Re: FYI: optimizing certain matrix arithmetic

[Jaroslav Hajek]

On Tue, Sep 29, 2009 at 12:26 PM, Michael Creel <address@hidden> wrote:
> On Tue, Sep 29, 2009 at 10:44 AM, Jaroslav Hajek <address@hidden> wrote:
>> On Tue, Sep 29, 2009 at 10:38 AM, Michael Creel <address@hidden> wrote:
>>> Hi all,
>>>
>>> On an Apple Macbook Pro running Ubuntu Jaunty amd64, using the benchmark
>>>
>>> %%%%%%%%%%%%%%%%%%%%%%
>>> n = 500;
>>> R = triu (rand (n));
>>> u = rand (n, 1);
>>>
>>> tic; for i = 1:1000; R \ u; endfor; toc
>>> tic; for i = 1:1000; u' / R; endfor; toc
>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>
>>> R = tril (rand (n));
>>> u = rand (n, 1);
>>>
>>> tic; for i = 1:1000; R \ u; endfor; toc
>>> tic; for i = 1:1000; u' / R; endfor; toc
>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>
>>> u = u + I*rand (n, 1);
>>> tic; for i = 1:1000; R \ u; endfor; toc
>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>
>>>
>>> n = 800;
>>> a = rand (n);
>>> b = rand (n) + i*rand (n);
>>> tic; a * b; toc
>>> tic; b * a; toc
>>> tic; a' * b; toc
>>> tic; b * a'; toc
>>> tic; a \ b; toc
>>> tic; b / a; toc
>>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>>>
>>> Octave3.0.1 that comes with Ubuntu Jaunty amd64, I get
>>>
>>>
>>> octave:4> bench
>>> Elapsed time is 0.20216 seconds.
>>> Elapsed time is 1.93894 seconds.
>>> Elapsed time is 2.33824 seconds.
>>> Elapsed time is 0.188448 seconds.
>>> Elapsed time is 1.95657 seconds.
>>> Elapsed time is 2.43552 seconds.
>>> Elapsed time is 4.08299 seconds.
>>> Elapsed time is 7.84752 seconds.
>>> Elapsed time is 0.213021 seconds.
>>> Elapsed time is 0.21117 seconds.
>>> Elapsed time is 0.218387 seconds.
>>> Elapsed time is 0.217174 seconds.
>>> Elapsed time is 0.452714 seconds.
>>> Elapsed time is 0.391383 seconds.
>>> octave:5>
>>>
>>>
>>>
>>> Matlab 2008b gives
>>>>> bench
>>> Elapsed time is 0.289161 seconds.
>>> Elapsed time is 0.566446 seconds.
>>> Elapsed time is 0.562623 seconds.
>>> Elapsed time is 0.253456 seconds.
>>> Elapsed time is 0.574304 seconds.
>>> Elapsed time is 0.570281 seconds.
>>> Elapsed time is 0.253070 seconds.
>>> Elapsed time is 0.572601 seconds.
>>> Elapsed time is 0.102086 seconds.
>>> Elapsed time is 0.102677 seconds.
>>> Elapsed time is 0.103080 seconds.
>>> Elapsed time is 0.103759 seconds.
>>> Elapsed time is 0.165608 seconds.
>>> Elapsed time is 0.181704 seconds.
>>>>>
>>>
>>>
>>> Octave 3.2.3+ from today, self compiled, gives
>>> octave:1> bench
>>> Elapsed time is 0.208794 seconds.
>>> Elapsed time is 0.189178 seconds.
>>> Elapsed time is 0.186724 seconds.
>>> Elapsed time is 0.188649 seconds.
>>> Elapsed time is 0.192915 seconds.
>>> Elapsed time is 0.19166 seconds.
>>> Elapsed time is 0.186277 seconds.
>>> Elapsed time is 0.19102 seconds.
>>> Elapsed time is 0.212707 seconds.
>>> Elapsed time is 0.211013 seconds.
>>> Elapsed time is 0.210491 seconds.
>>> Elapsed time is 0.210447 seconds.
>>> Elapsed time is 0.431791 seconds.
>>> Elapsed time is 0.367412 seconds.
>>> octave:2>
>>>
>>> Congratulations!
>>> Michael
>>>
>>
>> It's interesting you didn't get any speed-up in the second part of the
>> benchmark, compared to 3.0.1...
>> What BLAS and LAPACK are you using? What's your compiler configuration?
>> Also, what exactly is your tip? The "3.2.3+" is a bit unclear, did you
>> mean "3.3.50+", i.e. the development version?
>>
>> thanks
>>
>> --
>> RNDr. Jaroslav Hajek
>> computing expert & GNU Octave developer
>> Aeronautical Research and Test Institute (VZLU)
>> Prague, Czech Republic
>> url: www.highegg.matfyz.cz
>>
>
> Oops, sorry, it's 3.3.50+, updated this morning.
>
> I make using
> make -j2 CFLAGS="-O3 -march=native -funroll-loops" FFLAGS="-O3
> -march=native -funroll-loops" XTRA_CFLAGS="-O3 -march=native
> -funroll-loops" XTRA_CXXFLAGS="-O3 -march=native -funroll-loops"
>

In general, if you're with a newer gcc on a 64-bit architecture, I
advise you against -funroll-loops. For me, it usually gets some +1% of
additional speed of some operations, at the cost of increasing the
binaries' size by more than 50%. Seems like a bad tradeoff.

> ./configure reports
>  BLAS libraries:       -llapack -lcblas -lf77blas -latlas
>
> so I assume that Octave is using Atlas (the atlas dev package that
> comes with Kubuntu Jaunty amd64).
>
> Michael
>

Apparently, yes. Hmm. It's really weird you got almost exactly the same figures.
If you apply the attached patch, rebuild and re-run the benchmark,
what do you get?

-- 
RNDr. Jaroslav Hajek
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz

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