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| * implement LQUP decomposition [Clement] * implement LQUP routine * implement TRSM routine |
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| * implement Arne's asymptotically fast reduction algorithm [Martin] | * implement Arne's asymptotically fast elimination algorithm [Martin] |
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, Martin]
- implement LQUP routine [Clement]
- implement TRSM routine [Clement]
- 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 elimination 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