The Omega Test: a fast and practical integer programming algorithm for dependence analysis

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The Omega Test: a fast and practical integer programming algorithm for dependence analysis (1992)

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by William Pugh

Venue:	Communications of the ACM
Citations:	520 - 15 self

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@ARTICLE{Pugh92theomega,
    author = {William Pugh},
    title = {The Omega Test: a fast and practical integer programming algorithm for dependence analysis},
    journal = {Communications of the ACM},
    year = {1992},
    volume = {8},
    pages = {4--13}
}

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Abstract

The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0-Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worst-case exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...

Keyphrases

omega test practical integer dependence analysis thiwi sdomi present evi usei producti mips workstati complexi ty dependence analysi6 di rectus array pai ri omega testi dependence exi sts experi ments nteger programmib techni i0-motzki var ble eli937 ti last resort manysib7 ti n array reference sui table toi nteger programmi ng ti n worst-case exponenti al average ti compi ler

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