[GitHub] [systemds] kev-inn opened a new pull request, #1643: Implement SIMD usage for basic dense dense MM

[GitBox]

kev-inn opened a new pull request, #1643:
URL: https://github.com/apache/systemds/pull/1643

   # `DoubleVector` replacement for matrix multiply
   JDK 17 adds `Vector` classes to use SIMD instructions. This PR replaces the 
basic dense dense matrix multiply with an equivalent `DoubleVector` 
implementation. It is necessary to use JDK 17, therefore we should not merge 
this yet, but keep it in staging for future reference.
   
   As an experiment we check a simple matrix multiply:
   `Z = X %*% Y`, $X\in \mathbb{R}^{n\times k}, Y\in \mathbb{R}^{k\times m}$
   
   The experiment script performs 10 matrix multiplications and saves the time 
of the last 5 to give the JVM some time to optimize.
   
   ## Vary rows n, m fixed at 1000
   
   ### Alpha Node
   | $k = 1000$ | $k = 10000$ |
   | --------------- | --------------- |
   | 
![plot_alpha_n_1000](https://user-images.githubusercontent.com/41760497/174668244-dec90cb2-4ded-4e8a-9b9a-16408c818809.svg)
 | 
![plot_alpha_n_10000](https://user-images.githubusercontent.com/41760497/174668238-c9f6b988-6b55-4c1f-845c-399ad6bf1ed0.svg)
 |
   
   
   ### Lima Node
   | $k = 1000$ | $k = 10000$ |
   | --------------- | --------------- |
   | 
![plot_lima_n_1000](https://user-images.githubusercontent.com/41760497/174668254-4fb11b22-b6b3-45c4-883c-572f469ec9b9.svg)
 | 
![plot_lima_n_10000](https://user-images.githubusercontent.com/41760497/174668248-2a6d2b1c-d4b7-4296-9fed-ed3fed8d84d1.svg)
 |
   
   ## Vary cols m, n fixed at 1000
   
   ### Alpha Node
   | $k = 1000$ | $k = 10000$ |
   | --------------- | --------------- |
   | 
![plot_alpha_m_1000](https://user-images.githubusercontent.com/41760497/174668241-3a829378-525b-464e-bf4e-9d1eff373125.svg)
 | 
![plot_alpha_m_10000](https://user-images.githubusercontent.com/41760497/174668233-7c5120a1-b243-4fa6-bf3a-2e0c05d75308.svg)
 |
   
   ### Lima Node
   | $k = 1000$ | $k = 10000$ |
   | --------------- | --------------- |
   | 
![plot_lima_m_1000](https://user-images.githubusercontent.com/41760497/174668252-8fefdd71-dd72-4d24-a851-eea6f660b88d.svg)
 | 
![plot_lima_m_10000](https://user-images.githubusercontent.com/41760497/174668246-0824fbae-900f-49a9-9010-0edb8ffbc7fd.svg)
 |
   
   ## Conclusion
   The implementation seems to boost the performance in most cases. The case 
where we vary the number of columns n on the alpha node needs some more 
exploration, but it seems we are never worse than the current implementation.
   
   ## Experiment Script
   
   ```R
   X = read($Xfname);
   Y = read($Yfname);
   
   lim = 10;
   R = matrix(0, rows=lim, cols=1);
   for (i in 1:lim) {
     t1 = time();
     Z = X %*% Y;
     t2 = time();
     R[i,1] = (t2-t1)/1000000;
   }
   
   print(sum(Z));
   res = R[5:lim,];
   write(res, $fname, format="csv", sep="\t");
   ```


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