Open AccessProceedings Article10.1145/951710.951749

Lattice-based memory allocation

- 30 Oct 2003

- pp 298-308

107

TL;DR: A new mathematical framework is developed, based on critical lattices, that subsumes the previous approaches and provides new insight into the problem of memory reuse, and proposes and analyzes several practical strategies for finding strictly admissible integer latticing, either optimal or optimal up to a multiplicative factor, and, hence, memory-saving modular mappings.

Abstract: We investigate the problem of memory reuse, for reducing the necessary memory size, in the context of compilation of dedicated processors. Memory reuse is a well-known concept when allocating registers (i.e., scalar variables). Its (recent) extension to arrays was studied mainly by Lefebvre and Feautrier (for loop parallelization) and by Quillere and Rajopadhye (for circuit synthesis based on recurrence equations). Both consider affine mappings of indices to data, with modulo expressions in the first and (mainly) projections in the second. We develop a mathematical framework based on (integral) critical lattices that subsumes all previous approaches and gives new insights into the problem. Our technique consists first in building an abstract representation of conflicting indices (equivalent in a multi-dimensional space to the interference graph for register allocation), then in defining an integral lattice, admissible for the set of differences of conflicting indices, used to build a valid modular allocation. We also show the link with critical lattices, successive minima, and basis reduction, and we analyze various strategies for lattice-based memory allocation.

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1. What have the authors contributed in "Lattice-based memory allocation" ?

The authors investigate the technique of storing multiple array elements in the same memory cell, with the goal of reducing the amount of memory used by an array variable.. The authors place the problem in a broader mathematical context, showing its relation to real critical lattices, successive minima, and lattice basis reduction ; finally, they propose and analyze various strategies for lattice-based memory allocation.

2. What are the future works mentioned in the paper "Lattice-based memory allocation" ?

The authors have proposed herein a mathematical framework to study modular memory allocations.. Future work should take up some more sharply reasoned theoretical questions as well as effective practical implementation.. Can the authors identify classes of programs, in a more formal way, for which they can be sure that a simple-to-compute choice of basis will give good performance ?. In particular, maybe there are better heuristics based on the construction of a strictly admissible ( possibly rational ) lattice that can be converted into a strictly admissible integer lattice ?

3. what is the arithmetic of a program?

Keywords Program transformation, memory allocation, memory size reduction, admissible lattice, critical determinant, successive minima.

4. What is the key idea of the article?

The key idea is that once a schedule of operations has been determined, the schedule of references to a given location is known, and elements with disjoint lifetimes may share a single memory cell, in principle.

Figure 13: K part for (δbr, δbc) = (0, 0).

Figure 10: Same with schedule θ(i, j) = (i+ j, j).

Figure 1: Code for Example 1, the second loop starts 1 clock cycles later.

Figure 14: K part for (δbr, δbc) = (0, 1) and (δbr, δbc) = (1,−63).

Citations

•Proceedings Article•10.1145/2435264.2435273

Polyhedral-based data reuse optimization for configurable computing

Louis-Noël Pouchet, +3 more

- 11 Feb 2013

TL;DR: In this article, a C-to-FPGA framework is presented to implement data reuse through aggressive loop transformation-based program restructuring, which can satisfy hardware resource constraints (scratchpad size) while still aggressively exploiting data reuse.

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Sven Verdoolaege, +2 more

- 01 Jan 2007

- Eurasip Journal on Embedded Systems

TL;DR: This paper presents the compiler techniques for facilitating the migration from a sequential application specification to a parallel application specification using the process network model of computation, and describes a technique for compile-time memory requirement estimation.

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•Journal Article•10.1145/2675359

Improving Multibank Memory Access Parallelism with Lattice-Based Partitioning

Alessandro Cilardo, +1 more

- 09 Jan 2015

- ACM Transactions on Architecture and Cod...

TL;DR: This work addresses the problem of automated memory partitioning for emerging architectures, taking into account potentially parallel data accesses to physically independent banks, using the Z-polyhedral model for program analysis and adopting a partitioning scheme based on integer lattices.

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•Journal Article•10.1109/TVLSI.2008.2002049

Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation

Philippe Clauss, +3 more

- 01 Aug 2009

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•Book Chapter•10.1007/978-1-4614-6859-2_41

Polyhedral Process Networks

Sven Verdoolaege

- 01 Jan 2013

TL;DR: This chapter details the construction of the processes and the communication channels in a polyhedral process network if the application can be represented in the polyhedral model and a parallel specification can be derived automatically.

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TL;DR: How to Round Numbers Preliminaries and some Applications in Combinatorics Cuts and Joins Chromatic Number, Cliques and Perfect Graphs Minimizing a Submodular Function.

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444

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Lattice-based memory allocation

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Most frequently asked questions

1. What have the authors contributed in "Lattice-based memory allocation" ?

2. What are the future works mentioned in the paper "Lattice-based memory allocation" ?

3. what is the arithmetic of a program?

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Citations

Polyhedral-based data reuse optimization for configurable computing

pn: a tool for improved derivation of process networks

Improving Multibank Memory Access Parallelism with Lattice-Based Partitioning

Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation

Polyhedral Process Networks

References

Factoring Polynomials with Rational Coefficients

Factoring polynomials with rational coeficients

Handbook of Combinatorics

Geometry of Numbers

An algorithmic theory of numbers, graphs, and convexity

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