[parsec-users] Question regarding to fluidanimate in Parsec 3.0
Jim Dempsey
jim at quickthreadprogramming.com
Wed Oct 24 15:28:07 EDT 2012
Jason,
X = (A + B) + C
Y = A + (B + C)
Do not necessarily produce the same results in floating point arithmetic.
Algebraically that are the same, hardware wise, not necessarily so.
Due to finite precision capability of representing floating point numbers.
A, B, C may contain exact or approximate values from a prior computation or
initialization.
X =
(A + B) may result in an exact, truncated, round down or round up result.
Result from (A + B), then + C may result in an exact, truncated, round down
or round up result.
Y =
(B + C) may result in an exact, truncated, round down or round up result.
Result from (B + C), then + A may result in an exact, truncated, round down
or round up result.
Depending on what happened for rounding in (? + ?), and + ?
X == Y .or. X !=Y, However X ~= Y
When the operations are sequenced the same (and with same values each time),
then the uncertainty is the same.
Jim Dempsey
From: parsec-users-bounces at lists.cs.princeton.edu
[mailto:parsec-users-bounces at lists.cs.princeton.edu] On Behalf Of Jason Kwok
Sent: Wednesday, October 24, 2012 1:43 PM
To: parsec-users at lists.cs.princeton.edu
Subject: Re: [parsec-users] Question regarding to fluidanimate in Parsec 3.0
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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