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

2. 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

3. Explanation for LRU Model (I)

4. 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:

5. 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)