Naive guess happens as long as all three matrices t

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Unformatted text preview: ize goes up! How long does this happen? • Naive guess: happens as long as all three matrices fit in cache (N ≤ sqrt(C/3)) • On Itanium: should happen when N ≤ 104 Tuesday, February 2, 2010 Miss-rate regimes • • • • When a matrix fits entirely in cache, it experiences temporal and spatial locality • Misses: N2/b If a matrix is being walked in row-major order, it may experience spatial locality, but not temporal locality • • Only get a miss 1 out of b accesses Misses: N3/b Other times, a matrix experiences no locality • • Every access misses Misses: N3 (What about a matrix that only experiences temporal locality?) Tuesday, February 2, 2010 Predicting miss rates • To predict a miss rate, we need to determine, for each matrix: • Whether it experiences no locality, spatial locality, or both spatial and temporal locality • At which point the matrix transitions between the various regimes Tuesday, February 2, 2010 Stack distance • • Introduced by Mattson et al. in 1970 The stack distance of a memory location is the number of distinct cache lines touched between successive accesses to that location • Called stack distance because it can be calculated with a reuse stack • Also called reuse distance Tuesday, February 2, 2010 Stack distance • We introduce two types of stack distance: • dt(M): the stack distance between successive accesses to a given element of M • • • ds(M): the minimum stack distance between successive accesses to distinct elements of M that lay on the same cache line If C < b* dt(M), matrix does not have temporal locality • By the time we touch the same element again, we’ve brought in too many other elements into cache If C < b*ds(M), matrix does not have spatial locality Tuesday, February 2, 2010 C...
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This document was uploaded on 04/05/2014.

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