Linear algebra over small extensions of GF(2).

People

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

Improve performance of Travolta multiplication

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

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