Quantifier elimination in automatic loop parallelization
نویسندگان
چکیده
منابع مشابه
Quantifier Elimination in Automatic Loop Parallelization
We present an application of quantifier elimination techniques in the automatic parallelization of nested loop programs. The technical goal is to simplify affine inequalities whose coefficients may be unevaluated symbolic constants. The values of these so-called structure parameters are determined at run time and reflect the problem size. Our purpose here is to make the research community of qu...
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Quantifier elimination (QE) is a very powerful procedure for problems involving firstorder formulas over real fields. The cylindrical algebraic decomposition (CAD) is a technique for the “efficient” im plementation of QE, that effectively reduces an seemingly infinite problem into a finite (but potentially large) instance. For much more information about QE and CAD (including a reprint of Tar...
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An important problem in automatic parallelization of scientiic programs is to generate loops from an algebraic description of the iteration domain. The usual technique is to produce a perfectly nested set of loops, whose bounds consist in maxima and minima of several aane functions. However, perfect loop nests suuer from the run-time overhead of evaluating bound expressions and do not allow to ...
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An approach for automatically generating loop invariants using quantifier-elimination is proposed. An invariant of a loop is hypothesized as a parameterized formula. Parameters in the invariant are discovered by generating constraints on the parameters by ensuring that the formula is indeed preserved by the execution path corresponding to every basic cycle of the loop. The parameterized formula...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2006
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2005.09.012