3 ms·

Of course using an optimized blas is somewhat faster, but it is not three orders of magnitude faster!

by enriquto 7y ago

kmbriedis 7y ago
But it can be 20x
- Sean1708 7y ago
  I actually did some benchmarking on this once upon a time[1] and it turns out that it's actually really easy to write something that is only ~5x slower[2] (until you get to matrices that don't fit in RAM): (4, 4, 4) (5, 5, 5) (32, 32, 32) (33, 33, 33) (256, 256, 256) (257, 257, 257) (512, 512, 512) (513, 513, 513) (1024, 1024, 1024) (1025, 1025, 1025) –––––––– ––––––––– ––––––––– –––––––––––– –––––––––––– ––––––––––––––– ––––––––––––––– ––––––––––––––– ––––––––––––––– –––––––––––––––––– –––––––––––––––––– :naive 0.0 0.0 1.3e-5 2.0e-5 0.0114 0.0133 0.0942 0.106 3.25 2.39 :tiled 0.0 0.0 2.7e-5 2.2e-5 0.0139 0.0121 0.154 0.101 1.25 0.888 :fastf77 0.0 0.0 8.0e-6 8.5e-6 0.00543 0.00563 0.0426 0.0445 0.437 0.448 :blas 4.5e-6 4.0e-6 1.9e-5 2.1e-5 0.000972 0.00109 0.00712 0.00744 0.0582 0.0607 (Units are seconds per multiplication.) Obviously OpenBLAS is so easy to package that it's not really worth avoiding it, but it was very eye-opening to see just how easy it is to get within an order of magnitude (easier, in fact, than getting into the 10x-20x range). [1]: https://gist.github.com/Sean1708/69c5694048e9a9ca7bd84fcbc9ea6f45 https://gist.github.com/Sean1708/69c5694048e9a9ca7bd84fcbc9e... [2]: 8-core 3.4GHz Haswell i7 with 32kB L1, 256kB L2, 8MB L3, and 8GB RAM.
  - tda 7y ago
    Why is (1025, 1025, 1025) so much faster than (1024, 1024, 1024)?
    - kmbriedis 7y ago
      My guess that it's happening mostly due cache conflicts. With 1024 for a simplified L1 with 32kb you can fit exactly 8 lines of the inner dimmension in the cache, which means that (0,8,0) would have the same cache location as (0, 0, 0), which is bad for tiling

Of course using an optimized blas is somewhat faster, but it is not three orders of magnitude faster!

kmbriedis 7y ago

But it can be 20x

Sean1708 7y ago
I actually did some benchmarking on this once upon a time[1] and it turns out that it's actually really easy to write something that is only ~5x slower[2] (until you get to matrices that don't fit in RAM): (4, 4, 4) (5, 5, 5) (32, 32, 32) (33, 33, 33) (256, 256, 256) (257, 257, 257) (512, 512, 512) (513, 513, 513) (1024, 1024, 1024) (1025, 1025, 1025) –––––––– ––––––––– ––––––––– –––––––––––– –––––––––––– ––––––––––––––– ––––––––––––––– ––––––––––––––– ––––––––––––––– –––––––––––––––––– –––––––––––––––––– :naive 0.0 0.0 1.3e-5 2.0e-5 0.0114 0.0133 0.0942 0.106 3.25 2.39 :tiled 0.0 0.0 2.7e-5 2.2e-5 0.0139 0.0121 0.154 0.101 1.25 0.888 :fastf77 0.0 0.0 8.0e-6 8.5e-6 0.00543 0.00563 0.0426 0.0445 0.437 0.448 :blas 4.5e-6 4.0e-6 1.9e-5 2.1e-5 0.000972 0.00109 0.00712 0.00744 0.0582 0.0607 (Units are seconds per multiplication.) Obviously OpenBLAS is so easy to package that it's not really worth avoiding it, but it was very eye-opening to see just how easy it is to get within an order of magnitude (easier, in fact, than getting into the 10x-20x range). [1]: https://gist.github.com/Sean1708/69c5694048e9a9ca7bd84fcbc9ea6f45 https://gist.github.com/Sean1708/69c5694048e9a9ca7bd84fcbc9e... [2]: 8-core 3.4GHz Haswell i7 with 32kB L1, 256kB L2, 8MB L3, and 8GB RAM.
- tda 7y ago
  Why is (1025, 1025, 1025) so much faster than (1024, 1024, 1024)?
  - kmbriedis 7y ago
    My guess that it's happening mostly due cache conflicts. With 1024 for a simplified L1 with 32kb you can fit exactly 8 lines of the inner dimmension in the cache, which means that (0,8,0) would have the same cache location as (0, 0, 0), which is bad for tiling