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There are many algorithms for the space-time mapping of nested loops. Some of them even make the optimal choices within their framework. We propose a preprocessing phase for algorithms in the polytope model, which extends the model and yields space-time mappings whose schedule is, in some cases, orders of magnitude faster. These are cases in which the(More)
We present an application of quantifier elimination techniques in the automatic par-allelization 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(More)
— The polytope model has been used successfully as a tool for program analysis and transformation in the field of automatic loop parallelization. However, for the final step of automatic code generation, the generated code is either only usable on shared memory architectures or severely restricts the parallelization methods that can be applied. In this(More)
Automatic parallelization of imperative programs has focused on nests of do loops with aane bounds and aane dependences, because in this case execution domains and dependences are precisely known at compile-time. Parallelization can then be done using a suitable space-time transformation , yielding a logically synchronous program. Code generation consists(More)