Subject: Re: [ublas] Matrix multiplication performance
From: Michael Lehn (michael.lehn_at_[hidden])
Date: 2016-01-29 11:13:28
Oh noo, grr. Yes you are right. Sorry, the stuff gets generated
automatically and it again copied "fma.hpp" form the wrong
server/directory.
Could you check again:
http://www.mathematik.uni-ulm.de/~lehn/test_ublas/fma.hpp
The kernel requires MR=4 and NR=12 and uses the vfmadd231pd instruction
Quoting palik imre <imre_palik_at_[hidden]>:
> Are you sure about the replacement? this fma.hpp is practically
> identical with your avx.hpp
>
>
> On Friday, 29 January 2016, 0:21, Michael Lehn
> <michael.lehn_at_[hidden]> wrote:
>
>
> Could you also compile with -DHAVE_FMA? However, I noticed that I
> messed up the file ?fma.hpp? whenI created the page. So you should
> replace it with
> http://www.mathematik.uni-ulm.de/~lehn/test_ublas/fma.hpp
> At the moment I regenerate the pages on the website
>
>
> On 28 Jan 2016, at 18:08, palik imre <imre_palik_at_[hidden]> wrote:
>
> Wow:
> $ cd session4
> $ g++ -Ofast -mavx -Wall -std=c++11 -DNDEBUG -DHAVE_AVX -fopenmp
> -DM_MAX=1500 matprod.cc
> matprod.cc: In function ???double estimateGemmResidual(const MA&,
> const MB&, const MC0&, const MC1&)???:
> matprod.cc:94:40: warning: typedef ???TC0??? locally defined but not
> used [-Wunused-local-typedefs]
> typedef typename MC0::value_type TC0;
> ^
> $ ./a.out
> # m n k uBLAS: t1 MFLOPS Blocked: t2
> MFLOPS Diff nrm1
> 100 100 100 0.000465896 4292.8 0.00405376
> 493.369 200 200 200 0.0046712
> 3425.24 0.00244891 6533.51 300 300
> 300 0.0161551 3342.59 0.00314843 17151.4
> 1.94151e-16
> 400 400 400 0.032688 3915.81 0.00240584
> 53204 8.40477e-17
> 500 500 500 0.0544033 4595.31 0.00291218
> 85846.4 3.52062e-17
> 600 600 600 0.0838317 5153.18 0.00453539
> 95250.9 1.63452e-17
> 700 700 700 0.130899 5240.69 0.00585201
> 117225 8.44769e-18
> 800 800 800 0.201121 5091.46 0.010872
> 94186.5 4.72429e-18
> 900 900 900 0.286407 5090.65 0.0151735
> 96088.7 2.80443e-18
> 1000 1000 1000 0.432211 4627.37 0.0707567
> 28265.9 1.7626e-18
> 1100 1100 1100 0.511146 5207.9 0.0186911
> 142420 1.14521e-18
> 1200 1200 1200 0.666975 5181.6 0.025109
> 137640 7.79963e-19
> 1300 1300 1300 0.863769 5087.01 0.0283398
> 155047 5.45468e-19
> 1400 1400 1400 1.09638 5005.57 0.143209
> 38321.6 3.90302e-19
> 1500 1500 1500 1.40352 4809.33 0.120096
> 56204.9 2.8667e-19
> $ cd ../session2
> $ g++ -Ofast -mavx -Wall -std=c++11 -DNDEBUG -DHAVE_AVX -fopenmp
> -DM_MAX=1500 matprod.cc
> [ec2-user_at_ip-10-0-46-255 session2]$ ./a.out
> # m n k uBLAS: t1 MFLOPS Blocked: t2
> MFLOPS Diff nrm1
> 100 100 100 0.000471888 4238.29 0.000231317
> 8646.14 200 200 200 0.00431625
> 3706.92 0.00121122 13209.9 300 300
> 300 0.0153292 3522.69 0.00336464 16049.3
> 1.07937e-06
> 400 400 400 0.0317138 4036.1 0.00712568
> 17963.2 4.06488e-06
> 500 500 500 0.052809 4734.04 0.0121626
> 20554.9 9.09947e-06
> 600 600 600 0.0828121 5216.63 0.020657
> 20913 1.65243e-05
> 700 700 700 0.131053 5234.51 0.0318276
> 21553.6 2.71365e-05
> 800 800 800 0.196825 5202.58 0.0482679
> 21214.9 4.12109e-05
> 900 900 900 0.281006 5188.51 0.0671323
> 21718.3 5.93971e-05
> 1000 1000 1000 0.386332 5176.89 0.0906054
> 22073.7 8.23438e-05
> 1100 1100 1100 0.51667 5152.22 0.124346
> 21408.1 0.000109566
> 1200 1200 1200 0.668425 5170.37 0.159701
> 21640.5 0.000142817
> 1300 1300 1300 0.860445 5106.66 0.203472
> 21595.1 0.000182219
> 1400 1400 1400 1.08691 5049.18 0.249427
> 22002.4 0.000226999
> 1500 1500 1500 1.38244 4882.67 0.307519
> 21949.9 0.000280338
>
> This is on Haswell
>
>
> On Wednesday, 27 January 2016, 1:39, Michael Lehn
> <michael.lehn_at_[hidden]> wrote:
>
>
>
> On 23 Jan 2016, at 18:53, palik imre <imre_palik_at_[hidden]> wrote:
>
> Hi All,
> what's next? I mean what is the development process for ublas?
> Now we have a C-like implementation that outperforms both the
> mainline, and the branch version (axpy_prod). What will we do with
> that?
> As far as I see we have the following options:
> 1) Create a C++ template magic implementation out of it. But for
> this, at the least we would need compile-time access to the target
> instruction set. Any idea how to do that?
> 2) Create a compiled library implementation out of it, and choose
> the implementation run-time based on the CPU capabilities.
>
> 3) Include some good defaults/defines, and hope the user will use them.
> 4) Don't include it, and do something completely different.
>
>
> What do you think?
>
>
> At the moment I am not sure, but pretty sure, that you don?t have to
> rewrite uBLAS to support good performance. uBLAS is a pretty
> finelibrary and already has what you need. So just extend it. At
> least for 383 lines of code :-)
> As I was pretty busy the last days, so I could not continue until
> today. I made some minimal modifications to adopt the GEMM
> implementationto take advantage of uBLAS:
> - The GEMM frame algorithm and the pack functions now work with any
> uBLAS matrix that supports element access through the notation
> A(i,j)- Only for matrix C in the operation C <- beta*C + alpha*A*B
> it requires that the matrix is stored row-major or col-major. The
> other matrices canbe expressions. Here I need some help to get rid
> of this ugly lines of code:
> TC *C_ = &C(0,0); const size_type incRowC = &C(1,0) -
> &C(0,0); const size_type incColC = &C(0,1) - &C(0,0);
> - Things like the following should work without performance penalty
> (and in particularly without creating temporaries):
> blas::axpy_prod(3*A1+A2, B1 - B2, C, matprodUpdate) - And matrices
> A and B can be symmetric or whatever. Of course if A or B is
> triangular a specialized implementation can take advantage- The
> storage format does not matter. You can mix row-major and
> col-major, packed, ?
> Here is the page for this:
> http://www.mathematik.uni-ulm.de/~lehn/test_ublas/session4/page01.html
> Please note, creating the benchmarks for the symmetric matrix-matrix
> product really takes long because the current uBLAS implementation
> seemsto be much slower than for general matrices. So I reduced the
> problem size for now. It would be helpful if some people could
> reproduce the benchmarksand also check different cases:
> - different expressions- different element types, e.g. A with
> floats, B with double etc. At the moment there is only a micro
> kernel for double. The performance depends on thecommon type of A
> and B. So with complex<..> the reference implementation. But the
> performance should at least be constant in this case.
> It would in particular be nice to have benchmarks from people with
> an Intel Sandybridge or Haswell as the micro kernels are optimized
> for thesearchitectures. If interested I can extend the benchmarks
> to compare with Intel MKL. For Linux there is a free
> non-commercial version available.
>
> Cheers,
> Michael
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