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Abstract: Why do existing parallelizing compilers and environments fail to parallelize many realistic FORTRAN programs? One of the reasons is that these programs contain a number of linearized array references, such as A(M*N*i+N*j+k) or A(i*(i+1)/2+j). Performing exact dependence analysis for these references requires testing polynomial constraints for integer solutions. Most existing dependence analysis systems, however, restrict themselves to solving affine constraints only, so they have to make... (Update)
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...computations are not yet known. But some directions for further investigations are given in the conclusion. Some close work is done in [13], where the authors propose a method to simplify polynomial constraints over integers. It consists in trying to transform the polynomial...
...contradictions, equalities and redundant constraints can be detected and eliminated. Simplifying a set of constraints has been shown [11, 14, 17] to be critical in order to alleviate performance as well as compiler analysis. We have implemented the following simplification...
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BibTeX entry: (Update)
Vadim Maslov and William Pugh. Simplifying polynomial constraints over integers to make dependence analysis more precise. Technical Report CS-TR-3109.01, Dept. of Computer Science, University of Maryland, College Park, February 1994. Submitted to CONPAR '94. http://citeseer.ist.psu.edu/maslov94simplifying.html More
@techreport{ vadim94simplifying,
author = "Maslov, Vadim and Pugh, William",
title = "{S}implifying {P}olynomial {C}onstraints {O}ver {I}ntegers to {M}ake {D}ependence {A}nalysis {M}ore {P}recise",
number = "CS-TR-3109.1",
month = "Feb",
year = "94",
url = "citeseer.ist.psu.edu/maslov94simplifying.html" }
Citations (may not include all citations):258 Automatic translation of Fortran programs to vector form - Allen, Kennedy - 1987
167 Grobner bases: an algorithmic method in polynomial ideal the.. (context) - Buchberger - 1985
48 A framework for unifying reordering transformations - Kelly, Pugh - 1993
45 Symbolic dependence analysis for high-performance paralleliz.. (context) - Haghighat, Polychronopoulos - 1991
30 Elimination methods: an introduction (context) - Kapur, Lakshman - 1992
28 Going beyond integer programming with the Omega test to elim.. - Pugh, Wonnacott - 1992
24 Delinearization: an efficient way to break multiloop depende.. - Maslov - 1992
17 An evaluation of exact methods for analysis of value-based a.. (context) - Pugh, Wonnacott - 1993
16 Symbolic analysis: A basis for parallelization (context) - Haghighat, Polychronopoulos - 1993
13 Systems and Algorithms for Algebraic Computation (context) - Davenport, Siret et al. - 1988
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