S. Wetzel, Automatic code generation in the Polytope Model, mmoire de Master, Univ. Passa , Fak. Math & Inf., 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....limits it to regular transformations. In fact, in the basic model [5] only ane transformations (represented by a matrix) can be treated. Lately, the model was extended, rst, to deal with singular matrices [6] and second, to allow the use of ane by statement and piecewise ane transformations [3, 9]. Dealing with this second extension, in the code generation step, we have to construct the target program from a set of programs already deduced, called target program parts. Our main goal here is to improve this step by giving an ecient approach to derive the target program. In [4] we presented ....

....explain below how the polytope model has been extended to ane by statement and piecewise ane transformations. 4.1 Ane by statement transformations : a transformation is called ane by statement when it has an ane expression for each statement of the source program. The polytope model was extended [9, 3] to deal with these transformations as follows : We consider, instead of the whole source program, a set of programs, called source program parts, having, each, only one statement as abody loop. These programs have the same index space as the original program. We parallelize each source ....

S. Wetzel, Automatic code generation in the Polytope Model, mmoire de Master, Univ. Passa , Fak. Math & Inf., 1995.

....Ng ; The cardinal of F(t) gives the size of the data structure to be allocated at each time step. Actually, one has to compute p 0 (t) min ( x) p f (t) max ( x) 4) then allocate an array Front[t] of size [p f (t) How to compute these bounds is described in [15, 20]. Here, this size is constant and equal to M 1. As hinted before, three dates are of special importance in the course of execution: t 0 = min (x) t mid = min x2Rg (x) t e = max (x) 5) Finally, let us formalize the definition we had given to the period. The time elapsed between a ....

S. Wetzel. Automatic code generation in the polytope model. Master's thesis, U. of Passau, Germany, November 1996. http://brahms.fmi.uni-passau.de/cl/loopo/doc/.

....1) 6 Target Program One of the most intricate problems in parallelizing general loops is to generate code for the transformed program. Even for a set of loops of Class 4 which are not perfectly nested the target code may become very complex, but there are algorithms for an automatic generation [13, 21]. In general, there may not even be a target program which enumerates precisely all transformed points of the execution space: the central problem is to find computable bounds for the loops enumerating (a superset of) the execution set. 6.1 Synchronous Parallelism In general, a synchronous ....

S. Wetzel. Automatic code generation in the polytope model. Diplomarbeit, Fakultat fur Mathematik und Informatik, Universitat Passau, 1995.

....statement are re indexed according to their transformed coordinates. Second, the transformed statements in their respective index spaces (parts) are combined to a single target program. Aside from the two options of synchronous or asynchronous code 1 , three merging strategies are available [23]: The parts are simply combined with a parallel operator, i.e. there are several separate loop nests which are assumed to be executed in parallel. All index spaces of the parts are merged to one index space to construct a perfect loop nest. The statements inside the body are guarded by ....

S. Wetzel. Automatic code generation in the polytope model. Diplomarbeit, Fakultat fur Mathematik und Informatik, Universitat Passau, 1995.

....uniform and non uniform dependences. The allocator. Presently, LooPo provides only Feautrier s allocation method [6] which determines the placement of operations on virtual processors based on the owner computes rule. The target code generator. The target code generation proceeds in three phases [11]: first, the statements of the source program are transformed individually. Then, these transformed statements in their respective index spaces are merged to a single target program. Finally, the target parse tree is translated to one of a variety of possible output languages, e.g. parallel C, ....

S. Wetzel. Automatic code generation in the polytope model. Diplomarbeit, Fakultat fur Mathematik und Informatik, Universitat Passau, 1995. This article was processed using the L A T E X macro package with LLNCS style

....of F(t) gives the size of the data structure to be allocated at each time step. Actually, one has to compute p 0 0 (t) min x2F(t) x) p 0 f (t) max x2F(t) x) 4) then allocate an array Front[t] of size [p 0 0 (t) p 0 f (t) How to compute these bounds is described in [15, 20]. Here, this size is constant and equal to M 1. As hinted before, three dates are of special importance in the course of execution: t 0 = min x2Ng (x) t mid = min x2Rg (x) t e = max x2Ng (x) 5) Finally, let us formalize the definition we had given to the period. The time elapsed ....

S. Wetzel. Automatic code generation in the polytope model. Master's thesis, U. of Passau, Germany, November 1996. http://brahms.fmi.uni-passau.de/cl/loopo/doc/.

....in every statement are re indexed according to its transformed coordinates. Third, the transformed statements in their respective index spaces (parts) are merged to a single target program. Aside from the two options of synchronous or asynchronous code, three merging strategies are available (see [Wet95] for details) 1. The parts are simply combined with a parallel operator, i.e. there are several separate loop nests which are assumed to be executed in parallel. 2. All index spaces of the parts are merged to one index space to construct a perfect loop nest. The statements inside the body are ....

Sabine Wetzel. Automatic code generation in the polytope model. Master's thesis, Universitat Passau, November 1995. http://www.uni-passau.de/~loopo/doc/wetzeld. ps.Z.

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