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103
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
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
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
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
ComputerBased Tools For Regular Array Design
 in Systolic Array Processors
, 1989
"... . We present an overview of a prototype system based on a functional language for developing regular array circuits. The features of a simulator, floorplanner and expression transformer are discussed and illustrated. INTRODUCTION Implementing algorithms on a regular array of processors has many ad ..."
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Cited by 17 (9 self)
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graphs [5], recurrence equations [14], and algebraic techniques [16]. This paper presents an overview of a prototype system for regular array development. The system is based on ¯FP [15], a functional language with mechanisms for abstracting spatial and temporal iteration. These abstractions result in a
Optimal Mapping of Systolic Algorithms by Regular Instruction Shifts
"... This paper addresses the problem of determining efficient mappings of systems of affine recurrence equations into regular arrays, in a nearly spaceoptimal fashion. A new non linear allocation technique is presented : the Instruction Shift. It allows to synthesize planar regular arrays without incre ..."
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This paper addresses the problem of determining efficient mappings of systems of affine recurrence equations into regular arrays, in a nearly spaceoptimal fashion. A new non linear allocation technique is presented : the Instruction Shift. It allows to synthesize planar regular arrays without
Mathematical Tools for Loop Transformations: From Systems of Uniform Recurrence Equations to the Polytope Model
, 1997
"... Linear programming methods, optimizations on polytopes, manipulations of integral matrices, are now commonly used in the field of automatic parallelization, for example for detecting dependences, scheduling computations, mapping data and communications, generating code for computations and communica ..."
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Cited by 2 (1 self)
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and communications. The aim of this paper is to give an introduction to these techniques, mainly by showing how they have been progressively used, over the last past 25 years, for studying repetitive computations: first in the context of systems of uniform recurrence equations, then in the development of basic loop
Piecewise Affine Timing Functions
, 1992
"... Many systematic methods exist for mapping algorithms to processor arrays. The algorithm is usually specified as a set of recurrence equations, and the processor arrays are synthesized by finding timing and allocation functions which transform index points in the recurrences into points in a spaceti ..."
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Many systematic methods exist for mapping algorithms to processor arrays. The algorithm is usually specified as a set of recurrence equations, and the processor arrays are synthesized by finding timing and allocation functions which transform index points in the recurrences into points in a space
On the synthesis of regular VLSI architectures for the 1D discrete wavelet transform
 PROCEEDINGS OF SPIE CONF. ON MATHEMATICAL IMAGING: WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING II
, 1994
"... A methodology for synthesizing parallel computational structures has been applied to the Discrete Wavelet Transform algorithm. It is based on linear spacetime mapping with constraint driven localization. The data dependence analysis, localization of global variables, and spacetime mapping is prese ..."
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Cited by 3 (1 self)
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is presented, as well as one realization of a 3octave systolic array. The DWT algorithm may not be described by a set of Uniform or Affine Recurrence Equations (UREs, AREs), thus it may not be efficiently mapped onto a regular array. However it is still possible to map the DWT algorithm to a systolic array
Diophantine nonintegrability of a third order recurrence with the Laurent property
 J. Physics A
"... We consider a oneparameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, and moreover has the Laurent property: all of the iterates are Laurent polynomials in the initial data. However, we show ..."
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Cited by 2 (0 self)
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of differential Painlevé equations can be classified in terms of affine Weyl groups. Noumi and Yamada have shown that the symmetries of these ODEs are simultaneously compatible with associated discrete Painlevé equations [21], and this viewpoint has been explained geometrically by means of Cremona group actions
Results 1  10
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103