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An analytical model for ATLAS

An analytical model for ATLAS. matmul(c[i:i+NB-1,j:j+NB-1], a[i:i+NB-1,k:k+NB-1],b[k:k+NB-1,j:j+NB-1]) for (int j = 0; j < NB ; j++) for (int i = 0; i < NB; i++) for (int k = 0; k < NB; k++) c[i][j] += a[i][k] * b[k][j]. Modeling for Tile Size (NB).

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An analytical model for ATLAS

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  1. An analytical model for ATLAS

  2. matmul(c[i:i+NB-1,j:j+NB-1], a[i:i+NB-1,k:k+NB-1],b[k:k+NB-1,j:j+NB-1]) for (int j = 0; j < NB; j++) for (int i = 0; i < NB; i++) for (int k = 0; k < NB; k++) c[i][j] += a[i][k] * b[k][j]

  3. Modeling for Tile Size (NB) • Models of increasing complexity • 3*NB2 ≤ C • Whole work-set fits in L1 • NB2 + NB + 1 ≤ C • Fully Associative • Optimal Replacement • Line Size: 1 word • or • Line Size > 1 word • or • LRU Replacement

  4. Explanation for LRU Model (I)

  5. Explanation for LRU Model (II) Each iteration of j requires: -NB2 elems of A -a column of C (NB elems) -a column of B (NB elems) In the middle of iteration j+1, being able to reuse the Elements of A requires holding not one, but two colums of B; and one extra element of C. Thus:

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