Paul Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Proceedings of the International Conference on Supercomputing, pages 175-184, Tokyo, Japan, July 1993. ACM Press.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and the steps are the di erent dimensions of the execution space. The result is a generalised and exact version of Allen and Kennedy s codegen algorithm [6] Feautrier s early papers only address maximising parallelism. Minimising communication between processors is dealt with in a later papers [25, 26, 29] using so called placement functions, also called space mappings. The algorithms have been implemented in the PIPS project [66] and the LooPo project [56] both automatic parallelisation environments, under development since 1988 and 1994 respectively. PIPS is a powerful optimisation environment ....

Paul Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Proceedings of the International Conference on Supercomputing, pages 175-184, Tokyo, Japan, July 1993. ACM Press.

....the detection of parallelism. These works dioeer from ours for two main reasons: the parallelization happens at the procedure level, not at the object level and distribution issues are not addressed. We also have to cite the corpus of work devoted to automatic parallelization of Fortran programs [8, 18, 19] which, in a large part, consists in the denition of data dependence tests, with the goal of targeting distributed memory architectures. Detection of parallelism and automatic distribution are traditionally two dioeerent tasks in compilers parallelizers 18 since data structures, usually arrays of ....

P. Feautrier. Toward automatic partitioning of arrays for distributed memory computers. In Proceedings of the 1993 ACM International Conference on Supercomputing, Tokyo, Japan, July 1993.

.... the data distribution with an affine function and they try to optimize some communications (broadcasts, message vectorization) DR93, DR94] With a similar idea Feautrier introduces the computation of a placement function which completely characterizes the data and tasks distribution of a program [Fea93]. The placement gives the identity of the virtual processor that executes each instruction. The goal of the placement function is to minimize the volume of communication. Compared to the above methods, this approach works on any loop nest where the array accesses are affine functions and it is ....

....first three instructions are fully parallel and the last instruction has only two parallel loops (the innermost one on k is sequential) 1. 3 Placement function The placement function associates to each instruction a multidimensional affine function of the loop indices and the structure parameters [Fea93]. It specifies explicitly the placement of the instruction on a virtual processor grid, i.e. gives the identity of the virtual processor that executes each operation of the instruction. For a given instruction s, each dimension of its placement function is represented with a prototype s which ....

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P. Feautrier. Toward Automatic Partitioning of Arrays on Distributed Memory Computers. In ACM ICS'93, pages 175--184, Tokyo, July 1993.

....procedure to traverse the nesting tree from outside in. Such a strategy gives more opportunities to discover parallelism at the outer nesting levels, which induce less frequent communications than the inner nesting levels. The complexities of our algorithms are polynomial. Feautrier [9]: Feautrier s method is an automatic computation decomposition algorithm for arbitrary loop nestings. However, his method is very fine grained, dealing with the statements of the loop body individually. On the other hand, our method is coupled with program transformations. It organizes the loop ....

....than statements. This gives us the benefits of vectorized communications and less code generation overhead. Also, Feautrier does not consider the use of data redistribution at the moment. Darte and Robert [5, 6, 7] Darte and Robert followed the same statement distributing approach as Feautrier [9] did. They treated a class of more restricted loop nests, called uniform loop nests. These are perfect nests with constant data dependences. 7 Conclusion We have developed an algorithmic framework which can automatically select a good computation and data decomposition for a user program. There ....

Paul Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In ACM ICS '93, Tokyo, Japan, July 1993.

....constraints as a set of homogeneous linear equations which can be solved by the Gaussian elimination method. Both the LA and the CA are polynomial in complexity. They are the major contributions of this paper. Our approach has been influenced by the work of Lam et al. 3, 2, 1] Feautrier [14] and Chatterjee et al. 6, 9, 7] However, our work generalizes and improves their work in several ways. Some detailed comments are in Section 8. This paper is organized as follows. In Section 2, we give an overview of our compiler and major components of our automatic decomposition module. ....

....to traverse the nesting tree from outside in. Such a strategy makes more opportunities to discover parallelism at the outer nesting levels, which induces less frequent communications than if they are at the inner nesting levels. The complexities of our algorithms are polynomial. Feautrier [14]: The idea of expressing decomposition constraints as linear equations first came from Feautrier [14] However, the method presented in [14] seems not adequate for distributed memory machines, because the data decomposition only comes as a second thought. His method is very fine grained, dealing ....

[Article contains additional citation context not shown here]

Paul Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In ACM ICS '93, Tokyo, Japan, July 1993.

....exploration tree of all possibilities is generated to solve the dynamic problem, and limits redistribution at the outermost loop level in order to reduce the complexity. Their cost model is based only in the data movement, and propose branch and bound to further reduce complexity. 28 Chapter 2 [Fea93] considers the static distribution of data and computation among a two dimensional processors geometry, in a DMM. The source code is restricted to assignments and DO loops. He constructs the Dataflow Graph that allows the representation of communication patterns in the source program. He ....

P. Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Proceedings of the 7th ACM International Conference on Supercomputing, Tokyo, Japan, July 1993.

....processor graphs. Most importantly, these heuristics concentrate on compile time scheduling and cannot deal with dynamic behaviours. Much of research is currently pursued in the context of automatic data partitioning, i.e. in which the task mapping is determined through the data mapping solution [12, 20, 25, 34, 42, 38]. However, these approaches are aimed towards compile time scheduling and thus have a restricted application (e.g. they assume affine array index functions) Hence, they are not amenable for applications in which run time scheduling is necessary. Despite all these initiatives such as HPF, most ....

P. Feautrier, "Toward automatic partitioning of arrays on distributed memory computers," in Proc. 7th ACM Int. Conf. on Supercomputing, Tokyo, July 1993, pp. 175--184.

....program. One then obtains an affine schedule which gives the execution date of every operation. This schedule may be one dimensional [Fea92b] or possibly multi dimensional [Fea92a] A space mapping is also computed, yielding a virtual geometry or template on which operations are to be executed [Fea93]. This space mapping is again an affine function in the original loop counters. These elements compose a space time mapping 1 . Once a space time mapping is chosen, the corresponding parallel code has to be generated; this is the central theme of this paper. A space time mapping is in fact a ....

P. Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In ACM ICS'93, Tokyo, July 1993. also available as IBP/report 92.95.

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P Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Int'l Conf. on Supercomputing, July 1993. Japan.

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P Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Int'l Conf. on Supercomputing, July 1993. Japan.

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P Feautrier. Toward automatic partitioning of arrays on distributed memory computers. In Int'l Conf. on Supercomputing, July 1993. Japan.

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