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| ==== 2000 x 2000 ==== || n || M4rie mul || Magma mul || M4rie elim || Magma elim || || 2 || 0.36 || 0.15 || 0.24 || 0.17 || || 3 || 0.59 || 0.36 || 0.38 || 0.33 || || 4 || 0.61 || 0.68 || 0.39 || 0.48 || || 5 || 2.55 || 14.02 || 1.27 || 7.20 || || 6 || 3.47 || 14.30 || 1.45 || 7.36 || || 7 || 3.62 || 14.48 || 1.82 || 7.46 || || 8 || 4.80 || 19.67 || 2.77 || 9.95 || || 9 || 27.00 || 51.66 || 14.75 || 19.59 || || 10 || 47.89 || 51.44 || 28.95 || 19.09 || |
Linear algebra over small extensions of GF(2).
People
Martin Albrecht
- Ciaran Mullan
Library
The library is here: http://bitbucket.org/malb/m4rie
Get in contact with Martin Albrecht to get commit rights.
Sage Patch
A patch for Sage is here: https://bitbucket.org/malb/m4rie/downloads/m4rie_for_sage.patch
Todo
Implement simple functions in m4rie
Examples: stacking, augmenting, printing
Write C test code
Write C documentation
Implement methods of Sage class
Write documentation for Sage class
Improve performance of Travolta-Gaussian elimination
- use more than one table
Improve performance of Travolta multiplication
- get inspiration from M4RM
Implement Strassen multiplication
Preliminary Bench***market***ing
r1
1000 x 1000
n |
M4rie mul |
Magma mul |
M4rie elim |
Magma elim |
2 |
0.06 |
0.02 |
0.04 |
0.06 |
3 |
0.08 |
0.06 |
0.05 |
0.10 |
4 |
0.09 |
0.10 |
0.06 |
0.08 |
5 |
0.35 |
1.82 |
0.20 |
0.98 |
6 |
0.44 |
1.82 |
0.22 |
0.97 |
7 |
0.36 |
1.85 |
0.29 |
0.98 |
8 |
0.62 |
2.52 |
0.44 |
1.30 |
9 |
4.94 |
6.46 |
2.93 |
2.41 |
10 |
11.96 |
6.43 |
8.10 |
2.40 |
r2
1000 x 1000
n |
M4rie mul |
Magma mul |
M4rie elim |
Magma elim |
2 |
0.06 |
0.02 |
0.04 |
0.05 |
3 |
0.08 |
0.06 |
0.05 |
0.07 |
4 |
0.08 |
0.11 |
0.06 |
0.08 |
5 |
0.17 |
1.79 |
0.12 |
0.98 |
6 |
0.21 |
1.82 |
0.15 |
0.98 |
7 |
0.29 |
1.85 |
0.23 |
0.98 |
8 |
0.43 |
2.51 |
0.37 |
1.29 |
9 |
5.04 |
6.45 |
3.01 |
2.42 |
10 |
11.95 |
6.45 |
8.11 |
2.39 |
2000 x 2000
n |
M4rie mul |
Magma mul |
M4rie elim |
Magma elim |
2 |
0.36 |
0.15 |
0.24 |
0.17 |
3 |
0.59 |
0.36 |
0.38 |
0.33 |
4 |
0.61 |
0.68 |
0.39 |
0.48 |
5 |
2.55 |
14.02 |
1.27 |
7.20 |
6 |
3.47 |
14.30 |
1.45 |
7.36 |
7 |
3.62 |
14.48 |
1.82 |
7.46 |
8 |
4.80 |
19.67 |
2.77 |
9.95 |
9 |
27.00 |
51.66 |
14.75 |
19.59 |
10 |
47.89 |
51.44 |
28.95 |
19.09 |
r3
1000 x 1000
n |
M4rie mul |
Magma mul |
M4rie elim |
Magma elim |
2 |
0.06 |
0.02 |
0.04 |
0.08 |
3 |
0.07 |
0.06 |
0.04 |
0.08 |
4 |
0.08 |
0.11 |
0.05 |
0.10 |
5 |
0.17 |
1.79 |
0.09 |
0.95 |
6 |
0.21 |
1.81 |
0.12 |
0.98 |
7 |
0.29 |
1.85 |
0.19 |
1.00 |
8 |
0.43 |
2.51 |
0.33 |
1.29 |
9 |
4.84 |
6.44 |
2.82 |
2.41 |
10 |
11.84 |
6.43 |
8.12 |
2.41 |
2000 x 2000
n |
M4rie mul |
Magma mul |
M4rie elim |
Magma elim |
2 |
0.36 |
0.15 |
0.20 |
0.18 |
3 |
0.58 |
0.36 |
0.23 |
0.34 |
4 |
0.63 |
0.73 |
0.28 |
0.48 |
5 |
2.77 |
14.13 |
0.71 |
7.32 |
6 |
3.18 |
14.31 |
0.90 |
7.46 |
7 |
4.53 |
14.54 |
1.47 |
7.49 |
8 |
4.98 |
19.75 |
2.90 |
10.07 |
9 |
26.83 |
51.71 |
14.86 |
19.23 |
10 |
48.22 |
51.66 |
32.74 |
19.45 |