Re: [PATCH v3 net-next 11/14] af_unix: Assign a unique index to SCC.

[Kuniyuki Iwashima <kuniyu@amazon.com>]

From: Paolo Abeni <pabeni@redhat.com>
Date: Tue, 27 Feb 2024 12:19:40 +0100
> On Fri, 2024-02-23 at 13:40 -0800, Kuniyuki Iwashima wrote:
> > The definition of the lowlink in Tarjan's algorithm is the
> > smallest index of a vertex that is reachable with at most one
> > back-edge in SCC.  This is not useful for a cross-edge.
> > 
> > If we start traversing from A in the following graph, the final
> > lowlink of D is 3.  The cross-edge here is one between D and C.
> > 
> >   A -> B -> D   D = (4, 3)  (index, lowlink)
> >   ^    |    |   C = (3, 1)
> >   |    V    |   B = (2, 1)
> >   `--- C <--'   A = (1, 1)
> > 
> > This is because the lowlink of D is updated with the index of C.
> > 
> > In the following patch, we detect a dead SCC by checking two
> > conditions for each vertex.
> > 
> >   1) vertex has no edge directed to another SCC (no bridge)
> >   2) vertex's out_degree is the same as the refcount of its file
> > 
> > If 1) is false, there is a receiver of all fds of the SCC and
> > its ancestor SCC.
> > 
> > To evaluate 1), we need to assign a unique index to each SCC and
> > assign it to all vertices in the SCC.
> > 
> > This patch changes the lowlink update logic for cross-edge so
> > that in the example above, the lowlink of D is updated with the
> > lowlink of C.
> > 
> >   A -> B -> D   D = (4, 1)  (index, lowlink)
> >   ^    |    |   C = (3, 1)
> >   |    V    |   B = (2, 1)
> >   `--- C <--'   A = (1, 1)
> > 
> > Then, all vertices in the same SCC have the same lowlink, and we
> > can quickly find the bridge connecting to different SCC if exists.
> > 
> > However, it is no longer called lowlink, so we rename it to
> > scc_index.  (It's sometimes called lowpoint.)
> > 
> > Also, we add a global variable to hold the last index used in DFS
> > so that we do not reset the initial index in each DFS.
> > 
> > This patch can be squashed to the SCC detection patch but is
> > split deliberately for anyone wondering why lowlink is not used
> > as used in the original Tarjan's algorithm and many reference
> > implementations.
> > 
> > Signed-off-by: Kuniyuki Iwashima <kuniyu@amazon.com>
> > ---
> >  include/net/af_unix.h |  2 +-
> >  net/unix/garbage.c    | 15 ++++++++-------
> >  2 files changed, 9 insertions(+), 8 deletions(-)
> > 
> > diff --git a/include/net/af_unix.h b/include/net/af_unix.h
> > index ec040caaa4b5..696d997a5ac9 100644
> > --- a/include/net/af_unix.h
> > +++ b/include/net/af_unix.h
> > @@ -36,7 +36,7 @@ struct unix_vertex {
> >  	struct list_head scc_entry;
> >  	unsigned long out_degree;
> >  	unsigned long index;
> > -	unsigned long lowlink;
> > +	unsigned long scc_index;
> >  };
> >  
> >  struct unix_edge {
> > diff --git a/net/unix/garbage.c b/net/unix/garbage.c
> > index 1d9a0498dec5..0eb1610c96d7 100644
> > --- a/net/unix/garbage.c
> > +++ b/net/unix/garbage.c
> > @@ -308,18 +308,18 @@ static bool unix_scc_cyclic(struct list_head *scc)
> >  
> >  static LIST_HEAD(unix_visited_vertices);
> >  static unsigned long unix_vertex_grouped_index = UNIX_VERTEX_INDEX_MARK2;
> > +static unsigned long unix_vertex_last_index = UNIX_VERTEX_INDEX_START;
> >  
> >  static void __unix_walk_scc(struct unix_vertex *vertex)
> >  {
> > -	unsigned long index = UNIX_VERTEX_INDEX_START;
> >  	LIST_HEAD(vertex_stack);
> >  	struct unix_edge *edge;
> >  	LIST_HEAD(edge_stack);
> >  
> >  next_vertex:
> > -	vertex->index = index;
> > -	vertex->lowlink = index;
> > -	index++;
> > +	vertex->index = unix_vertex_last_index;
> > +	vertex->scc_index = unix_vertex_last_index;
> > +	unix_vertex_last_index++;
> >  
> >  	list_add(&vertex->scc_entry, &vertex_stack);
> >  
> > @@ -342,13 +342,13 @@ static void __unix_walk_scc(struct unix_vertex *vertex)
> >  
> >  			vertex = edge->predecessor->vertex;
> >  
> > -			vertex->lowlink = min(vertex->lowlink, next_vertex->lowlink);
> > +			vertex->scc_index = min(vertex->scc_index, next_vertex->scc_index);
> >  		} else if (next_vertex->index != unix_vertex_grouped_index) {
> > -			vertex->lowlink = min(vertex->lowlink, next_vertex->index);
> > +			vertex->scc_index = min(vertex->scc_index, next_vertex->scc_index);
> 
> I guess the above will break when unix_vertex_last_index wraps around,
> or am I low on coffee? (I guess there is not such a thing as enough
> coffee to allow me reviewing this whole series at once ;)
> 
> Can we expect a wrap around in host with (surprisingly very) long
> uptimes? 

Then, the number of inflight AF_UNIX sockets is at least 2^64 - 1.
After this series, struct unix_sock is 1024 bytes, so... the host
would have roughly

  2^10 * 2^64 == 2^74 bytes == 2^34 TBi == 17179869184 TBi

memory!

So, we need not expect a wrap around :)