[parsec-users] Question regarding to fluidanimate in Parsec 3.0

Robert Smolinski rsmolin2 at illinois.edu
Wed Oct 24 15:27:47 EDT 2012


The answer is "yes" to both of your first questions. If you used 
integers or infinite-precision floating point arithmetic than the 
results would be identical.

Rounding error is one cause of your problems in Fluidanimate. Imagine 
adding three numbers but you can only one digit of precision (1 + .3 + 
.3). If we were to add the first two together first we would get ((1 + 
.3) +.3) = (1 + .3) = 1. However, if we add the second two first (1 + 
(.3 + .3)) = (1 + .6) = 2. Kind of a trivial example but it illustrates 
the danger of floating point arithmetic.

The second possible cause is cancellation error that occurs when you 
subtract two floating-point numbers that are close together. This form 
of error can be very dangerous because you lose both precision and 
accuracy. Wikipedia would probably be a better place to understand this 
form of error. Fluidanimate does subtract two floating point numbers in 
multiple spots making it a possibility, and thread ordering can again 
make the amount of cancellation error introduced very different.


On 10/24/2012 01:43 PM, Jason Kwok wrote:
> Hi Rob,
>
> I want to make sure I understand your argument because I think there 
> are two independent things:  Floating point inaccuracy and path 
> dependence.
>
> Are you saying that the non-deterministic order coupled with floating 
> point inaccuracy combined caused the delta?  As in, if the 
> calculations were integer-based, then the non-deterministic ordering 
> would still produce identical results?
>
> If the order in which the particles are getting updated impacts values 
> being used in subsequent calculations, then it’s not just due to 
> floating point inaccuracy.
>
> Thanks,
> Jason
>
> ------------------------------------------------------------------------
> Date: Tue, 23 Oct 2012 18:39:24 -0500
> From: rsmolin2 at illinois.edu
> To: parsec-users at lists.cs.princeton.edu
> Subject: Re: [parsec-users] Question regarding to fluidanimate in 
> Parsec 3.0
>
> Hi Jason,
>
> This is expected behavior for fluidanimate since each border cell 
> (e.g. a cell that can be modified by 2 or more threads concurrently) 
> doesn't enforce updates in a deterministic order. Non-determinism 
> combined with the fact that finite-precison floating point arithmetic 
> is not commutative or associative leads to your test failing when you 
> test exact equality. Most programs using floating point arithmetic 
> usually test for equality by making sure the absolute difference 
> between the computed value and expected value is less than some small 
> amount (e.g. 10^-7).
>
> To get a better understanding of floating-point arithmetic you might 
> want to read "What Every Computer Scientist Should Know About 
> Floating-Point Arithmetic" as there are many small details in 
> floating-point arithmetic that might trip you up in your future research.
>
>
> Rob.
>
>
> On 10/23/2012 03:00 PM, Jason Kwok wrote:
>
>     Hi All,
>
>        I noticed some inconsistency between the results produced by
>     fluidanimate single-threaded version and multi-threaded version.
>
>        here is what I did:
>
>        I built fluidanimate & fluidcmp on my ubuntu 10.04 box, I ran
>     fluidanimate on simLarge "in_300K.fluid" dataset as follows:
>     *./fluidanimate 1 5 in_300K.fluid t1f5out1.fluid*
>     ***./fluidanimate 1 5 in_300K.fluid t1f5out2.fluid*
>     *   ./fluidcmp **t1f5out1.fluid **t1f5out2.fluid **--ptol 0 --vtol
>     0 --bbox 0*
>     *Position test:        PASS*
>     *     Velocity test:        PASS*
>     *     Bounding box test:    PASS*
>
>     *./fluidanimate 2 5 in_300K.fluid t2f5out1.fluid*
>     ***./fluidanimate 2 5 in_300K.fluid t2f5out2.fluid*
>     *   ./fluidcmp **t2f5out1.fluid **t2f5out2.fluid **--ptol 0 --vtol
>     0 --bbox 0*
>     *Position test: FAIL*
>     *     Velocity test: FAIL*
>     *     Bounding box test:    PASS*
>
>     *./fluidcmp **t1f5out1.fluid **t2f5out1.fluid **--ptol 0 --vtol 0
>     --bbox 0*
>     *Position test: FAIL*
>     *     Velocity test: FAIL*
>     *     Bounding box test:    PASS*
>
>        As you can see, the tests passed on 1 thread but failed on 2
>     threads on different runs for exact same number of frame, the
>     results between 1 and 2 threads for 5 frames are also different. I
>     would expect the calculation should be the same regardless of how
>     many threads it uses as long as the number of frames are the same.
>        I have tried with just 1 frame, the results are the same as
>     above. you probably notice that I set the tolerance value to 0 for
>     all tests, which means all compared data should be exactly same to
>     pass. In verbose mode, I can see that the failed tests are
>     actually due to very small difference between the data value being
>     compared.
>
>        My questions is, is this behavior expected? should I use a
>     bigger tolerance value? if so, why the single thread version never
>     has different data values?
>
>     Thanks,
>     Jason
>
>
>
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