It seems to work when the distribution has enough samples. I tried with 40 hosts and a distribution with 100,000 samples.
We go from kl =~ 1e-4 (with as much as 10% difference) to kl =~ 1e-7 (with no more than 0.5% difference). I will do some more experiements and try to think of patterns where this would not work.
~expected~ ~actual~ ~delta~ ~delta%~ ~weight~
dc1 102400 102400 0 0.000000 1008
host0 2438 2390 -48 -1.968827 24
host1 2438 2370 -68 -2.789171 24
host2 2438 2493 55 2.255947 24
host3 2438 2396 -42 -1.722724 24
host4 2438 2497 59 2.420016 24
host5 2438 2520 82 3.363413 24
host6 2438 2500 62 2.543068 24
host7 2438 2380 -58 -2.378999 24
host8 2438 2488 50 2.050861 24
host9 2438 2435 -3 -0.123052 24
host10 2438 2440 2 0.082034 24
host11 2438 2472 34 1.394586 24
host12 2438 2346 -92 -3.773585 24
host13 2438 2411 -27 -1.107465 24
host14 2438 2513 75 3.076292 24
host15 2438 2421 -17 -0.697293 24
host16 2438 2469 31 1.271534 24
host17 2438 2419 -19 -0.779327 24
host18 2438 2424 -14 -0.574241 24
host19 2438 2451 13 0.533224 24
host20 2438 2486 48 1.968827 24
host21 2438 2439 1 0.041017 24
host22 2438 2482 44 1.804758 24
host23 2438 2415 -23 -0.943396 24
host24 2438 2389 -49 -2.009844 24
host25 2438 2265 -173 -7.095980 24
host26 2438 2374 -64 -2.625103 24
host27 2438 2529 91 3.732568 24
host28 2438 2495 57 2.337982 24
host29 2438 2433 -5 -0.205086 24
host30 2438 2485 47 1.927810 24
host31 2438 2377 -61 -2.502051 24
host32 2438 2441 3 0.123052 24
host33 2438 2421 -17 -0.697293 24
host34 2438 2359 -79 -3.240361 24
host35 2438 2509 71 2.912223 24
host36 2438 2425 -13 -0.533224 24
host37 2438 2419 -19 -0.779327 24
host38 2438 2403 -35 -1.435603 24
host39 2438 2458 20 0.820345 24
host40 2438 2458 20 0.820345 24
host41 2438 2503 65 2.666120 24
~expected~ ~actual~ ~delta~ ~delta%~ ~weight~
dc1 102400 102400 0 0.000000 1008
host0 2438 2438 0 0.000000 24.559919
host1 2438 2438 0 0.000000 24.641221
host2 2438 2440 2 0.082034 23.486113
host3 2438 2437 -1 -0.041017 24.525875
host4 2438 2436 -2 -0.082034 23.644304
host5 2438 2440 2 0.082034 23.245287
host6 2438 2442 4 0.164069 23.617162
host7 2438 2439 1 0.041017 24.746174
host8 2438 2436 -2 -0.082034 23.584667
host9 2438 2439 1 0.041017 24.140637
host10 2438 2438 0 0.000000 24.060084
host11 2438 2441 3 0.123052 23.730349
host12 2438 2437 -1 -0.041017 24.948602
host13 2438 2437 -1 -0.041017 24.280851
host14 2438 2436 -2 -0.082034 23.402216
host15 2438 2436 -2 -0.082034 24.272037
host16 2438 2437 -1 -0.041017 23.747867
host17 2438 2436 -2 -0.082034 24.266271
host18 2438 2438 0 0.000000 24.158545
host19 2438 2440 2 0.082034 23.934788
host20 2438 2438 0 0.000000 23.630851
host21 2438 2435 -3 -0.123052 24.001950
host22 2438 2440 2 0.082034 23.623120
host23 2438 2437 -1 -0.041017 24.343138
host24 2438 2438 0 0.000000 24.595820
host25 2438 2439 1 0.041017 25.547510
host26 2438 2437 -1 -0.041017 24.753111
host27 2438 2437 -1 -0.041017 23.288606
host28 2438 2437 -1 -0.041017 23.425059
host29 2438 2438 0 0.000000 24.115941
host30 2438 2441 3 0.123052 23.560539
host31 2438 2438 0 0.000000 24.459911
host32 2438 2440 2 0.082034 24.096746
host33 2438 2437 -1 -0.041017 24.241316
host34 2438 2438 0 0.000000 24.715044
host35 2438 2436 -2 -0.082034 23.424601
host36 2438 2436 -2 -0.082034 24.123606
host37 2438 2439 1 0.041017 24.368997
host38 2438 2440 2 0.082034 24.331532
host39 2438 2439 1 0.041017 23.803561
host40 2438 2437 -1 -0.041017 23.861094
host41 2438 2442 4 0.164069 23.468473
On 04/26/2017 11:08 PM, Loic Dachary wrote:
>
>
> On 04/25/2017 05:04 PM, Pedro López-Adeva wrote:
>> Hi Loic,
>>
>> Well, the results are better certainly! Some comments:
>>
>> - I'm glad Nelder-Mead worked. It's not the one I would have chosen
>> because but I'm not an expert in optimization either. I wonder how it
>> will scale with more weights[1]. My attempt at using scipy's optimize
>> didn't work because you are optimizing an stochastic function and this
>> can make scipy's to decide that no further steps are possible. The
>> field that studies this kind of problems is stochastic optimization
>> [2]
>
> You were right, it does not always work. Note that this is *not* about the conditional probability bias. This is about the uneven distribution due to the low number of values in the distribution. I think this case should be treated separately, with a different method. In Ceph clusters, large and small, the number of PGs per host is unlikely to be large enough to get enough samples. It is not an isolated problem, it's what happens most of the time.
>
> Even in a case as simple as 12 devices starting with:
>
> ~expected~ ~actual~ ~delta~ ~delta%~ ~weight~
> host1 2560.000000 2580 20.000000 0.781250 24
> device12 106.666667 101 -5.666667 -5.312500 1
> device13 213.333333 221 7.666667 3.593750 2
> device14 320.000000 317 -3.000000 -0.937500 3
> device15 106.666667 101 -5.666667 -5.312500 1
> device16 213.333333 217 3.666667 1.718750 2
> device17 320.000000 342 22.000000 6.875000 3
> device18 106.666667 102 -4.666667 -4.375000 1
> device19 213.333333 243 29.666667 13.906250 2
> device20 320.000000 313 -7.000000 -2.187500 3
> device21 106.666667 94 -12.666667 -11.875000 1
> device22 213.333333 208 -5.333333 -2.500000 2
> device23 320.000000 321 1.000000 0.312500 3
>
> res = minimize(crush, weights, method='nelder-mead',
> options={'xtol': 1e-8, 'disp': True})
>
> device weights [ 1. 3. 3. 2. 3. 2. 2. 1. 3. 1. 1. 2.]
> device kl 0.00117274995028
> ...
> device kl 0.00016530695476
> Optimization terminated successfully.
> Current function value: 0.000165
> Iterations: 117
> Function evaluations: 470
>
> we still get a 5% difference on device 21:
>
> ~expected~ ~actual~ ~delta~ ~delta%~ ~weight~
> host1 2560.000000 2559 -1.000000 -0.039062 23.805183
> device12 106.666667 103 -3.666667 -3.437500 1.016999
> device13 213.333333 214 0.666667 0.312500 1.949328
> device14 320.000000 325 5.000000 1.562500 3.008688
> device15 106.666667 106 -0.666667 -0.625000 1.012565
> device16 213.333333 214 0.666667 0.312500 1.976344
> device17 320.000000 320 0.000000 0.000000 2.845135
> device18 106.666667 102 -4.666667 -4.375000 1.039181
> device19 213.333333 214 0.666667 0.312500 1.820435
> device20 320.000000 324 4.000000 1.250000 3.062573
> device21 106.666667 101 -5.666667 -5.312500 1.071341
> device22 213.333333 212 -1.333333 -0.625000 2.039190
> device23 320.000000 324 4.000000 1.250000 3.016468
>
>
>> - I used KL divergence for the loss function. My first attempt was
>> using as you standard deviation (more commonly known as L2 loss) with
>> gradient descent, but it didn't work very well.
>>
>> - Sum of differences sounds like a bad idea, +100 and -100 errors will
>> cancel out. Worse still -100 and -100 will be better than 0 and 0.
>> Maybe you were talking about the absolute value of the differences?
>>
>> - Well, now that CRUSH can use multiple weight the problem that
>> remains I think is seeing if the optimization problem is: a) reliable
>> and b) fast enough
>>
>> Cheers,
>> Pedro.
>>
>> [1] http://www.benfrederickson.com/numerical-optimization/
>> [2] https://en.wikipedia.org/wiki/Stochastic_optimization
>>
>> 2017-04-22 18:51 GMT+02:00 Loic Dachary <loic@xxxxxxxxxxx>:
>>> Hi Pedro,
>>>
>>> I tried the optimize function you suggested and got it to work[1]! It is my first time with scipy.optimize[2] and I'm not sure this is done right. In a nutshell I chose the Nedler-Mead method[3] because it seemed simpler. The initial guess is set to the target weights and the loss function simply is the standard deviation of the difference between the expected object count per device and the actual object count returned by the simulation. I'm pretty sure this is not right but I don't know what else to do and it's not completely wrong either. The sum of the differences seems simpler and probably gives the same results.
>>>
>>> I ran the optimization to fix the uneven distribution we see when there are not enough samples, because the simulation runs faster than with the multipick anomaly. I suppose it could also work to fix the multipick anomaly. I assume it's ok to use the same method even though the root case of the uneven distribution is different because we're not using a gradient based optimization. But I'm not sure and maybe this is completely wrong...
>>>
>>> Before optimization the situation is:
>>>
>>> ~expected~ ~objects~ ~delta~ ~delta%~
>>> ~name~
>>> dc1 1024 1024 0 0.000000
>>> host0 256 294 38 14.843750
>>> device0 128 153 25 19.531250
>>> device1 128 141 13 10.156250
>>> host1 256 301 45 17.578125
>>> device2 128 157 29 22.656250
>>> device3 128 144 16 12.500000
>>> host2 512 429 -83 -16.210938
>>> device4 128 96 -32 -25.000000
>>> device5 128 117 -11 -8.593750
>>> device6 256 216 -40 -15.625000
>>>
>>> and after optimization we have the following:
>>>
>>> ~expected~ ~objects~ ~delta~ ~delta%~
>>> ~name~
>>> dc1 1024 1024 0 0.000000
>>> host0 256 259 3 1.171875
>>> device0 128 129 1 0.781250
>>> device1 128 130 2 1.562500
>>> host1 256 258 2 0.781250
>>> device2 128 129 1 0.781250
>>> device3 128 129 1 0.781250
>>> host2 512 507 -5 -0.976562
>>> device4 128 126 -2 -1.562500
>>> device5 128 127 -1 -0.781250
>>> device6 256 254 -2 -0.781250
>>>
>>> Do you think I should keep going in this direction ? Now that CRUSH can use multiple weights[4] we have a convenient way to use these optimized values.
>>>
>>> Cheers
>>>
>>> [1] http://libcrush.org/main/python-crush/merge_requests/40/diffs#614384bdef0ae975388b03cf89fc7226aa7d2566_58_180
>>> [2] https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html
>>> [3] https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html#optimize-minimize-neldermead
>>> [4] https://github.com/ceph/ceph/pull/14486
>>>
>>> On 03/23/2017 04:32 PM, Pedro López-Adeva wrote:
>>>> There are lot of gradient-free methods. I will try first to run the
>>>> ones available using just scipy
>>>> (https://docs.scipy.org/doc/scipy-0.18.1/reference/optimize.html).
>>>> Some of them don't require the gradient and some of them can estimate
>>>> it. The reason to go without the gradient is to run the CRUSH
>>>> algorithm as a black box. In that case this would be the pseudo-code:
>>>>
>>>> - BEGIN CODE -
>>>> def build_target(desired_freqs):
>>>> def target(weights):
>>>> # run a simulation of CRUSH for a number of objects
>>>> sim_freqs = run_crush(weights)
>>>> # Kullback-Leibler divergence between desired frequencies and
>>>> current ones
>>>> return loss(sim_freqs, desired_freqs)
>>>> return target
>>>>
>>>> weights = scipy.optimize.minimize(build_target(desired_freqs))
>>>> - END CODE -
>>>>
>>>> The tricky thing here is that this procedure can be slow if the
>>>> simulation (run_crush) needs to place a lot of objects to get accurate
>>>> simulated frequencies. This is true specially if the minimize method
>>>> attempts to approximate the gradient using finite differences since it
>>>> will evaluate the target function a number of times proportional to
>>>> the number of weights). Apart from the ones in scipy I would try also
>>>> optimization methods that try to perform as few evaluations as
>>>> possible like for example HyperOpt
>>>> (http://hyperopt.github.io/hyperopt/), which by the way takes into
>>>> account that the target function can be noisy.
>>>>
>>>> This black box approximation is simple to implement and makes the
>>>> computer do all the work instead of us.
>>>> I think that this black box approximation is worthy to try even if
>>>> it's not the final one because if this approximation works then we
>>>> know that a more elaborate one that computes the gradient of the CRUSH
>>>> algorithm will work for sure.
>>>>
>>>> I can try this black box approximation this weekend not on the real
>>>> CRUSH algorithm but with the simple implementation I did in python. If
>>>> it works it's just a matter of substituting one simulation with
>>>> another and see what happens.
>>>>
>>>> 2017-03-23 15:13 GMT+01:00 Loic Dachary <loic@xxxxxxxxxxx>:
>>>>> Hi Pedro,
>>>>>
>>>>> On 03/23/2017 12:49 PM, Pedro López-Adeva wrote:
>>>>>> Hi Loic,
>>>>>>
>>>>>> >From what I see everything seems OK.
>>>>>
>>>>> Cool. I'll keep going in this direction then !
>>>>>
>>>>>> The interesting thing would be to
>>>>>> test on some complex mapping. The reason is that "CrushPolicyFamily"
>>>>>> is right now modeling just a single straw bucket not the full CRUSH
>>>>>> algorithm.
>>>>>
>>>>> A number of use cases use a single straw bucket, maybe the majority of them. Even though it does not reflect the full range of what crush can offer, it could be useful. To be more specific, a crush map that states "place objects so that there is at most one replica per host" or "one replica per rack" is common. Such a crushmap can be reduced to a single straw bucket that contains all the hosts and by using the CrushPolicyFamily, we can change the weights of each host to fix the probabilities. The hosts themselves contain disks with varying weights but I think we can ignore that because crush will only recurse to place one object within a given host.
>>>>>
>>>>>> That's the work that remains to be done. The only way that
>>>>>> would avoid reimplementing the CRUSH algorithm and computing the
>>>>>> gradient would be treating CRUSH as a black box and eliminating the
>>>>>> necessity of computing the gradient either by using a gradient-free
>>>>>> optimization method or making an estimation of the gradient.
>>>>>
>>>>> By gradient-free optimization you mean simulated annealing or Monte Carlo ?
>>>>>
>>>>> Cheers
>>>>>
>>>>>>
>>>>>>
>>>>>> 2017-03-20 11:49 GMT+01:00 Loic Dachary <loic@xxxxxxxxxxx>:
>>>>>>> Hi,
>>>>>>>
>>>>>>> I modified the crush library to accept two weights (one for the first disk, the other for the remaining disks)[1]. This really is a hack for experimentation purposes only ;-) I was able to run a variation of your code[2] and got the following results which are encouraging. Do you think what I did is sensible ? Or is there a problem I don't see ?
>>>>>>>
>>>>>>> Thanks !
>>>>>>>
>>>>>>> Simulation: R=2 devices capacity [10 8 6 10 8 6 10 8 6]
>>>>>>> ------------------------------------------------------------------------
>>>>>>> Before: All replicas on each hard drive
>>>>>>> Expected vs actual use (20000 samples)
>>>>>>> disk 0: 1.39e-01 1.12e-01
>>>>>>> disk 1: 1.11e-01 1.10e-01
>>>>>>> disk 2: 8.33e-02 1.13e-01
>>>>>>> disk 3: 1.39e-01 1.11e-01
>>>>>>> disk 4: 1.11e-01 1.11e-01
>>>>>>> disk 5: 8.33e-02 1.11e-01
>>>>>>> disk 6: 1.39e-01 1.12e-01
>>>>>>> disk 7: 1.11e-01 1.12e-01
>>>>>>> disk 8: 8.33e-02 1.10e-01
>>>>>>> it= 1 jac norm=1.59e-01 loss=5.27e-03
>>>>>>> it= 2 jac norm=1.55e-01 loss=5.03e-03
>>>>>>> ...
>>>>>>> it= 212 jac norm=1.02e-03 loss=2.41e-07
>>>>>>> it= 213 jac norm=1.00e-03 loss=2.31e-07
>>>>>>> Converged to desired accuracy :)
>>>>>>> After: All replicas on each hard drive
>>>>>>> Expected vs actual use (20000 samples)
>>>>>>> disk 0: 1.39e-01 1.42e-01
>>>>>>> disk 1: 1.11e-01 1.09e-01
>>>>>>> disk 2: 8.33e-02 8.37e-02
>>>>>>> disk 3: 1.39e-01 1.40e-01
>>>>>>> disk 4: 1.11e-01 1.13e-01
>>>>>>> disk 5: 8.33e-02 8.08e-02
>>>>>>> disk 6: 1.39e-01 1.38e-01
>>>>>>> disk 7: 1.11e-01 1.09e-01
>>>>>>> disk 8: 8.33e-02 8.48e-02
>>>>>>>
>>>>>>>
>>>>>>> Simulation: R=2 devices capacity [10 10 10 10 1]
>>>>>>> ------------------------------------------------------------------------
>>>>>>> Before: All replicas on each hard drive
>>>>>>> Expected vs actual use (20000 samples)
>>>>>>> disk 0: 2.44e-01 2.36e-01
>>>>>>> disk 1: 2.44e-01 2.38e-01
>>>>>>> disk 2: 2.44e-01 2.34e-01
>>>>>>> disk 3: 2.44e-01 2.38e-01
>>>>>>> disk 4: 2.44e-02 5.37e-02
>>>>>>> it= 1 jac norm=2.43e-01 loss=2.98e-03
>>>>>>> it= 2 jac norm=2.28e-01 loss=2.47e-03
>>>>>>> ...
>>>>>>> it= 37 jac norm=1.28e-03 loss=3.48e-08
>>>>>>> it= 38 jac norm=1.07e-03 loss=2.42e-08
>>>>>>> Converged to desired accuracy :)
>>>>>>> After: All replicas on each hard drive
>>>>>>> Expected vs actual use (20000 samples)
>>>>>>> disk 0: 2.44e-01 2.46e-01
>>>>>>> disk 1: 2.44e-01 2.44e-01
>>>>>>> disk 2: 2.44e-01 2.41e-01
>>>>>>> disk 3: 2.44e-01 2.45e-01
>>>>>>> disk 4: 2.44e-02 2.33e-02
>>>>>>>
>>>>>>>
>>>>>>> [1] crush hack http://libcrush.org/main/libcrush/commit/6efda297694392d0b07845eb98464a0dcd56fee8
>>>>>>> [2] python-crush hack http://libcrush.org/dachary/python-crush/commit/d9202fcd4d17cd2a82b37ec20c1bd25f8f2c4b68
>>>>>>>
>>>>>>> On 03/19/2017 11:31 PM, Loic Dachary wrote:
>>>>>>>> Hi Pedro,
>>>>>>>>
>>>>>>>> It looks like trying to experiment with crush won't work as expected because crush does not distinguish the probability of selecting the first device from the probability of selecting the second or third device. Am I mistaken ?
>>>>>>>>
>>>>>>>> Cheers
>>>>>>>>
>>>>>>>> On 03/18/2017 10:21 AM, Loic Dachary wrote:
>>>>>>>>> Hi Pedro,
>>>>>>>>>
>>>>>>>>> I'm going to experiment with what you did at
>>>>>>>>>
>>>>>>>>> https://github.com/plafl/notebooks/blob/master/replication.ipynb
>>>>>>>>>
>>>>>>>>> and the latest python-crush published today. A comparison function was added that will help measure the data movement. I'm hoping we can release an offline tool based on your solution. Please let me know if I should wait before diving into this, in case you have unpublished drafts or new ideas.
>>>>>>>>>
>>>>>>>>> Cheers
>>>>>>>>>
>>>>>>>>> On 03/09/2017 09:47 AM, Pedro López-Adeva wrote:
>>>>>>>>>> Great, thanks for the clarifications.
>>>>>>>>>> I also think that the most natural way is to keep just a set of
>>>>>>>>>> weights in the CRUSH map and update them inside the algorithm.
>>>>>>>>>>
>>>>>>>>>> I keep working on it.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> 2017-03-08 0:06 GMT+01:00 Sage Weil <sage@xxxxxxxxxxxx>:
>>>>>>>>>>> Hi Pedro,
>>>>>>>>>>>
>>>>>>>>>>> Thanks for taking a look at this! It's a frustrating problem and we
>>>>>>>>>>> haven't made much headway.
>>>>>>>>>>>
>>>>>>>>>>> On Thu, 2 Mar 2017, Pedro López-Adeva wrote:
>>>>>>>>>>>> Hi,
>>>>>>>>>>>>
>>>>>>>>>>>> I will have a look. BTW, I have not progressed that much but I have
>>>>>>>>>>>> been thinking about it. In order to adapt the previous algorithm in
>>>>>>>>>>>> the python notebook I need to substitute the iteration over all
>>>>>>>>>>>> possible devices permutations to iteration over all the possible
>>>>>>>>>>>> selections that crush would make. That is the main thing I need to
>>>>>>>>>>>> work on.
>>>>>>>>>>>>
>>>>>>>>>>>> The other thing is of course that weights change for each replica.
>>>>>>>>>>>> That is, they cannot be really fixed in the crush map. So the
>>>>>>>>>>>> algorithm inside libcrush, not only the weights in the map, need to be
>>>>>>>>>>>> changed. The weights in the crush map should reflect then, maybe, the
>>>>>>>>>>>> desired usage frequencies. Or maybe each replica should have their own
>>>>>>>>>>>> crush map, but then the information about the previous selection
>>>>>>>>>>>> should be passed to the next replica placement run so it avoids
>>>>>>>>>>>> selecting the same one again.
>>>>>>>>>>>
>>>>>>>>>>> My suspicion is that the best solution here (whatever that means!)
>>>>>>>>>>> leaves the CRUSH weights intact with the desired distribution, and
>>>>>>>>>>> then generates a set of derivative weights--probably one set for each
>>>>>>>>>>> round/replica/rank.
>>>>>>>>>>>
>>>>>>>>>>> One nice property of this is that once the support is added to encode
>>>>>>>>>>> multiple sets of weights, the algorithm used to generate them is free to
>>>>>>>>>>> change and evolve independently. (In most cases any change is
>>>>>>>>>>> CRUSH's mapping behavior is difficult to roll out because all
>>>>>>>>>>> parties participating in the cluster have to support any new behavior
>>>>>>>>>>> before it is enabled or used.)
>>>>>>>>>>>
>>>>>>>>>>>> I have a question also. Is there any significant difference between
>>>>>>>>>>>> the device selection algorithm description in the paper and its final
>>>>>>>>>>>> implementation?
>>>>>>>>>>>
>>>>>>>>>>> The main difference is the "retry_bucket" behavior was found to be a bad
>>>>>>>>>>> idea; any collision or failed()/overload() case triggers the
>>>>>>>>>>> retry_descent.
>>>>>>>>>>>
>>>>>>>>>>> There are other changes, of course, but I don't think they'll impact any
>>>>>>>>>>> solution we come with here (or at least any solution can be suitably
>>>>>>>>>>> adapted)!
>>>>>>>>>>>
>>>>>>>>>>> sage
>>>>>>>>>> --
>>>>>>>>>> To unsubscribe from this list: send the line "unsubscribe ceph-devel" in
>>>>>>>>>> the body of a message to majordomo@xxxxxxxxxxxxxxx
>>>>>>>>>> More majordomo info at http://vger.kernel.org/majordomo-info.html
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> Loïc Dachary, Artisan Logiciel Libre
>>>>>> --
>>>>>> To unsubscribe from this list: send the line "unsubscribe ceph-devel" in
>>>>>> the body of a message to majordomo@xxxxxxxxxxxxxxx
>>>>>> More majordomo info at http://vger.kernel.org/majordomo-info.html
>>>>>>
>>>>>
>>>>> --
>>>>> Loïc Dachary, Artisan Logiciel Libre
>>>> --
>>>> To unsubscribe from this list: send the line "unsubscribe ceph-devel" in
>>>> the body of a message to majordomo@xxxxxxxxxxxxxxx
>>>> More majordomo info at http://vger.kernel.org/majordomo-info.html
>>>>
>>>
>>> --
>>> Loïc Dachary, Artisan Logiciel Libre
>> --
>> To unsubscribe from this list: send the line "unsubscribe ceph-devel" in
>> the body of a message to majordomo@xxxxxxxxxxxxxxx
>> More majordomo info at http://vger.kernel.org/majordomo-info.html
>>
>
--
Loïc Dachary, Artisan Logiciel Libre
--
To unsubscribe from this list: send the line "unsubscribe ceph-devel" in
the body of a message to majordomo@xxxxxxxxxxxxxxx
More majordomo info at http://vger.kernel.org/majordomo-info.html
