On Wed, Apr 11, 2018 at 11:20:04AM +0100, Catalin Marinas wrote:
> On Fri, Apr 06, 2018 at 03:22:49PM +0200, Andrea Parri wrote:
> > On Thu, Apr 05, 2018 at 05:58:57PM +0100, Will Deacon wrote:
> > > I've been kicking the tyres further on qspinlock and with this set of 
> > > patches
> > > I'm happy with the performance and fairness properties. In particular, the
> > > locking algorithm now guarantees forward progress whereas the 
> > > implementation
> > > in mainline can starve threads indefinitely in cmpxchg loops.
> > > 
> > > Catalin has also implemented a model of this using TLA to prove that the
> > > lock is fair, although this doesn't take the memory model into account:
> > > 
> > > https://git.kernel.org/pub/scm/linux/kernel/git/cmarinas/kernel-tla.git/commit/
> > 
> > Nice!  I'll dig into this formalization, but my guess is that our model
> > (and axiomatic models "a-la-herd", in general) are not well-suited when
> > it comes to study properties such as fairness, liveness...
> Maybe someone with a background in formal methods could give a better
> answer. How TLA+ works is closer to rmem [1] (operational model,
> exhaustive memoised state search) than herd. Liveness verification
> requires checking that, under certain fairness properties, some state is
> eventually reached. IOW, it tries to show that either all state change
> graphs lead to (go through) such state or that there are cycles in the
> graph and the state is never reached. I don't know whether herd could be
> modified to check liveness. I'm not sure it can handle infinite loops
> either (the above model checks an infinite lock/unlock loop on each
> CPU and that's easier to implement in a tool with memoised states).
> The TLA+ model above assumes sequential consistency, so no memory
> ordering taken into account. One could build an operational model in
> TLA+ that's equivalent to the axiomatic one (e.g. following the Flat
> model equivalence as in [2]), however, liveness checking (at least with
> TLA+) is orders of magnitude slower than safety. Any small variation has
> an exponential impact on the state space, so likely to be impractical.
> For specific parts of the algorithm, you may be able to use a poor man's
> ordering by e.g. writing two accesses in two different orders so the
> model checks both combinations.
> There are papers (e.g. [3]) on how to convert liveness checking to
> safety checking but I haven't dug further. I think it's easier/faster if
> you do liveness checking with a simplified model and separately check
> the safety with respect to memory ordering on tools like herd.

Indeed.  A fundamental problem, AFAICT, is to formalize that concept of
'[it] will _eventually_ happen'.  Consider a simple example:

        { x = 0}

        P0      |   P1
        x = 1   |   while (!x)
                |        ;

herd 'knows' that:

        - on the 1st iteration of the 'while' loop, the load from x
          can return the value 0 or 1 (only);

        - on the 2nd iteration of the 'while' loop, the load from x
          can return the value 0 or 1;

        - [ ... and 'so on'! ]

but this is pretty much all herd knows about this snippet by now ... ;)


> [1] http://www.cl.cam.ac.uk/~sf502/regressions/rmem/
> [2] http://www.cl.cam.ac.uk/~pes20/armv8-mca/armv8-mca-draft.pdf
> [3] https://www.sciencedirect.com/science/article/pii/S1571066104804109
> -- 
> Catalin

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