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Conference Papers Year : 2023

Algebraic Tiling


In this paper, we present an ongoing work whose aim is to propose a new loop tiling technique where tiles are characterized by their volumes-the number of embedded iterations-instead of their sizes-the lengths of their edges. Tiles of quasi-equal volumes are dynamically generated while the tiled loops are running, whatever are the original loop bounds, which may be constant or depending linearly of surrounding loop iterators. The adopted strategy is to successively and hierarchically slice the iteration domain in parts of quasi-equal volumes, from the outermost to the innermost loop dimensions. Since the number of such slices can be exactly chosen, quasi-perfect load balancing is reached by choosing, for each parallel loop, the number of slices as being equal to the number of parallel threads, or to a multiple of this number. Moreover, the approach avoids partial tiles by construction, thus yielding a perfect covering of the iteration domain minimizing the loop control cost. Finally, algebraic tiling makes dynamic scheduling of the parallel threads fairly purposeless for the handled parallel tiled loops.
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Dates and versions

hal-03944790 , version 1 (18-01-2023)


  • HAL Id : hal-03944790 , version 1


Clément Rossetti, Philippe Clauss. Algebraic Tiling. IMPACT 2023, 13th International Workshop on Polyhedral Compilation Techniques, Jan 2023, Toulouse, France. ⟨hal-03944790⟩
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