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74
Dataflow Analysis of Array and Scalar References
 International Journal of Parallel Programming
, 1991
"... Given a program written in a simple imperative language (assignment statements, for loops, affine indices and loop limits), this paper presents an algorithm for analyzing the patterns along which values flow as the execution proceeds. For each array or scalar reference, the result is the name an ..."
Abstract

Cited by 254 (3 self)
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and iteration vector of the source statement as a function of the iteration vector of the referencing statement. The paper discusses several applications of the method: conversion of a program to a set of recurrence equations, array and scalar expansion, program verification and parallel program
Some efficient solutions to the affine scheduling problem  Part I Onedimensional Time
, 1996
"... Programs and systems of recurrence equations may be represented as sets of actions which are to be executed subject to precedence constraints. In many cases, actions may be labelled by integral vectors in some iteration domain, and precedence constraints may be described by affine relations. A s ..."
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Cited by 266 (22 self)
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Programs and systems of recurrence equations may be represented as sets of actions which are to be executed subject to precedence constraints. In many cases, actions may be labelled by integral vectors in some iteration domain, and precedence constraints may be described by affine relations. A
The Naive Execution of Affine Recurrence Equations
 INTERNATIONAL CONFERENCE ON APPLICATIONSPECIFIC ARRAY PROCESSORS
, 1995
"... In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the Alpha language was developed as the basis of a computer aided design methodology for regular array architectures. Alpha is used to initially specify algorithms at a very high algorith ..."
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Cited by 7 (4 self)
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In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the Alpha language was developed as the basis of a computer aided design methodology for regular array architectures. Alpha is used to initially specify algorithms at a very high
The Mapping of Linear Recurrence Equations on Regular Arrays
 Journal of VLSI Signal Processing
, 1989
"... The parallelization of many algorithms can be obtained using spacetime transformations which are applied on nested doloops or on recurrence equations. In this paper, we analyze systems of linear recurrence equations, a generalization of uniform recurrence equations. The first part of the paper des ..."
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Cited by 69 (7 self)
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describes a method for finding automatically whether such a system can be scheduled by an affine timing function, independent of the size parameter of the algorithm. In the second part, we describe a powerful method that makes it possible to transform linear recurrences into uniform recurrence equations
From ALPHA to Imperative Alpha to Imperative Code: A Transformational Compiler for an Array Based Functional Language
, 1995
"... Practical parallel programming demands that the details of distributing data to processors and interprocessor communication be managed by the compiler. These tasks quickly become too difficult for a programmer to do by hand for all but the simplest parallel programs. Yet, many parallel languages sti ..."
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still require the programmer to manage much of the the parallelism. I discuss the synthesis of parallel imperative code from algorithms written in a functional language called Alpha. Alpha is based on systems of affine recurrence equations and was designed to specify algorithms for regular array
A Toolbox for Affine Recurrence Equations Parallelization
 In International Conference and Exhibition on HighPerformance Computing and Networking
, 1995
"... this paper are defined by systems of affine recurrence equations (SARE in the following). The space \Theta time mapping is based on an affine schedule function and a linear allocation. Systolic or more generally processor array solutions can be synthesized. The soobtained architectures usually requ ..."
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Cited by 3 (0 self)
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this paper are defined by systems of affine recurrence equations (SARE in the following). The space \Theta time mapping is based on an affine schedule function and a linear allocation. Systolic or more generally processor array solutions can be synthesized. The soobtained architectures usually
Embedding of Systems of Affine Recurrence Equations in Coq
 in « Proc. TPHOLs 2003, 16th International Conference on Theorem Proving in Higher Order Logics », series LNCS
, 2003
"... Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification ..."
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Cited by 4 (1 self)
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Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification
A Library for Doing Polyhedral Operations
, 1993
"... Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra are useful for doing loop transformations and other program restructuring transformatio ..."
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Cited by 119 (13 self)
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transformations which are needed in parallelizing compilers. Thus a need for a library of polyhedral operations has recently been recognized in the parallelizing compiler community. Polyhedra are also used in the definition of domains of variables in systems of affine recurrence equations (SARE). Alpha is a
Compilation of Structured Polyhedral Equations
"... Abstract—The polyhedral model is an established mathematical formalism for automatic parallelization of an important class of programs. In 1989, Mauras defined ALPHA, a polyhedral equational language based on systems of affine recurrence equations over polyhedral domains. In 1995, Dupont de Dinec ..."
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Abstract—The polyhedral model is an established mathematical formalism for automatic parallelization of an important class of programs. In 1989, Mauras defined ALPHA, a polyhedral equational language based on systems of affine recurrence equations over polyhedral domains. In 1995, Dupont de
An Efficient Allocation Strategy for Mapping Affine Recurrences into Space and Time Optimal Regular Processor Arrays
, 1994
"... This paper adresses the problem of efficient mappings of nested loops, and more generally of systems of affine recurrence equations, into regular arrays. The presented technique is based on the transformation of an initial systolic mapping. By studying the processor element (PE) activity, a nearl ..."
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Cited by 2 (0 self)
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This paper adresses the problem of efficient mappings of nested loops, and more generally of systems of affine recurrence equations, into regular arrays. The presented technique is based on the transformation of an initial systolic mapping. By studying the processor element (PE) activity, a
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