An analytical model for ATLAS

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Presentation transcript:

An analytical model for ATLAS Joint work with Keshav Pingali (Cornell) Gerald DeJong Maria Garzaran

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 LRU Replacement

Explanation for LRU Model (I)

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:

Finding MU, NU, KU Following our code-generating strategy, we need If we simplify MU=NU, we get Once NU is obtained, MU*NU+ MU + NU + TR ≤ NR NU2+ 2*NU + (TR-NR) ≤ 0 MU = (NR-TR-NU) / (NU+1)