Paper Info
Title
Tight bounds on cache use for stencil operations on rectangular grids
Abstract
We derive tight bounds on cache misses for evaluation of explicit stencil operators on rectangular grids. Our lower bound is based on the isoperimetric property of the discrete crosspolytope. Our upper bound is based on a good surface-to-volume ratio of a parallelepiped spanned by a reduced basis of the interference lattice of a grid. Measurements show that our algorithm typically reduces the number of cache misses by a factor of three, relative to a compiler optimized code. We show that stencil calculations on grids whose interference lattices have a short vector feature abnormally high numbers of cache misses. We call such grids unfavorable and suggest to avoid these in computations by appropriate padding. By direct measurements on a MIPS R10000 processor we show a good correlation between abnormally high numbers of cache misses and unfavorable three-dimensional grids.
Year
DOI
Venue
2002
10.1145/567112.567115
J. ACM
Keywords
DocType
Volume
fundamental parallelepiped,cache use,cache memory,tight bound,reduced basis,lattice,interference lattice,explicit stencil operator,good correlation,lower and upper bounds,short vector feature abnormally,structured grids,high number,rectangular grid,abnormally high number,unfavorable three-dimensional grid,scientific computing,cache misses,stencil calculation,stencil operation,good surface-to-volume ratio
Journal
49
Issue
ISSN
Citations 
3
0004-5411
4
PageRank 
References 
Authors
0.54
7
2
Name
Order
Citations
PageRank
Michael A. Frumkin112619.68
Rob F. Van der Wijngaart237445.61