|
Size: 667
Comment:
|
Size: 1271
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 11: | Line 11: |
| * Robert Miller | * Robert Miller (especially sparse GF(2)) |
| Line 18: | Line 18: |
| * Implement Strassen (variant) for dense matrix reduction. The result should be faster than anything else available. Greg has two strategies in mind. We'll implement both and compare their speed. * Improve/implement multi-core matrix multiplication and if feasible multi-core reduction * If there is time: sparse matrix techniques |
* implement LQUP decomposition [Clement] * implement LQUP routine * implement TRSM routine * implement efficient column swaps/rotations [Martin] * SSE2 might help a lot here * implement memory efficient mzd_addmul_strassen [Martin] * See Clement's et al. paper on memory efficient Strassen-Winograd * implement Arne's asymptotically fast reduction algorithm [Martin] * implement multi-core multiplication with optimal speed-up * OpenMP seems to be nice and easy * 2 cores probably main target, but think about 4 cores too * improve efficiency of M4RM * try 7 instead of 8 Gray code tables to leave room for the actual matrix in L1 * try to fit three matrices rather than two into L2 or understand why it works so good for two * detect L1/L2 cache sizes at runtime and choose optimal parameters for them * implement Bill's half table idea and benchmark it |
Dev Days 1: Exact Linear Algebra
- Michael Abshoff
- Martin Albrecht
- Nick Alexander
- Gregory Bard
- Rob Beezer
- Tom Boothby
- Craig Citro
- Burcin Erocal
- Robert Miller (especially sparse GF(2))
- David Roe (p-adic linear algebra?)
- Arne Storjohann
- William Stein
- Ralf-Philipp Weinmann
GF(2)
- implement LQUP decomposition [Clement]
- implement LQUP routine
- implement TRSM routine
- implement efficient column swaps/rotations [Martin]
- SSE2 might help a lot here
- implement memory efficient mzd_addmul_strassen [Martin]
- See Clement's et al. paper on memory efficient Strassen-Winograd
- implement Arne's asymptotically fast reduction algorithm [Martin]
- implement multi-core multiplication with optimal speed-up
- OpenMP seems to be nice and easy
- 2 cores probably main target, but think about 4 cores too
- improve efficiency of M4RM
- try 7 instead of 8 Gray code tables to leave room for the actual matrix in L1
- try to fit three matrices rather than two into L2 or understand why it works so good for two
- detect L1/L2 cache sizes at runtime and choose optimal parameters for them
- implement Bill's half table idea and benchmark it