Abstract
Tiling focuses on very structured computations expressed in perfectly nested loops to expose parallelism or otherwise optimise data locality. In this chapter, the class of perfectly nested loops we consider is defined. Like other iteration-reordering transformations, tiling does not change what is inside an iteration but simply transforms the loop nest into a new one with the same iterations but a new execution order. Since the iterations of a loop nest are considered to be atomic units, it is sufficient to define the data dependences in the loop nest at the level of its iterations. We use a dependence vector abstraction, which encompasses both distance and direction vectors, to capture the vector difference of two dependent iterations. We will also use a dependence polyhedron abstraction to represent a dependence vector equivalently.
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© 2000 Springer Science+Business Media New York
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Xue, J. (2000). Nonsingular Transformations and Permutability. In: Loop Tiling for Parallelism. The Springer International Series in Engineering and Computer Science, vol 575. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4337-4_2
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DOI: https://doi.org/10.1007/978-1-4615-4337-4_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6948-6
Online ISBN: 978-1-4615-4337-4
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