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...esearch community. The comparison with other approaches from the literature is in some cases infeasible because there is insufficient information for us to reconstruct a complete transformation (e.g. =-=[2]-=-). For others [37, 36, 35], a complete description of the algorithm allows us to manually construct the transformation; but since we do not have access to an implementation that can be run to determin...

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...our representation lies in the simplicity of the formalism to compose non-unimodular transformations across long, flexible sequences. Existing formalisms have been designed for black-box optimization =-=(8, 11, 12)-=- , and applying a classical loop transformation within them — as proposed in (9, 10, 3) — requires a syntactic form of the program to anchor the transformation to existing statements. Up to now, the e...

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...rms[17]. Ahmed et al. have also developed a heuristic procedure thatsnds outermost fully permutable loop nests in two steps: thesrst turns arbitrary loop nests into a highdimensional perfect loop nest=-=[1, 2]-=-, and then unimodular techniques are used to create fully permutable loop nests. The approach of just blocking fully permutable loop nests, however, is inadequate. Most programs cannot be made into on...

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...sformations. Loop transformations that enhance data locality, such as tiling [7, 33, 34, 16], and fusion [18], or code transformations such as data shackling [14] and the product-space transformation =-=[1]-=- are techniques to increase data reuse. These compiler transformations rely, sometimes implicitely, on models of memory behavior to predict performance in order to select which optimizations are appli...

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..., [74], and analytic models of the impact of tiling on locality in perfectly nested loops have been developed [20], [42], [52]. Frameworks for handling imperfectly nested loops have been presented in =-=[1]-=-, [45], and [65]. Ahmed et al. [1] have developed a framework that embeds an arbitrary collection of loops into an equivalent perfectly nested loop that can be tiled; this allows a cleaner treatment o...

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...program transformations; this framework relies on a unified representation of loops and statements, the foundations of which where presented in [10], improving on classical polyhedral representations =-=[13, 34, 17, 22, 1, 23]-=-. Using this representation, a large array of useful and efficient program transformations (loop fusion, tiling, array forward substitution, statement reordering, software pipelining, array padding, ...

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...6, 47, 42], and analytic models of the impact of tiling on locality in perfectly nested loops have been developed [18, 31, 39]. Frameworks for handling imperfectly nested loops have been presented in =-=[2, 33, 42]-=-. Ahmed et. al. [2] have developed a framework that embeds an arbitrary collection of loops into an equivalent perfectly nested loop that can be tiled; this allows a cleaner treatment of imperfectly n...