
+ PyObject *pair = PyList_GET_ITEM(pairs, i);
+ PyObject *value = PyTuple_GET_ITEM(pair, 1);
 w_object(value, p);
 }
+ Py_DECREF(pairs);
 }
 else if (PyCode_Check(v)) {
 PyCodeObject *co = (PyCodeObject *)v;
I can clean it up and convert it to a PR if we decide we want to go this route.

> I can clean it up and convert it to a PR if we decide 
> we want to go this route.
+1 This is by far the smallest intervention that has been discussed.

Here's pure python code for experimentation:
 from marshal import dumps, loads
 def marshal_set(s):
 return dumps(sorted(s, key=dumps))
 def unmarshal_set(m):
 return frozenset(loads(m))
 def test(s):
 assert unmarshal_set(marshal_set(s)) == s
 
 test({("string", 1), ("string", 2), ("string", 3)})

New changeset 33d95c6facdfda3c8c0feffa7a99184e4abc2f63 by Brandt Bucher in branch 'main':
bpo-37596: Make `set` and `frozenset` marshalling deterministic (GH-27926)
https://github.com/python/cpython/commit/33d95c6facdfda3c8c0feffa7a99184e4abc2f63

This is a bona fide enhancement and thus out of scope for backports. Since this is merged for 3.11, I'm closing the issue.
Thanks, everyone, this was some non-trivial design and implementation effort!

Should the error paths decref the key and return NULL as they do elsewhere in the function?

Hm, not quite sure what you mean. Are you talking about just replacing each of the new gotos with "Py_DECREF(pairs); return;"?
Error handling for this whole module is a bit unconventional. Some of the error paths in this function decrement the recursion depth counter, but I *think* that’s actually incorrect here... it looks like it’s our caller’s (w_object) responsibility to do that, error or no error.

Looking again, I think code is correct as-is (am not sure about the depth adjustment though).
Stylistically, it is different from the other blocks w_complex_object() that always have a "return" after setting p->error. The new code jumps to "anyset_done" and then falls through the "elif" block rather than issuing a "return".
Since nothing else happens below the if-elif-else chain, this is without consequence.

Thanks! This comes right in time, because we're working on freezing many more modules, and modules containing frozen sets didn't have a consistent frozen representation. Now they do!
(See issue45019, issue45020)

New changeset 51999c960e7fc45feebd629421dec6524a5fc803 by Brandt Bucher in branch 'main':
bpo-37596: Clean up the set/frozenset marshalling code (GH-28068)
https://github.com/python/cpython/commit/51999c960e7fc45feebd629421dec6524a5fc803

I reopen the issue.
test_marshal failed on AMD64 Arch Linux Usan 3.x:
https://buildbot.python.org/all/#/builders/719/builds/108
======================================================================
FAIL: test_deterministic_sets (test.test_marshal.BugsTestCase) [set([('string', 1), ('string', 2), ('string', 3)])]
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/buildbot/buildarea/3.x.pablogsal-arch-x86_64.clang-ubsan/build/Lib/test/test_marshal.py", line 365, in test_deterministic_sets
 self.assertNotEqual(repr_0, repr_1)
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
AssertionError: b"{('string', 1), ('string', 2), ('string', 3)}\n" == b"{('string', 1), ('string', 2), ('string', 3)}\n"
======================================================================
FAIL: test_deterministic_sets (test.test_marshal.BugsTestCase) [frozenset([('string', 1), ('string', 2), ('string', 3)])]
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/buildbot/buildarea/3.x.pablogsal-arch-x86_64.clang-ubsan/build/Lib/test/test_marshal.py", line 365, in test_deterministic_sets
 self.assertNotEqual(repr_0, repr_1)
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
AssertionError: b"frozenset({('string', 1), ('string', 2), ('string', 3)})\n" == b"frozenset({('string', 1), ('string', 2), ('string', 3)})\n"

The test failed at:
 def test_deterministic_sets(self):
 # bpo-37596: To support reproducible builds, sets and frozensets need to
 # have their elements serialized in a consistent order (even when they
 # have been scrambled by hash randomization):
 for kind in ("set", "frozenset"):
 for elements in (
 "float('nan'), b'a', b'b', b'c', 'x', 'y', 'z'",
 # Also test for bad interactions with backreferencing:
 "('string', 1), ('string', 2), ('string', 3)",
 ):
 s = f"{kind}([{elements}])"
 with self.subTest(s):
 # First, make sure that our test case still has different
 # orders under hash seeds 0 and 1. If this check fails, we
 # need to update this test with different elements:
 args = ["-c", f"print({s})"]
 _, repr_0, _ = assert_python_ok(*args, PYTHONHASHSEED="0")
 _, repr_1, _ = assert_python_ok(*args, PYTHONHASHSEED="1")
 self.assertNotEqual(repr_0, repr_1) # <=== HERE
 (...)
It checks that the representation of a set is different for two different PYTHONHASHSEED values (0 and 1). On my Fedora 34, I confirm that they are different:
PYTHONHASHSEED=0:
vstinner@apu$ PYTHONHASHSEED=0 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"
{('string', 1), ('string', 2), ('string', 3)}
vstinner@apu$ PYTHONHASHSEED=0 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"
{('string', 1), ('string', 2), ('string', 3)}
vstinner@apu$ PYTHONHASHSEED=0 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"
{('string', 1), ('string', 2), ('string', 3)}
versus PYTHONHASHSEED=1:
vstinner@apu$ PYTHONHASHSEED=1 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"
{('string', 3), ('string', 1), ('string', 2)}
vstinner@apu$ PYTHONHASHSEED=1 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"
{('string', 3), ('string', 1), ('string', 2)}
vstinner@apu$ PYTHONHASHSEED=1 ./python -c "print(set([('string', 1), ('string', 2), ('string', 3)]))"

Thanks for finding this, Victor.
That failure is surprising to me. Is it really possible for the order of the elements in a set to vary based on platform or build configuration (even with a fixed PYTHONHASHSEED at runtime)?
Really, this looks like it’s only a bug in the test’s (read "my") assumptions, not really in marshal itself. I’m glad I added this little sanity check, though.

I'm compiling Clang now to try to reproduce using a UBSan build (I'm on Ubuntu, though).
I'm not entirely familiar with how these sanitizer builds work... could the implication be that we're hitting undefined behavior at some point? Or is it just a red herring?
Note also that the "set([float('nan'), b'a', b'b', b'c', 'x', 'y', 'z'])" and "frozenset([float('nan'), b'a', b'b', b'c', 'x', 'y', 'z'])" tests seem to be working just fine... meaning their ordering on this buildbot is different under PYTHONHASHSEEDs 0 and 1 (as expected). It may still be a platform-or-configuration-dependent ordering, though.
Raymond: off the top of your head, are there any obvious reasons this could be happening?

Found it. This particular build is configured with HAVE_ALIGNED_REQUIRED=1, which forces it to use fnv instead siphash24 as its string hashing algorithm.