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  1. Transactions on Programming Languages and Systems (TOPLAS)
  2. ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 34
  3. Issue 1, April 2012
  4. Parameterized loop tiling
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ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 38
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 37
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 36
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 35
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 34
Issue 4, December 2012
Issue 3, October 2012
Issue 2, June 2012
Issue 1, April 2012
Editorial
Implicit dynamic frames
Parameterized loop tiling
A data-centric approach to synchronization
ScalaExtrap: Trace-based communication extrapolation for SPMD programs
Algorithmic verification of asynchronous programs
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 33
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 32
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 31
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 30
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 29
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 28
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 27
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 26
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 25
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 24
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 23
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 22
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 21
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 20
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 19
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 18
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 17
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 16
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 15
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 14
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 13
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 12
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 11
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 10
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 9
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 8
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 7
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 6
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 5
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 4
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 3
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 2
ACM Transactions on Programming Languages and Systems (TOPLAS) : Volume 1

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Parameterized loop tiling

Content Provider ACM Digital Library
Author Rajopadhye, Sanjay Renganarayanan, Lakshminarayanan Kim, Daegon Strout, Michelle Mills
Copyright Year 2012
Abstract Loop tiling is a widely used program optimization that improves data locality and enables coarse-grained parallelism. Parameterized tiled loops, where the tile sizes remain symbolic parameters until runtime, are quite useful for iterative compilers and autotuners that produce highly optimized libraries and codes. Although it is easy to generate such loops for (hyper-) rectangular iteration spaces tiled with (hyper-) rectangular tiles, many important computations do not fall into this restricted domain. In the past, parameterized tiled code generation for the general case of convex iteration spaces being tiled by (hyper-) rectangular tiles has been solved with bounding box approaches or with sophisticated and expensive machinery. We present a novel formulation of the parameterized tiled loop generation problem using a polyhedral set called the $\textit{outset}.$ By reducing the problem of parameterized tiled code generation to that of generating standard loops and simple postprocessing of these loops, the outset method achieves a code generation efficiency that is comparable to existing code generation techniques, including those for fixed tile sizes. We compare the performance of our technique with several other tiled loop generation methods on kernels from BLAS3 and scientific computations. The simplicity of our solution makes it well suited for use in production compilers—in particular, the IBM XL compiler uses the inset-based technique introduced in this article for register tiling. We also provide a complete coverage of parameterized tiling of perfect loop nests by describing three related techniques: (i) a scheme for separating full and partial tiles; (ii) a scheme for generating tiled loops directly from the abstract syntax tree representation of loops; (iii) a formal characterization of parameterized loop tiling using bilinear forms and a Symbolic Fourier-Motzkin Elimination (SFME)-based parameterized tiled loop generation method.
Starting Page 1
Ending Page 41
Page Count 41
File Format PDF
ISSN 01640925
e-ISSN 15584593
DOI 10.1145/2160910.2160912
Volume Number 34
Issue Number 1
Journal ACM Transactions on Programming Languages and Systems (TOPLAS)
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2012-05-04
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Fourier-Motzkin elimination Parameterized tiling Bounding box Code generation
Content Type Text
Resource Type Article
Subject Software
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