isl: An Integer Set Library for the Polyhedral Model
In compiler research, polytopes and related mathematical objects have been successfully used for several decades to represent and manipulate computer programs in an approach that has become known as the polyhedral model. The key insight is that the kernels of many compute-intensive applications are composed of loops with bounds that are affine combinations of symbolic constants and outer loop iterators. The iterations of a loop nest can then be represented as the integer points in a (parametric) polytope and manipulated as a whole, rather than as individual iterations. A similar reasoning holds for the elements of an array and for mappings between loop iterations and array elements.
Unable to display preview. Download preview PDF.
- 3.Bastoul, C.: Code generation in the polyhedral model is easier than you think. In: PACT 2004, pp. 7–16. IEEE Computer Society, Los Alamitos (2004)Google Scholar
- 5.Beletska, A., Barthou, D., Bielecki, W., Cohen, A.: Computing the transitive closure of a union of affine integer tuple relations. In: COCOA 2009, pp. 98–109. Springer, Heidelberg (2009)Google Scholar
- 7.Chen, C.: Omega+ library (2009), http://www.cs.utah.edu/~chunchen/omega/
- 9.Cook, W., Rutherford, T., Scarf, H.E., Shallcross, D.F.: An implementation of the generalized basis reduction algorithm for integer programming. Cowles Foundation Discussion Papers 990, Cowles Foundation, Yale University (August 1991)Google Scholar
- 13.Free Software Foundation, Inc.: GMP, available from ftp://ftp.gnu.org/gnu/gmp
- 14.Fukuda, K., Liebling, T.M., Lütolf, C.: Extended convex hull. In: Proceedings of the 12th Canadian Conference on Computational Geometry, pp. 57–63 (2000)Google Scholar
- 16.Kelly, W., Maslov, V., Pugh, W., Rosser, E., Shpeisman, T., Wonnacott, D.: The Omega library. Tech. rep., University of Maryland (November 1996)Google Scholar
- 17.Kelly, W., Pugh, W., Rosser, E., Shpeisman, T.: Transitive closure of infinite graphs and its applications. Int. J. Parallel Program. 24(6), 579–598 (1996)Google Scholar
- 18.Loechner, V.: PolyLib: A library for manipulating parameterized polyhedra. Tech. rep., ICPS, Université Louis Pasteur de Strasbourg, France (March 1999)Google Scholar
- 21.Rambau, J.: TOPCOM: Triangulations of point configurations and oriented matroids. In: Cohen, A.M., Gao, X.S., Takayama, N. (eds.) ICMS 2002, pp. 330–340 (2002)Google Scholar
- 22.Verdoolaege, S., Janssens, G., Bruynooghe, M.: Equivalence checking of static affine programs using widening to handle recurrences. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 599–613. Springer, Heidelberg (2009)Google Scholar