pagerank-datatype - Comparison of PageRank using float vs bfloat16 as the storage type

Comparison of PageRank using float vs bfloat16 as the storage type (pull, CSR).

This experiment was for comparing the result between: 1. Find pagerank using float as the storage type. 2. Find pagerank using bfloat16 as the storage type.

Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure. Unfortunately it seems bfloat16 cannot be used for PageRank as its too inaccurate (atleast when simply replacing float vectors with bfloat16 vectors). Using fp16 might work, but likely give negligible performance improvement over float. Note that neither approach makes use of SIMD instructions which are available on all modern hardware.

All outputs are saved in out and a small part of the output is listed here. The input data used for this experiment is available at "graphs", and the SuiteSparse Matrix Collection. This experiment was done with guidance from Prof. Dip Sankar Banerjee and Prof. Kishore Kothapalli.

```bash $ g++ -O3 main.cxx $ ./a.out ~/data/min-1DeadEnd.mtx $ ./a.out ~/data/min-2SCC.mtx $ ...

...

Loading graph /home/subhajit/data/web-Stanford.mtx ...

order: 281903 size: 2312497 {}

order: 281903 size: 2312497 {} (transposeWithDegree)

[00375.217 ms; 062 iters.] [0.0000e+00 err.] pagerankFloat

[00298.391 ms; 047 iters.] [4.1805e-02 err.] pagerankBfloat16

...

Loading graph /home/subhajit/data/soc-LiveJournal1.mtx ...

order: 4847571 size: 68993773 {}

order: 4847571 size: 68993773 {} (transposeWithDegree)

[11260.648 ms; 050 iters.] [0.0000e+00 err.] pagerankFloat

[13895.689 ms; 068 iters.] [4.3118e-02 err.] pagerankBfloat16

...

```

References

• PageRank Algorithm, Mining massive Datasets (CS246), Stanford University
• Convert FP32 to Bfloat16 in C++
• Why is there no 2-byte float and does an implementation already exist?
• Is it safe to reinterpret_cast an integer to float?
• SuiteSparse Matrix Collection

- C++
Published by wolfram77 over 3 years ago