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Some advances in the polyhedral model

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dc.contributor.authorGupta, Gautam, author
dc.contributor.authorRajopadhye, Sanjay Vishnu, advisor
dc.contributor.authorBöhm, Anton Pedro Willem, 1948-, committee member
dc.contributor.authorChong, Edwin Kah Pin, committee member
dc.contributor.authorMcConnell, Ross M., committee member
dc.date.accessioned2007-01-03T04:41:41Z
dc.date.available2007-01-03T04:41:41Z
dc.date.issued2010
dc.descriptionDepartment Head: L. Darrell Whitley.
dc.description.abstractThe polyhedral model is a mathematical formalism and a framework for the analysis and transformation of regular computations. It provides a unified approach to the optimization of computations from different application domains. It is now gaining wide use in optimizing compilers and automatic parallelization. In its purest form, it is based on a declarative model where computations are specified as equations over domains defined by "polyhedral sets". This dissertation presents two results. First is an analysis and optimization technique that enables us to simplify---reduce the asymptotic complexity---of such equations. The second is an extension of the model to richer domains called Ƶ-Polyhedra. Many equational specifications in the polyhedral model have reductions---application of an associative and commutative operator to collections of values to produce a collection of answers. Moreover, expressions in such equations may also exhibit reuse where intermediate values that are computed or used at different index points are identical. We develop various compiler transformations to automatically exploit this reuse and simplify the computational complexity of the specification. In general, there is an infinite set of applicable simplification transformations. Unfortunately, different choices may result in equivalent specifications with different asymptotic complexity. We present an algorithm for the optimal application of simplification transformations resulting in a final specification with minimum complexity. This dissertation also presents the Ƶ-Polyhedral model, an extension to the polyhedral model to more general sets, thereby providing a transformation framework for a larger set of regular computations. For this, we present a novel representation and interpretation of Ƶ-Polyhedra and prove a number of properties of the family of unions of Ƶ-Polyhedra that are required to extend the polyhedral model. Finally, we present value based dependence analysis and scheduling analysis for specifications in the Ƶ-Polyhedral model. These are direct extensions of the corresponding analyses of specifications in the polyhedral model. One of the benefits of our results in the Ƶ-Polyhedral model is that our abstraction allows the reuse of previously developed tools in the polyhedral model with straightforward pre- and post-processing.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierGupta_colostate_0053A_10059.pdf
dc.identifierETDF2010100008COMS
dc.identifier.urihttp://hdl.handle.net/10217/40288
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectpolyhedra models
dc.subjectcompilers
dc.subjectprogram analysis
dc.subjectpolyhedral model
dc.subjectloop optimization
dc.subject.lcshPolyhedral functions
dc.subject.lcshCode generators
dc.subject.lcshCompilers (Computer programs)
dc.subject.lcshComputer science-Mathematics
dc.titleSome advances in the polyhedral model
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineComputer Science
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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