M. Haghighat and C. Polychronopoulos, "Symbolic Dependence Analysis for High-Performance Parallelizing Compilers," Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, pp. 310--330. Cambridge, Mass.: MIT Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... [Li92, MAL92] There also has been significant new work in data dependence analysis for parallelizing compilers, including techniques for more exact subscript analysis [Pug92] more efficient analysis in practical situations [MHL91, GKT91] and enhancing tests with symbolic analysis capabilities [HP91] In our work, we have focused on machines that provide a hardware supported global address space to the programmer and the compiler. They represent an important and widely available class of parallel machines. Discussions on complementing techniques for code generation on message passing ....

Mohammad Haghighat and Constantine Polychronopoulos. Symbolic Dependence Analysis for HighPerformance Parallelizing Compilers. Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, MIT Press, Cambridge, MA, pages 310--330, 1991.

....) direction vectors while Banerjee s Inequalities with directions may test as many as O(3 ) direction vectors. The same holds for the Omega test, which also can test all direction vectors. Haghighat and Polychronopoulos, presented a dependence test to handle nonlinear, symbolic expressions [21]. Their algorithm is essentially a symbolic version of Banerjee s Inequalities test. However, their test did not include the extensions to Banerjee s Inequalities to test dependence direction vectors and to handle triangular loops, nor does it include our extension to handle nonlinear expressions ....

Mohammad Haghighat and Constantine Polychronopoulos. Symbolic Dependence Analysis for High-Performance Parallelizing Compilers. Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, MIT Press, Cambridge, Mass., pages 310--330, 1991.

....than Banerjee s Inequalities with directions, since we test at most O(n 2 ) direction vectors while Banerjee s Inequalities with directions may test as many as O(3 n ) direction vectors. Haghighat and Polychronopoulos, presented a dependence test to handle nonlinear, symbolic expressions [20]. Their algorithm is essentially a symbolic version of Banerjee s Inequalities test. However, their test did not include the extensions to Banerjee s Inequalities to test dependence direction vectors and to handle triangular loops, nor does it include our extension to handle nonlinear expressions ....

Mohammad Haghighat and Constantine Polychronopoulos. Symbolic Dependence Analysis for High-Performance Parallelizing Compilers. Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, MIT Press, Cambridge, MA, pages 310--330, 1991.

....Dn Gamma1 i n ) We call this rectangular linearization. Triangular linearization (see Section 1.2) that is used quite often in scientific codes is not handled. ffl Even for the case of rectangular linearization it cannot handle constraints imposed by triangular iteration space. Parafrase 2. In [HP91] the authors propose to use a symbolic version of Banerjee s inequalities for dependence testing, but it is known that Banerjee s inequalities do not detect independence in case of linearized subscript functions [Mas92] To alleviate the inexactness of Banerjee s inequalities, Haghighat and ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing, August 1991.

....Dn Gamma1 i n ) We call this rectangular linearization. Triangular linearization (see Section 1.2) that is used quite often in scientific codes is not handled. ffl Even for the case of rectangular linearization it cannot handle constraints imposed by triangular iteration space. Parafrase 2. In [HP91] the authors propose to use a symbolic version of Banerjee s inequalities for dependence testing, but it is known that Banerjee s inequalities do not detect independence in case of linearized subscript functions [Mas92] To alleviate the inexactness of Banerjee s inequalities, Haghighat and ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing, August 1991.

....90 of time is spent) Providing information about loop dependencies, allows the compiler to better schedule loop execution or perhaps parallelize vectorize loops if such specialized hardware is available. Dependence analysis has been the topic of a lot of research [AK87, Ban88, Fea91, GKT91, Hag90, MHL91, Jus95] A typical use of dependence analysis is illustrated by the loop in Figure 1.1. In this example, dependence analysis is used to determine that there is a flow dependence from statement S1 to statement S2 with dependence distance of (4) This means that the array reference at ....

....easily write an algorithm to transform an expression tree (not considering reaching definitions) into a sum of products abstract representation. Figure 4.12 shows an example expression represented textually, as an expression tree and as a sum of products. This strategy is used by Haghighat in [Hag90] Performing arithmetic (addition, subtraction, multiplication) on such a representation is just a programming exercise. Standardizing a representation for division is more complex, but some work on this has been also done by Haghighat [HP96] with source of [DST93] In McCAT, only symbolic ....

[Article contains additional citation context not shown here]

Mohammad Reza Haghighat. Symbolic dependence analysis for high performance parallelizing compilers. Master's thesis, University of Illinois at Urbana-Champaign, May 1990.

....these cases. Third, if a variable is conditionally incremented in a loop by a constant with unknown sign, then the compiler cannot determine if the sequence is increasing or decreasing. Other researchers have recently examined various aspects of subscript expressions [Shen, Li, and Yew 1990; Haghighat 1990], with similar results. These results represent a first approximation to help determine what types of data dependence tests should be applied. Further study is needed, particularly in analyzing pairwise comparisons of references to the same array at all levels in each loop nest. 7. RELATED WORK ....

Haghighat, M. R. 1990. Symbolic dependence analysis for high performance parallelizing compilers. Technical Report 995 (May), University of Illinois (CSRD). M.S. Thesis.

....for handling nonaffine terms were much more primitive than those described in Section 4. Methods for incorporating assertions about invariant scalar variables into dependence analysis algorithms and producing queries to ask the user have been part of the compiler folklore for some time (see Haghighat and Polychronopoulos [1991] for a discussion) However, previous work has not addressed how to ask concise questions given that some information is already known, or how to identify dependences that are unconditional. Techniques for testing conditional dependences have generally focused on specialpurpose methods for common ....

Haghighat, M. and Polychronopoulos, C. 1991. Symbolic dependence analysis for highperformance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing.

....resolve these cases. Third, if a variable is conditionally incremented in a loop by a constant with unknown sign, then the compiler cannot determine if the sequence is increasing or decreasing. Other researchers have recently examined various aspects of subscript expressions with similar results [12, 18]. These results represent a first approximation to help determine what types of data dependence tests should be applied. Further study is needed, particularly in analyzing pairwise comparisons of references to the same array at all levels in each loop nest. 50 AAAA AAAA AAAA AAAA AAAA AAAA AAAA ....

Mohammad Reza Haghighat. Symbolic dependence analysis for high performance parallelizing compilers. Technical Report 995, University of Illinois, Center for Supercomputing Research & Development, Urbana, Illinois, May 1990. M.S. thesis.

....whether or not a program point is reached, leaving only the predicates selecting among possible reaching values. This potentially increases the congruences to be found over Dehbonei and Jouvelot s method. Haghighat Haghighat s symbolic analysis also relies on symbolic expressions [Hag90, HP90, HP93] He has highly developed methods for rewriting expressions and solving recurrences, while our methods seem stronger in representing and matching patterns of operators which are poorly understood (except for being known compositional) In particular, our methods for representing and ....

....also derived from the earlier work of Reif et al. RT81] Full GSA form could perhaps also be employed in this construction; thinned GSA form omits some of the predicates they are interested in propagating. Haghighat Haghighat s symbolic analysis relies purely on symbolic expressions [Hag90, HP90, HP93] His methods for expression manipulation are more highly developed than 146 ours, while we have more efficient (or at least more explicitly described) techniques for building an initial expression from dataflow information. Haghighat uses symbolic expressions to describe the output ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high performance parallelizing compilers. In Proceedings of the Third Workshop on Languages and Compilers for Parallel Computing, Irvine, CA, August 1990.

....affecting whether or not a program point is reached, leaving only the predicates selecting among possible reaching values. This potentially increases the congruences to be found over Dehbonei and Jouvelot s method. Haghighat Haghighat s symbolic analysis also relies on symbolic expressions [Hag90, HP90, HP93] He has highly developed methods for rewriting expressions and solving recurrences, while our methods seem stronger in representing and matching patterns of operators which are poorly understood (except for being known compositional) In particular, our methods for representing and ....

....being also derived from the earlier work of Reif et al. RT81] Full GSA form could perhaps also be employed in this construction; thinned GSA form omits some of the predicates they are interested in propagating. Haghighat Haghighat s symbolic analysis relies purely on symbolic expressions [Hag90, HP90, HP93] His methods for expression manipulation are more highly developed than 146 ours, while we have more efficient (or at least more explicitly described) techniques for building an initial expression from dataflow information. Haghighat uses symbolic expressions to describe the output ....

Mohammad Reza Haghighat. Symbolic dependence analysis for high performance parallelizing compilers. Master's thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign, May 1990. Also available as CSRD Rpt. No. 995.

....analysis, provides the framework for symbolic analysis. Data flow along SSA edges is analyzed to deduce constraints and relationships on symbolic expressions, which may be in turn propagated. Studies have shown that symbolic analysis is essential for precise analysis of scientific programs [25, 27, 49]. The symbolic analyzer performs the following steps. Constant propagation uses the sparse conditional constant algorithm to eliminate as many symbolics as initially feasible [53] Auxiliary induction variable substitution replaces auxiliary induction variables by functions of loop index ....

....applied where applicable. Batch analysis is performed after each transformation phase to update the dependence information for the entire program. Parafrase2 adds scheduling and improved program analysis and transformations [44] More advanced interprocedural and symbolic analysis is planned [27]. Parafrase 2 uses Faust as a front end to provide interactive parallelization and graphical displays [26] Ptran is also an automatic parallelizer with extensive program analysis. It computes the SSA and program dependence graphs, and performs constant propagation and interprocedural analysis ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high performance parallelizing compilers. In Proceedings of the Third Workshop on Languages and Compilers for Parallel Computing, Irvine, CA, August 1990.

....subscripts, and is unsuitable for most loop transformations since distance and direction vectors are not calculated. Lichnewsky and Thomasset describe symbolic dependence testing in the vatil vectorizer [39] Haghighat and Polychronopoulos propose a flow analysis framework to aid symbolic tests [22]. Execution conditions may also be used to refine dependence tests. Wolfe s All Equals test checks for loopindependent dependences invalidated by control flow within the loop [53] Lu and Chen s subdomain test incorporates information about indices from conditionals within the loop body [40] ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high performance parallelizing compilers. In Proceedings of the Third Workshop on Languages and Compilers for Parallel Computing, Irvine, CA, August 1990.

....to become affine, but he does not describe how this is achieved. In [PW93b] the authors propose to compute upper and lower bounds on dependences. However, their techniques can not prove that dependence from statement S 1 to S 2 is not carried by loop i in Figure 3(a) A number of papers [AK87, HP91, LT88] suggest using symbolically enhanced versions of GCD test and Banerjee s inequalities. These techniques work only for memory based dependence analysis and they are inexact even in this domain. 8 Source code availability The implementation of our algorithms is integrated into the UMCP ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing, August 1991.

....cannot hope to resolve these cases. Third, if a variable is conditionally incremented in a loop by a constant with unknown sign, then the compiler cannot determine if the sequence is increasing or decreasing. Other researchers have recently examined various aspects of subscript expressions [Haghighat 1990; Shen et al. 1990] with similar results. These results represent a first approximation to help determine what types of data dependence tests should be applied. Further study is needed, particularly in analyzing pairwise comparisons of references to the same array at all levels in each loop ....

Haghighat, M. R. 1990. Symbolic dependence analysis for high performance parallelizing compilers. Tech. Rep. 995 (May), M.S. thesis, Univ. of Illinois (CSRD), Urbana, Ill.

....affect statement execution [15] Supporting Analysis. Scalar data flow analysis, including def use chains, constant propagation and symbolic analysis, provides additional information about the values and relationship of variables. They can vastly improve the precision of dependence analysis [19, 20]. Def use chains expose dependences among scalar variables as well as linking all accesses to each array for dependence testing. A critical contribution of scalar data flow analysis is recognizing scalars that are killed, or redefined, on every iteration of a loop and may be made private, thus ....

....read from an input file or index arrays used in subscript expressions. Symbolic terms in subscript expressions are a key limiting factor in precise dependence analysis. One study found that over 50 of the array references in some numerical packages contained at least one unknown symbolic term [20]. The index arrays entry in Table 3 demonstrates that three programs contained index arrays in subscript expressions that prevented parallelization. We are using a three pronged approach to improving the precision of dependence information in the presence of symbolics: 1) sophisticated ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances in Languages and Compilers for Parallel Computing, Irvine, CA, August 1990. The MIT Press.

....been developed [5, 20] for the case of subscripted variables with linear subscript expressions. For subscripted variables 5 involving arbitrary indexing expressions, the problem cannot be solved in general. Recently, some symbolic tests have been proposed for partially linear array subscripts [8] and subscripted variables with coupled subscripts [16] In this paper we will consider dependences with constant associated distance known at compile time. 3.2 Chains and Recurrences A chain C ij is an ordered set of arcs C ij = d ik , d kl , d mj between two statements S i and ....

Haghighat M.R. and Polychronopoulos C.D., "Symbolic Dependence Analysis for High Performance Parallelizing Compilers", Proc. of the 3rd Workshop on Programming Languages and Compilers for Parallel Computing, Irvine-California USA, Pitman/MIT, August 1990.

....of [LCD91] which could not be handled by any compiler tested by [LCD91] 5. 1 Related Work Methods for incorporating assertions about invariant scalar variables into dependence analysis algorithms and producing queries to ask the user have been part of the compiler folklore for some time (see [HP91] for a recent discussion) However, previous work has not addressed how to ask concise questions given that some information is already known. Kathryn McKinley [McK90] describes how to handle index arrays in dependence analysis. Her work enumerates many typical cases and discusses how each can be ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing, August 1991.

....of [LCD91] which could not be handled by any compiler tested by [LCD91] 5. 1 Related Work Methods for incorporating assertions about invariant scalar variables into dependence analysis algorithms and producing queries to ask the user have been part of the compiler folklore for some time (see [HP91] for a recent discussion) However, previous work has not addressed how to ask concise questions given that some information is already known. Kathryn McKinley [McK90] describes how to handle index arrays in dependence analysis. Her work enumerates many typical cases and discusses how each can be ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for high-performance parallelizing compilers. In Advances In Languages And Compilers for Parallel Processing, August 1991.

....treated the same as expanded scalars, which are explicit arrays. From now on, we will refer to both such variables and as array variables . Subscripts involving induction variables may require significant effort to analyze, just as their Fortran counterparts have generated a great deal of research [41, 40]. The transformations applied so far have scalar expanded any do converted procedure s arguments and the variables that are live across the recursive call, and have split the procedure into a downward and upward loop. Because these two loops share common data there are potentially dependences from ....

Mohammad Haghighat. Symbolic Dependence Analysis for High Performance Parallelizing Compilers. PhD thesis, University of Illinois at Urbana-Champaign, May 1990. CSRD report no. 995.

....and otivation Accurate and efficient data dependency analysis is an important cornerstone of any parallelizing compiler. For programs using arrays and nested loops, various powerful dependence analysis methods have been widely established [Ban88, Wol89, ZLC90, GGT91, DEML91, XKP91, Fea91, HP91, Pug91, Mas92, XK92, WT92] The basic dependence problem is to decide whether two subscripted references to the same array in a loopnest access the same memory location under certain constraints imposed by the boundaries of the loop iteration space. In general, the dependence problem reduces to ....

....and monotonic induction variables, but does not calculate the formulas. Non linear and geometric induction variables are currently being incorporated without any serious problems. A framework to solve the dependence problem in the presence of unknown symbolic expressions has been introduced in [HP91, HP93] The approach uses forward flow analysis in order to do symbolic constant propagation, partial symbolic execution and approximate semantic analysis in the program, before applying classical data dependence testers. The symbolic constant flow analysis is applied on multi level linked list ....

M. Haghighat and C. Polychronopoulos. Symbolic dependence analysis for highperformance parallelizing compilers. Pitman, London and MIT Press, Cambridge, MA, 1991.

....of the code s sequential execution time. 3.3. 1 Range Test To handle such nonlinear expressions, we have developed a symbolic dependence test called the range test [BE94b] The range test can be considered an extension of a symbolic version of Triangular Banerjee s Inequalities test [WB87, Ban88, HP91] In the range test, we mark a loop as parallel if we can prove that the range of elements accessed by an iteration of that loop do not overlap with the range of elements accessed by other iterations. We determine whether these ranges overlap by comparing the minimum and maximum values of these ....

Mohammad Haghighat and Constantine Polychronopoulos. Symbolic Dependence Analysis for HighPerformance Parallelizing Compilers. Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, MIT Press, Cambridge, MA, pages 310--330, 1991.

No context found.

M. Haghighat and C. Polychronopoulos, "Symbolic Dependence Analysis for High-Performance Parallelizing Compilers," Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, pp. 310--330. Cambridge, Mass.: MIT Press, 1991.

No context found.

Mohammad Haghighat and Constantine Polychronopoulos. Symbolic Dependence Analysis for High-Performance Parallelizing Compilers. Parallel and Distributed Computing: Advances in Languages and Compilers for Parallel Processing, MIT Press, Cambridge, MA, pages 310--330, 1991.

No context found.

M. Haghighat and C. Polychronopoulos. Symbolic Dependence Analysis for High-PerformanceParallelizing Compilers. In D. Gelernter, T. Gross, A. Nicolau, and D. Padua, editors, Advances in Languages and Compilers for Parallel Processing, pages 310--330. MIT Press, 1991.

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