A. Darte. Techniques de parall'elisation automatique de nids de boucles. PhD thesis, LIP ENS-Lyon, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....graphe de d ependances. Il en existe plusieurs variantes, dont le data ow graph, le 8 data dependence graph [71] 5] le program dependence graph [45] ou le dependence ow graph [84] L utilisation de ces graphes dans le cas particulier de la parall elisation est d ecrit dans [95] 43] 5] ou [33], et pour la comparaison de sous programmes dans [86] ou [6] Consid erant l exemple centaur, on peut d eplorer le trop petit nombre d applications en vraie grandeur, c est a dire produisant des outils s appliquant a des programmes r eels, de mani ere ecace. On soulignera cependant les ....

Darte A. "Techniques de parallelisation automatique de nids de boucles". PhD thesis, ENS Lyon, Universite Lyon-1, 1993.

....necessary, unless one programs a redundancy eliminator. Another solution is to use PIP for computing maxima and minima, in which case redundancy is automatically eliminated [CBF95] Non unimodular transformations In case T is not unimodular, the solution is to build its Hermite normal form T = HU [Dar93, Xue94]. One builds, according to the above method, a loop nest which scans U (D) Since, due to the special form of H, the transformation y = Hz is monotonic with respect to lexicographic ordering, it is enough to apply H to the loop counters of the new loop nest in order to generate the correct code. ....

A. Darte. Techniques de parall'elisation automatique de nids de boucles. PhD thesis, ENS Lyon, April 1993.

.... y is a monotone increasing function of z. Since Q is unimodular, we may find a loop nest wich scans the Z polyhedron QD S by the above method. This loop nest is then rewritten in term of y by applying the matrix H . In particular, the diagonal elements of H give the steps of the new loop nest [Dar93, Ris94, Xue94] The most complicated case is the one in which we have to rewrite several statements with different transformations. Each transformation has the same target space and is supposed to have full rank. However, it is not necessary to suppose that the whole transformation is one to ....

....process for this case may be explained simply in term of loop rewriting. Let us suppose first that the schedule for statement S, S is one dimensional and is defined by a primitive timing vector 1 h S . One extends h S to a unimodular matrix by constructing its Hermite normal form [Dar93] A more complicated process is needed when the timing vector is not primitive or when the schedule is multidimensional, see [Col94] If the schedule has been computed from the dataflow graph, one has to do some form of data expansion to obtain a correct program. Single assignment conversion is ....

A. Darte. Techniques de parall'elisation automatique de nids de boucles. PhD thesis, ENS Lyon, April 1993.

....be immediately extended to multi dimensional schedules, since steps or periods along these dimensions are not simply the gcd of their corresponding scheduling vector entries. Given the matrix of the transformation, the steps are in fact the diagonal coefficients of the Hermite form of this matrix [Dar93]. We will here restrict ourselves to one dimensional schedules but give multi dimensional generalizations when appropriate. Even though the bulk of our algorithms would not change, taking multi dimensional schedules into account needs more comprehensive linear algebra techniques. 3 Reindexation ....

A. Darte. Techniques de parall'elisation automatique de nids de boucles. PhD thesis, LIP, ENS Lyon, France, 1993.

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A. Darte. Techniques de parall'elisation automatique de nids de boucles. PhD thesis, LIP ENS-Lyon, 1993.

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