William Pugh
Abstract
Data dependence distance is widely used to characterize data dependences in advance optimizing compilers. The standard definition of dependence distance assumes that loops are normalized (have constant lower bounds and a step of 1); there is not a commonly accepted definition for unnormalized loops. We have identified several potential definitions, all of which give the same answer for normalized loops. There are a number of subtleties involved in choosing between these definitions, and no one definition is suitable for all applications.
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Index Terms
- Definitions of dependence distance
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Reviews
Gerald David Chandler
The advent of vector and other parallel processing computers led to the development of systems for automatically transforming sequential programs into forms that use hardware parallelism. A key element in determining whether loop-reorganizing transformations preserve program semantics is the notion of data dependence distance vectors, which formalizes the idea of how much loop indexes differ for two statements accessing the same element of a subscripted array. Pugh points out that in systems such as KAP and Para frase-2 different definitions of dependence distance are used and that these definitions are not equivalent when loops are not normalized (that is, when the loop index does not start at 1 and have a step of 1). He says this has led to incorrect analysis and transformation of some statements by KAP and Parafrase-2. To clarify these problems, Pugh considers four alternative definitions, two of which incorporate normalizing elements, and concludes that no one definition is best for all cases. This short paper should be clear to a specialist in the field. It is unlikely the paper would be of interest to others, and it could not be understood without considerable background obtained elsewhere.
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