Bug 15329 - _dl_sort_fini and _dl_sort_init don't keep SCCs contiguous
_dl_sort_fini and _dl_sort_init don't keep SCCs contiguous
 Status: NEW None glibc Unclassified dynamic-link (show other bugs) unspecified P2 minor --- Not yet assigned to anyone

 Reported: 2013-04-02 09:09 UTC by Don Hatch 2021-10-27 14:59 UTC (History) 5 users (show) adhemerval.zanella carlos fweimer law marat fweimer: security-

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 Don Hatch 2013-04-02 09:09:41 UTC ```Found this by surprise while unit/stress testing _dl_sort_fini and the corresponding init sorting code (specifically, testing the init code on all graphs of up to 4 nodes). Previously, it wasn't clear to me whether the existing topsorting algorithm keeps SCCs (strongly connected components) contiguous-- it seemed to, for the most part, but I didn't have a proof that it did, nor a counterexample showing it didn't. Here's a small counterexample showing it doesn't. The static dependency graph has 4 nodes 0,1,2,3, and 5 edges: 0 depends on 1,2,3 1 depends on 0 2 doesn't depend on anything 3 depends on 0 In this case the dag of SCCs has two nodes and one edge: {0,1,3} depends on {2}. So it would be good if the sort would put 2 last. But it doesn't-- it produces [0 3 2 1]. To put it another way, 1 depends (transitively) on 2, but 2 doesn't depend (transitively) on 1, so it's desireable for 1 to come before 2 in the output order. The following probably isn't very interesting, but here are the steps the sorting code takes: initial order: [0 1 2 3] move 0 after 3 -> [1 2 3 0], 0 has been seen once move 1 after 0 -> [2 3 0 1], 1 has been seen once move 2 after 0 -> [3 0 2 1], 2 has been seen once move 3 after 0 -> [0 3 2 1], 3 has been seen once move 0 after 1 -> [3 2 1 0], 0 has been seen twice move 3 after 0 -> [2 1 0 3], 3 has been seen twice move 2 after 0 -> [1 0 2 3], 2 has been seen twice move 1 after 0 -> [0 1 2 3], 1 has been seen twice (original order!) move 0 after 3 -> [1 2 3 0], 0 has been seen 3 times move 1 after 0 -> [2 3 0 1], 1 has been seen 3 times move 2 after 0 -> [3 0 2 1], 2 has been seen 3 times move 3 after 0 -> [0 3 2 1], 3 has been seen 3 times move 0 after 1 -> [3 2 1 0], 0 has been seen 4 times move 3 after 0 -> [2 1 0 3], 3 has been seen 4 times move 2 after 0 -> [1 0 2 3], 2 has been seen 4 times move 1 after 0 -> [0 1 2 3], 1 has been seen 4 times (original order!) move 0 after 3 -> [1 2 3 0], 0 has been seen 5 times move 1 after 0 -> [2 3 0 1], 1 has been seen 5 times move 2 after 0 -> [3 0 2 1], 2 has been seen 5 times move 3 after 0 -> [0 3 2 1], 3 has been seen 5 times Now object 3 has been seen 5 times which exceeds its limit, so 0 gets locked in place, all seen counts get cleared, and we go on to sort the last three items, which have no order conflicts within themselves and so the output order is [0 3 2 1]. This is something to keep in mind when overhauling the sorting code, which already needs to be done for bug 15310 (sorting is O(n^3)) and bug 15311 (static deps can be violated by dynamic ones). It should be possible to make a fast, robust, easier-to-analyze implementation that keeps SCCs contiguous.```