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Ublas : |
Subject: Re: [ublas] Matrix multiplication performance
From: Michael Lehn (michael.lehn_at_[hidden])
Date: 2016-01-30 07:33:13
On my Haswell your code performs very well. For N=M=K it reaches single threaded 32GFLOPS
compared to 37GFLOPS with my FMA kernel. So I would say this is close!
I did the flowing two things:
1) Compiled with “-mfma”
2) Used MR=4 NR=8 and the other defaults
Here the results:
(A) Your code
[lehn_at_node042 session5]$ g++ -mfma -Wall -Ofast -I ../boost_1_60_0/ -std=c++11 -DHAVE_GCCVEC -DNDEBUG matprod.cc
[lehn_at_node042 session5]$ ./a.out
# m n k uBLAS: t1 MFLOPS Blocked: t2 MFLOPS Res
100 100 100 0.000993595 2012.89 0.000402098 4973.91 0
200 200 200 0.00508121 3148.86 0.0016022 9986.3 0
300 300 300 0.0148755 3630.13 0.00250342 21570.5 1.92273e-16
400 400 400 0.0304433 4204.53 0.00562129 22770.6 8.3039e-17
500 500 500 0.0515749 4847.32 0.00889942 28091.7 3.47892e-17
600 600 600 0.0821662 5257.63 0.0144308 29936 1.6149e-17
700 700 700 0.128187 5351.55 0.0224022 30622 8.38824e-18
800 800 800 0.190724 5369.01 0.0340685 30057.1 4.69155e-18
900 900 900 0.272908 5342.46 0.0474595 30720.9 2.78366e-18
1000 1000 1000 0.375997 5319.19 0.0635467 31472.9 1.75117e-18
1100 1100 1100 0.504189 5279.76 0.0856357 31085.2 1.14159e-18
1200 1200 1200 0.646057 5349.37 0.110654 31232.5 7.74152e-19
1300 1300 1300 0.828805 5301.61 0.137722 31904.8 5.43016e-19
1400 1400 1400 1.0273 5342.18 0.171288 32039.6 3.87778e-19
1500 1500 1500 1.26946 5317.24 0.208467 32379.3 2.85337e-19
1600 1600 1600 1.58969 5153.21 0.264495 30972.3 2.13061e-19
1700 1700 1700 2.67863 3668.3 0.30419 32302.2 1.62006e-19
^C
(B) My FMA Kernel
[lehn_at_node042 session5]$ g++ -mfma -Wall -Ofast -I ../boost_1_60_0/ -std=c++11 -DHAVE_FMA -DNDEBUG matprod.cc
[lehn_at_node042 session5]$ ./a.out
# m n k uBLAS: t1 MFLOPS Blocked: t2 MFLOPS Res
100 100 100 0.0010306 1940.61 0.000378977 5277.37 7.66934
200 200 200 0.0049895 3206.74 0.00101729 15728.1 0.236755
300 300 300 0.0150318 3592.39 0.00294536 18333.9 0
400 400 400 0.0306356 4178.14 0.00495991 25806.9 0.00179347
500 500 500 0.052443 4767.08 0.00784496 31867.6 0.000927111
600 600 600 0.0824758 5237.9 0.0127618 33850.9 8.49298e-18
700 700 700 0.128639 5332.73 0.0192815 35578.1 0.0107258
800 800 800 0.192102 5330.51 0.0294848 34729.7 0.00548943
900 900 900 0.272509 5350.28 0.0407217 35804 2.34506e-18
1000 1000 1000 0.372414 5370.37 0.0557306 35886.9 0.00180032
1100 1100 1100 0.495172 5375.91 0.0759043 35070.5 0.00111911
1200 1200 1200 0.643628 5369.56 0.0936622 36898.5 7.13231e-19
1300 1300 1300 0.831523 5284.28 0.119804 36676.5 0.000485489
1400 1400 1400 1.07165 5121.07 0.148407 36979.5 0.000334856
1500 1500 1500 1.26523 5334.99 0.179347 37636.6 2.74426e-19
1600 1600 1600 1.57777 5192.13 0.224779 36444.7 0.00017181
1700 1700 1700 2.67335 3675.54 0.259066 37928.6 0.000126808
1800 1800 1800 3.35908 3472.38 0.305459 38185.1 1.22716e-19
^C
(C) Your code with the parameters you suggested.
[lehn_at_node042 session5]$ g++ -mfma -Wall -Ofast -I ../boost_1_60_0/ -std=c++11 -DHAVE_GCCVEC -DBS_D_MR=2 -DBS_D_NR=16 -DBS_D_KC=512 -DNDEBUG matprod.cc
[lehn_at_node042 session5]$ ./a.out
# m n k uBLAS: t1 MFLOPS Blocked: t2 MFLOPS Res
100 100 100 0.000991205 2017.75 0.000371863 5378.32 0
200 200 200 0.00492544 3248.44 0.000893081 17915.5 0
300 300 300 0.0149147 3620.6 0.00288725 18702.9 0
400 400 400 0.0304561 4202.77 0.00533248 24003.9 0
500 500 500 0.0519717 4810.31 0.0094423 26476.6 0
600 600 600 0.0815292 5298.72 0.0160959 26839.2 8.50004e-18
700 700 700 0.127243 5391.25 0.0241644 28388.9 5.82176e-18
800 800 800 0.190188 5384.16 0.0379423 26988.3 3.67296e-18
900 900 900 0.270269 5394.62 0.0526334 27701.1 2.34234e-18
1000 1000 1000 0.369451 5413.44 0.0710608 28144.9 1.53537e-18
1100 1100 1100 0.491269 5418.62 0.0953915 27906 1.03025e-18
1200 1200 1200 0.638369 5413.8 0.119802 28847.5 7.13779e-19
1300 1300 1300 0.822215 5344.1 0.15489 28368.5 5.07376e-19
1400 1400 1400 1.03643 5295.12 0.191441 28666.8 3.69364e-19
1500 1500 1500 1.26753 5325.32 0.231101 29208 2.74895e-19
1600 1600 1600 1.60965 5089.31 0.289249 28321.6 2.0631e-19
1700 1700 1700 2.67171 3677.79 0.333099 29498.7 1.57713e-19
1800 1800 1800 3.34254 3489.56 0.397267 29360.6 1.2262e-19
^C
[lehn_at_node042 session5]$
Cheers,
Michael
On 29 Jan 2016, at 23:31, palik imre <imre_palik_at_[hidden]> wrote:
> Here is a more sane kernel using gcc simd vectors:
>
> template <typename Index, typename T>
> typename std::enable_if<std::is_floating_point<T>::value,
> void>::type
> ugemm(Index kc, T alpha,
> const T *A, const T *B,
> T beta,
> T *C, Index incRowC, Index incColC)
> {
> static const Index MR = BlockSize<T>::MR;
> static const Index NR = BlockSize<T>::NR;
> static const unsigned div = 32/sizeof(T);
> typedef T vx __attribute__((vector_size (32)));
>
> vx P[MR*NR/div] __attribute__ ((aligned (128))) = {};
> const vx *B_ = (vx *)B;
> for (Index l=0; l<kc; ++l) {
> for (Index j=0; j<(NR/div); ++j) {
> for (Index i=0; i<MR; ++i) {
> P[i * NR/div + j] += A[i + l * MR]*B_[l*(NR/div)+j];
> }
> }
> }
>
> T *P_ = (T *)P;
> for (Index i=0; i<MR; ++i) {
> for (Index j=0; j<NR; ++j) {
> C[i*incRowC+j*incColC] *= beta;
> C[i*incRowC+j*incColC] += alpha*P_[i * NR + j];
> }
> }
> }
>
>
> this plugs nicely to Michael's code, and slightly faster than my previous try (but still nowhere near to Michael's hand crafted kernel).
>
> The good blocksize for double is MR=2, NR=16, KC=512
> multiply MR and NR by 2 for float.
>
>
> Cheers,
>
> Imre
>