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    Transforming Complex Loop Nests For Locality

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    Author
    Kennedy, Ken; Yi, Qing
    Date
    February 19, 2002
    Abstract
    Because of the increasing gap between the speeds of processors and standard memory chips, many compiler techniques have been developed to enhance locality of applications. This paper focuses on automatically optimizing complicated loop structures, for which existing techniques are either ineffective or require too much computation time to be practical for a commercial compiler. Building on traditional unimodular transformations on perfectly nested loops, we have developed a novel transformation called dependence hoisting. This transformation facilitates fusion of a set of arbitrarily nested loops at the outermost position of a code segment containing these loops. This transformation is especially useful when the loops to befused are nested inside one another and when some loops cannot be legallydistributed before fusion. We have also developed a transformation framework called computation slicing which applies dependence hoisting to block arbitrary loop nests for better locality. In terms of both asymptotic complexity, which is comparable to that of standard unimodular loop transformations, and actual running time, as measured in our experimental results, computation slicing should be efficient enough for inclusion in commercial production compilers. We have implemented the framework as a Fortransource-to-source translator. Our implementation has successfully blocked four numerical benchmark kernels: Cholesky, QR, LU factorization without pivoting,and LU factorization with partial pivoting. The automatically-blocked benchmarks achieved performance improvements similar to those attained by manually blocked programs in LAPACK. The automatic blocking of QR and LU with partial pivoting is a notable achievement because these benchmarks include loop nests that are considered difficult—to our knowledge, no previous compiler implementation has completely automated the blocking of QR and LU with pivoting. This fact indicates that our technique can in practice match or exceed the effectiveness of many general loop transformation frameworks.
    Citation
    Kennedy, Ken and Yi, Qing. "Transforming Complex Loop Nests For Locality." (2002) https://hdl.handle.net/1911/96293.
    Type
    Technical report
    Citable link to this page
    https://hdl.handle.net/1911/96293
    Rights
    You are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map