M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24--33, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....be used to convert programs with ane dependencies into this form, our analysis will be most useful in cases where an expanded form was obtained for other reasons (e.g. parallelism detection) and one now seeks to reduce storage requirements. We will refer to the example in Figure 1, borrowed from [18]. It clearly falls within our input domain, as the dependencies have constant distance, and iteration (i; j) assigns to A[i] j] This example could represent a computation where a one dimensional arrayA[i]isbeing updated over a time dimension j, and the intermediate results are being stored. We ....

....arrayA[i]isbeing updated over a time dimension j, and the intermediate results are being stored. We assume that only the element A[n] m] is used outside the loop; the other values are only temporary. 3. 2 Occupancy Vectors We arrive at a simple model of storage reuse via the occupancy vector [18]. Informally, an occupancy vector for a given array de nes equivalence classes over the locations of the array. Two locations of an array are stored in the same location following a storage transformation if and only if they are separated byanintegral multiple of the occupancy vector: ######### ....

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M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. ACM SIGPLAN Notices, 33(11):24-33, Nov. 1998.

....and execution orderings, we restrict our attention to ane dependences and ane schedules [7] The second assumption concerns our approach to the optimized storage mapping. Instead of allowing a fully associative map of size m, as above, we employ the occupancy vector as a mechanism of storage reuse [23]. Chapter 2 contains more background information on ane schedules and occupancy vectors. In this context, we show how to determine 1) a good storage mapping for a given schedule, 2) a good schedule for a given storage mapping, and 3) a good storage mapping that is valid for all legal schedules. ....

....with occupancy vectors, the polyhedral model, and ane scheduling can skip most of this chapter, but might want to review our notation in Sections 2.2.3 and 2.3.1. 2. 1 Occupancy Vectors To arrive at a simple model of storage reuse, we borrow the notion of an occupancy vector from Strout et al. [23]. The strategy is to reduce storage requirements by de ning equivalence classes over the locations of an array. Following a storage transformation, all members of a given equivalence class in the original array will be mapped to the same location in the new array. The equivalence relation is: R ....

[Article contains additional citation context not shown here]

M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24-33, 1998.

....be used to convert programs with ane dependencies into this form, our analysis will be most useful in cases where an expanded form was obtained for other reasons (e.g. parallelism detection) and one now seeks to reduce storage requirements. We will refer to the example in Figure 1, borrowed from [18]. It clearly falls within our input domain, as the dependencies have constant distance, and iteration (i; j) assigns to A[i] j] This example could represent a computation where a one dimensional array A[i] is being updated over a time dimension j, and the intermediate results are being stored. We ....

....array A[i] is being updated over a time dimension j, and the intermediate results are being stored. We assume that only the element A[n] m] is used outside the loop; the other values are only temporary. 3. 2 Occupancy Vectors We arrive at a simple model of storage reuse via the occupancy vector [18]. Informally, an occupancy vector for a given array de nes equivalence classes over the locations of the array. Two locations of an array are stored in the same location following a storage transformation if and only if they are separated by an integral multiple of the occupancy vector: De nition ....

[Article contains additional citation context not shown here]

M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. ACM SIGPLAN Notices, 33(11):24-33, Nov. 1998.

....be used to convert programs with ane dependences into this form, our analysis will be most useful in cases where an expanded form was obtained for other reasons (e.g. to detect parallelism) and one now seeks to reduce storage requirements. We will refer to the example in Figure 1, borrowed from [17]. It clearly falls within our input domain, as the dependences have constant distance, and iteration (i; j) assigns to A[i] j] This example represents a computation where a one dimensional array A[i] is being updated over a time dimension j, and the intermediate results are being stored. We ....

....dimension j, and the intermediate results are being stored. We assume that only the element A[n] m] is used outside the loop; the other values are only temporary. 3. 2 Occupancy Vectors To arrive at a simple model of storage reuse, we borrow the notion of an occupancy vector from Strout et al. [17]. The strategy is to reduce storage requirements by de ning equivalence classes over the locations of an array. Following a storage transformation, all members of a given equivalence class in the original array will be mapped to the same location in the new array. The equivalence relation is: R ....

[Article contains additional citation context not shown here]

M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24-33, 1998.

....be achieved if the array statements are transformed into various loops and loop fusion and array contraction are then applied. They do not consider loop shifting in their formulation. Strout et al. consider the minimum working set which permits tiling for loops with regular stencil of dependences [28]. Their method applies to perfectly nested loops only. In [6] Ding indicates the potential of combining loop fusion and array contraction through an example. However, he does not apply loop shifting and does not provide formal algorithms and evaluations. Loop fusion has been studied extensively. ....

M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Proceedings of the Eighth International Conference on Architectural Support for Programming Languages and Operating Systems, pages 24-33, San Jose, CA, October 1998.

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M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24--33, 1998.

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M.Strout, L.Carter, J.Ferrante, B.Simon, "Schedule-independent storage mapping for loops", Proc. ASPLOS-VIII, pp.24-33, San Jose CA, Oct. 1998.

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M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In 8th International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS'98), pages 24--33, San Jose, USA, 1998. ACM Press.

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M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24--33, 1998.

No context found.

M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In Architectural Support for Programming Languages and Operating Systems, pages 24--33, 1998.

No context found.

M. M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-Independent Storage Mapping for Loops. ACM SIG-PLAN Notices, 33(11):24--33, Nov. 1998.

No context found.

M. Strout, L. Carter, J. Ferrante, and B. Simon. Schedule-independent storage mapping for loops. In ASPLOS [ASPLOS1998].

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