Integer affine transformations of parametric ℤ-polytopes and applications to loop nest optimization

The size required to store an array is crucial for an embedded system, as it affects the memory size, the energy per memory access and the overall system cost. Existing techniques for finding the minimum number of resources required to store an array are less efficient for codes with large loops and not regularly occurring memory accesses. They have to approximate the accessed parts of the array leading to overestimation of the required resources. Otherwise their exploration time is increased with an increase over the number of the different accessed parts of the array. We propose a methodology to compute the minimum resources required for storing an array which keeps the exploration time low and provides a near-optimal result for regularly and non-regularly occurring memory accesses and overlapping writes and reads.

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“…Ref. [Seghir et al 2012] proposes a lattice intersection approach to count the integer points in Z-polytopes. Ref.…”

Section: Symbolic/polyhedral Approaches and Approximationsmentioning

confidence: 99%

Array Size Computation under Uniform Overlapping and Irregular Accesses

Kritikakou

Catthoor

Kelefouras

et al. 2016

ACM Trans. Des. Autom. Electron. Syst.

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“…In Darte et al [2005], lattices represent the iteration space for the memory allocation problem. Seghir et al [2012] propose a lattice intersection to count the integers in Z-polytopes. When the iteration space cannot be efficiently represented by lattice, the aforementioned approaches either approximate the space by solidifying holes or split it, leading to an increased number of linear equations and search time.…”

Section: Related Workmentioning

confidence: 99%

A scalable and near-optimal representation of access schemes for memory management

Kritikakou

Catthoor

Kelefouras

et al. 2014

ACM Trans. Archit. Code Optim.

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Memory management searches for the resources required to store the concurrently alive elements. The solution quality is affected by the representation of the element accesses: a sub-optimal representation leads to overestimation and a non-scalable representation increases the exploration time. We propose a methodology to near-optimal and scalable represent regular and irregular accesses. The representation consists of a set of pattern entries to compactly describe the behavior of the memory accesses and of pattern operations to consistently combine the pattern entries. The result is a final sequence of pattern entries which represents the global access scheme without unnecessary overestimation.

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“…Lefebvre and Feautrier [1998] study memory allocations through lattices. Seghir et al [2012] propose a lattice intersection approach to count the integer points in Z-polytopes. SUIF [Maydan et al 1993] and PIPS [Creusillet and Irigoin 1996] add additional constraints to the linear-constraint-based representation for a hole.…”

Section: Symbolic Approaches (Including Polyhedral Techniques)mentioning

confidence: 99%

Near-optimal and scalable intrasignal in-place optimization for non-overlapping and irregular access schemes

Kritikakou

Catthoor

Kelefouras

et al. 2013

ACM Trans. Des. Autom. Electron. Syst.

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Storage-size management techniques aim to reduce the resources required to store elements and to concurrently provide efficient addressing during element accessing. Existing techniques are less appropriate for large iteration spaces with increased numbers of irregularly spread holes. They either have to approximate the accessed regions, leading to overestimation of the final resources, or they require prohibited exploration time to find the storage size. In this work, we present a near-optimal and scalable methodology for storage-size, intrasignal, in-place optimization, that is, to compute the minimum amount of resources required to store the elements of a group (array), for irregular complex access schemes in the target domain of non-overlapping store and load accesses.

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Integer affine transformations of parametric ℤ-polytopes and applications to loop nest optimization

Cited by 7 publications

References 37 publications

Array Size Computation under Uniform Overlapping and Irregular Accesses

Array Size Computation under Uniform Overlapping and Irregular Accesses

A scalable and near-optimal representation of access schemes for memory management

Near-optimal and scalable intrasignal in-place optimization for non-overlapping and irregular access schemes

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