Matrix multiplication not returning on certain matrix content (Intel)

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Philipp il 10 Apr 2024 alle 13:27

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Modificato: Bruno Luong il 11 Apr 2024 alle 20:06

Hi,

I have a certain matrix multiplication which is not returning on my Intel machine (Win11 Pro, Intel i7-8700). When I exchange the content of the matrices with random numbers I can obtain a result within seconds. I could reproduce this problem on several Intel machines (and different Matlab versions). I relate this problem to Intel MKL. One matrix contains a lot of entries close to zero (10^-322) which probably causes the problem.

To reproduce it, download the two matrices:

https://gigamove.rwth-aachen.de/de/download/2639a5ac631684e42df43009ba30f109

and run the command:

scc=At*scc;

Is this operation running through on your machine?

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John D'Errico il 10 Apr 2024 alle 14:23

It is generally a bad idea to force someone to download a file from off-site. We don't know if you are planting a trojan on our system. Honestly, I won't touch it to test your question as a download. Maybe others will be more willing to take a chance on an unknown person, posting a link to an unkown file. I hope they don't take the risk since you could have made this much simpler.

Just attach a .mat file that contains the matrices. Click on the paper clip icon on a comment.

Philipp il 10 Apr 2024 alle 14:30

It's about 4 GB and I don't know if I can reproduce it on any other size and I have no intent to invest any more time into this. The provided link directs to a German university (over https) with a download service for larger files. The university scans the files internally for viruses. It's the best I can do.

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Bruno Luong il 10 Apr 2024 alle 14:56

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Modificato: Bruno Luong il 10 Apr 2024 alle 14:59

Apri in MATLAB Online

The matrix contains many non normalized floating point numbers and operations on these numbers are very slow;

>> load('C:\Users\bruno\Downloads\test.mat')
>> size(At)
ans =
       17534       17532
       
>> size(scc)
ans =
17532        8281
>> tic; B=At*scc(:,1); toc
Elapsed time is 1.105924 seconds.
>> tic; B=At*scc(:,1:10); toc
Elapsed time is 10.237435 seconds.
>> tic; B=At*scc(:,1:100); toc
Elapsed time is 108.484422 seconds.

On my machine it takes 1 sec by column of scc. So eventually I guess it will finish in less than 3h.

Note that for normalized numbers the operation is roughly 200 time faster.

So for now I think there is no bug. Just let the thing run over night (Sorry I won't do that).

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Steven Lord il 10 Apr 2024 alle 16:39

Apri in MATLAB Online

What would you recommend we do when you pass a denormal/subnormal number to our functions?

Check for their presence and issue a warning? That means that everyone who calls those functions, both those whose data includes denormal numbers and those whose data does not, will pay the cost of checking for denormal numbers every time those functions are called. That's not going to happen unless it were free and it wouldn't be free.
Check for their presence and throw an error? Again, you're forcing everyone to pay the cost of checking.
Check for their presence and replace them with a normal number (0 or realmin, perhaps?) In addition to the cost of checking, this would silently (or perhaps not silently, if we were to warn we were making that replacement) modify the data you pased into the function.
Encourage hardware manufacturers to improve the performance of their instructions on denormal numbers? This could be a long term solution, but it could be a tough sell due to bang-for-buck considerations. And it's not one that would be limited to MATLAB and not one that we could implement ourselves.

An approach you could use, if you wanted to guard yourself against denormal numbers, would be to implement item 3 yourself at the time the data is loaded into MATLAB, when it is first created, and/or when you perform an operation that you believe will introduce denormal numbers.

format longg
A = [1; 0; realmin; eps(0)]
A = 4x1
                         1
                         0
      2.2250738585072e-308
     4.94065645841247e-324
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
A(abs(A)<realmin) = 0
A = 4x1
                         1
                         0
      2.2250738585072e-308
                         0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

One more point: I haven't looked at your matrices to determine how many denormals they contain. But I have to wonder if you're misinterpreting the data, or imported the data into MATLAB incorrectly. Often I see numbers with varying orders of magnitude crop up when interpreting the hex pattern of double or single precision data as single or double precision respectively.

A = pi
A = 
          3.14159265358979
B = typecast(A, 'single')
B = 1x2
1.0e+00 *

    3.370281e+12        2.142699
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

The second element of B is on the same order of magnitude as pi, but the first is much, much larger. But if we look at their hex patterns:

format hex
A
A = 
   400921fb54442d18
B
B = 1x2
1.0e+00 *

   54442d18   400921fb
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

Same bits, different interpretation.

Walter Roberson il 11 Apr 2024 alle 19:26

Hmmm... I wonder if the hardware could convert the numbers to 80 bit floats, do the operation, and convert back?

Bruno Luong il 11 Apr 2024 alle 19:56

Modificato: Bruno Luong il 11 Apr 2024 alle 20:06

https://en.wikipedia.org/wiki/Double-precision_floating-point_format

https://en.wikipedia.org/wiki/Extended_precision

Certainly a very nice idea. But one of the reasons: As the exponet has only 4 more bits, its is still not enough to convert all denormalized 64 bits numbers to normalized 80 bits. It needs +6 bits exponent since 2^6 >= 52 > 2^5 > 2^4

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