Discrete Mathematics University of Kentucky CS 275 Spring ... - MGNet

portable Level 3 BLAS Winograd variant of Strassen's matrix-matrix multiply
algorithm, Journal of Computational Physics, 110 (1994), pp. 1-10 for an
answer).
The 22 steps are the following:
Step W mk C 11 C 12 C 21 C 22 W kn Operation
1 S 7 B 22 4B 12
2 S 3 A 11 4A 21
3 M 4 S 3 S 7
4 S 1 A 21 +A 22
5 S 5 B 12 4B 11
6 M 5 S 1 S 5
7 S 6 B 22 4S 5
8 S 2 S 1 4A 11
9 M 1 S 2 S 6
10 S 4 A 12 4S 2
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Step W mk C 11 C 12 C 21 C 22 W kn Operation
11 M 6 S 4 B 22
12 T 3 M 5 +M 6
13 M 2 A 11 B 11
14 T 1 M 1 +M 2
15 C 12 T 1 +T 3
16 T 2 T 1 +M 4
17 S 8 S 6 4B 21
18 M 7 A 22 S 8
19 C 21 T 2 4M 7
20 C 22 T 2 +M 5
21 M 3 A 12 B 21
22 C 11 M 2 +M 3
There are four tricky steps in the table above, depending on whether or not k is
even or odd. Each step makes certain that we do not use more memory than is
allocated for a submatrix or temporary. For example,
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