Citations: Nonlinear array dependence analysis - Pugh, Wonnacott (ResearchIndex)

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D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York.

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Compile-time Composition of Run-time Data and Iteration.. - Strout, Carter, Ferrante (2003) (4 citations) (Correct)

.... in many important applications, such as sparse matrix computations and unstructured mesh applications [18] Fortunately, the Kelly and Pugh framework allows the description of indirect memory references (such as A[B[i] through the use of Presburger arithmetic with uninterpreted function symbols [20]. We exploit this ability to specify data mappings and dependences between interations involving indirect memory references. Describing the e#ect of run time iteration and data reorderings in a compile time framework provides several advantages. First, both run time and compile time ....

....of the time loop. IRREG experiences small improvements in execution time due to sparse tiling; however, sparse tiling a#ects the overhead in IRREG more than in MOLDYN. 6. RELATED WORK Researchers have looked at extending data dependence analysis to run time to handle non a#ne memory references [20, 23]. These techniques typically attempt to disprove a dependence at runtime in order to exploit parallelism. Instead, our work requires the run time traversal of dependences between loops. Previous work has already explored how to generate code when the algorithm and the sparse data structure are ....

Pugh and Wonnacott. Nonlinear array dependence analysis. Technical Report CS-TR-3372, Dept. of Computer Science, Univ. of Maryland, nov 1994.

Compile-time Composition of Run-time Data and Iteration.. - Strout, Carter, Ferrante (2003) (4 citations) (Correct)

.... which occur in many important applications such as sparse matrix and unstructured mesh computations [21] Fortunately, the Kelly and Pugh framework describes non a#ne memory references (such as indirect memory references A[B[i] by using Presburger arithmetic with uninterpreted function symbols [23]. We exploit this ability to specify data mappings between loop iterations and data locations, and dependences between loop iterations, when non a#ne memory references are involved. We can also express run time data and iteration reordering transformations for locality, which include consecutive ....

....we review the Kelly Pugh iteration reordering framework terminology using the simplified moldyn code in Figure 1 as an example. Pugh and Wonnacott introduced the idea of using uninterpreted function symbols to statically describe the values in index arrays and other non a#ne memory references [23]. Here we use this idea to describe some of the data mappings and dependences in the simplified moldyn example (Figure 1) which involve indirect memory references. 3.1 Loops, Statements, and Data The traditional literature on loop transformations represents each iteration within a loop nest as ....

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B. Pugh and D. Wonnacott. Nonlinear array dependence analysis. Technical Report CS-TR-3372, Dept. of Computer Science, Univ. of Maryland, nov 1994.

A Comparative Study of Reaching-definitions Analyses - Collard, Knoop (1998) (Correct)

....software called PIP [16] based on the simplex, to directly compute max . ffl The execution of a simplified, efficient but not complete algorithm [31] The algorithm by Pugh was extended by Wonnacott and Pugh to handle arbitrary if conditions, arbitrary loop bounds and arbitrary array subscripts [33, 39, 40]. The same extension of Feautrier s technique was made by Barthou et al. 10, 6, 5] One way to speed up an IRDA is to stop the analysis when, for all y, the source of hr; yi is non empty. When going back to the control flow graph perspective , this makes much sense: When going upward the CFG, ....

D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York.

Integrating Data And Task Parallelism In Scientific Programs - Ewa Deelman Wesley (Correct)

....to a unique element in that variable s array. Note that assignments to two distinct array elements are valid in SAF; repeated assignments to the same array element are not valid. To determine whether assignments are made to the same array elements, we use various dependence 172 tests (cf. [6, 7]) If the results of the dependence tests are negative within a loop, then no two elements are reassigned in the loop, and no temporal dimension is needed. The temporal dimension is so named because it represents a time stamp for each iteration. In the case of loops, its value can be simply the ....

W. Pugh and D. Wonnacott. Nonlinear array dependence analysis. In B. K. Szymanski and B. Sinharoy, editors, Languages, Compilers and Run-Time Systems for Scalable Computers, pages 1--14. Kluwer Academic Publishers, Boston, 1995.

A Precise Fixpoint Reaching Definition Analysis for Arrays - Collard, Griebl (1999) (2 citations) (Correct)

....programs increases dramatically with the size of the input program. In addition, since the basic approach relies on the structure of the input program, an extension to programs without any structure, e.g. containing arbitrary gotos, is not straight forward. Current methods in this framework [9, 3, 15] would just fail. A simple way out would be to use a preprocessing phase for structuring the program. However, this leads, in general, to significant code duplication. Furthermore, in an interactive compiler environment, the user will not be able to recognize his or her program. 5 Our MFP ....

....element (A[0] may be uninitialized when read. Moreover, we know this read is the very first instance of statement 7 (i = 0; j = 0) ffl For a parametric instance h7; i; ji, ff (8) gives all the definition instances that may reach this use. This result has the same precision as with methods in [3, 15, 2]. 7 Implementation The analysis presented in this paper is developped on top of two compiler platforms: LooPo, developped at the University of Passau, and SUIF, from Stanford. A preliminary phase has been implemented for each of these platforms, the one for LooPo in Passau and the one for SUIF ....

D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York. 14

Maximal Static Expansion - Barthou, Cohen, Collard (1998) (9 citations) (Correct)

....one can find a static expansion which is also in single assignment form. Feautrier [14] coined the term static control programs for this class of programs. In the case of programs with general control and unrestricted arrays subscripts, array reaching definition analyses are approximate [9, 4, 2, 27, 28]: Several writes may be the unique definition of a given value, but the analysis cannot tell. 8] describes how to obtain a single assignment program at the price of dynamic restoration of data flow. Many studies are related to array privatization. As hinted above, Maydan et al. 20] proposed an ....

D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York.

Maximal Static Expansion - Barthou, Cohen, Collard (1998) (9 citations) (Correct)

....loop. The example in 5 section 2.3 shows that our method not only may expand along diagonals in the iteration space but may also do some blocking along these diagonals. In the case of programs with general control and unrestricted arrays subscripts, array data flow analyses are approximate [7, 10, 11]: Several writes may be the unique definition of a given value, but the analysis cannot tell. From the result of such an analysis, how to obtain a single assignment program to the price of dynamic restoration of data flows had been described in [8] 3 Static Expansion Let Omega be the set of all ....

D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York.

Unified Interprocedural Parallelism Detection - Hoeflinger, Paek (2000) (Correct)

.... Non ane subscript expressions occur in irregular codes (subscripted subscript access) in FFT codes (subscripts frequently involving 2 I ) and as a result of compiler transformations (induction variable closed forms and inline expansion of subroutines) To solve this problem, Pugh, et al.[17] enhanced the Omega test with techniques for replacing the non ane terms in array subscripts with symbolic variables. This technique does not work in all situations, however. The Range Test [3, 4] was built to provide a better solution to this problem. It handles non ane subscript expressions ....

....on the loop variants. The ARDs partially ll the role of the constraints, but if non ane expressions are used, there is no way to extract linear coecients for the non ane parts. A technique for replacing the non ane parts of an expression with uninterpreted function symbols has been developed [17], but it is not general enough to work in all situations. So even using the ARD, the Omega Test could not handle non ane subscript expressions because its mechanism is simply not well de ned for such expressions. Likewise, if the Range Test were to use the ARD to represent value ranges for ....

W. Pugh and D. Wonnacott. Nonlinear Array Dependence Analysis. Technical Report 123, Univ of Maryland at College Park, November 1994.

A Unified Symbolic Evaluation Framework for Parallelizing.. - Fahringer, Scholz (1999) (4 citations) (Correct)

....as shown in Table 2. Our techniques for comparing both linear and non linear symbolic expressions and the ability of our symbolic evaluation to propagate constraints through a program enables us to handle the majority of these references. Note that there are a few sophisticated dependence tests [43, 4, 38, 49] that handle both linear and non linear symbolic expressions. Also some of these approaches appear to be more powerful than our techniques, they also have some drawbacks associated with them, for instance, restricted program models (no GOTOs and procedure calls) 4] introduction of a large number ....

William Pugh and David Wonnacott. Nonlinear array dependence analysis. In In 3rd Workshop on Languages, Compilers, and Run-Time Systems for Scalable Computers, Troy, New York, May 1995.

Maximal Static Expansion - Barthou, Cohen, Collard (1998) (9 citations) (Correct)

....affine subscripts, one can find a static expansion which is also in single assignment form. Feautrier [8] coined the term static control programs for this class of programs. In the case of programs with general control and unrestricted arrays subscripts, array data flow analyses are approximate [3, 2, 16, 17]: Several writes may be the unique definition of a given value, but the analysis cannot tell. 9] describes how to obtain a single assignment program to the price of dynamic restoration of data flow. 3 real A[1. 4 N 1,1. 2] for i = 1 to 2 N do for j = 1 to 2 N do fexpansion of statement Sg ....

D. Wonnacott and W. Pugh. Nonlinear array dependence analysis. In Proc. Third Workshop on Languages, Compilers and Run-Time Systems for Scalable Computers, 1995. Troy, New York.

Constraint-Based Array Dependence Analysis - William Pugh, David Wonnacott (1998) (14 citations) Self-citation (Pugh Wonnacott) (Correct)

....and notice is given that copying is by permission of the Association for Computing Machinery, Inc. ACM) To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and or a fee. c fl 1998 ACM 0164 0925 98 0300 0388 5.00 2 Delta W. Pugh and D. Wonnacott for i : 2 to n do sum : 0.0 for l : 1 to i 1 do sum : sum A[l,i] B[l] endfor B[i] B[i] sum endfor (a) forall i : 1 to n do sum[i] 0.0 endfor for l : 1 to n 1 do B[l] B[l] sum[l] forall i : l 1 to n do sum[i] sum[i] A[l,i] B[l] endfor endfor (b) Fig. 1. a) From Petersen and Padua ....

Pugh, W. and Wonnacott, D. 1995b. Nonlinear array dependence analysis. In Third Workshop on Languages, Compilers, and Run-Time Systems for Scalable Computers. Troy, New York.

Constraint-Based Array Dependence Analysis - William Pugh, David Wonnacott (1998) (14 citations) Self-citation (Pugh Wonnacott) (Correct)

....and notice is given that copying is by permission of the Association for Computing Machinery, Inc. ACM) To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and or a fee. c fl 1998 ACM 0164 0925 98 0300 0388 5.00 2 Delta W. Pugh and D. Wonnacott for i : 2 to n do sum : 0.0 for l : 1 to i 1 do sum : sum A[l,i] B[l] endfor B[i] B[i] sum endfor (a) forall i : 1 to n do sum[i] 0.0 endfor for l : 1 to n 1 do B[l] B[l] sum[l] forall i : l 1 to n do sum[i] sum[i] A[l,i] B[l] endfor endfor (b) Fig. 1. a) From Petersen and Padua ....

Pugh, W. and Wonnacott, D. 1994b. Nonlinear array dependence analysis. Tech. Rep. CS-TR3372, Dept. of Computer Science, University of Maryland, College Park. Nov.

Constant Propagation Through Array Variables - Wonnacott (1999) Self-citation (Wonnacott) (Correct)

....This di erence has lead to the restriction of many analysis and optimization techniques, such as constant propagation [Muc97] to scalar variables. A number of techniques have recently been developed for accurately describing the ow of values in array variables [Fea91, MAL92, TP92, PW93, PW94, Tu95, BCF97, GLL97, PW98, SK98] Of these, only the work of Sarkar and Knobe discussed the use of their analysis for constant propagation. Constant propagation provides two kinds of bene ts during optimization. It enables optimizations such as constant folding and algebraic simpli cation, which ....

....about memory aliasing, but not the ow of values in array variables. More recent techniques have been developed to provide this value based dependence information about arrays. This section describes the representation produced by our algorithms for value based array dependence analysis [PW93, PW94, PW98] Most systems for analysis of scalars provide information about which de nitions reach which uses. To provide accurate information about arrays, we must also describe either (a) which loop iterations of the de nition and use are connected, or (b) which elements of the array carry the ow ....

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William Pugh and David Wonnacott. Nonlinear array dependence analysis. Technical Report CS-TR-3372, Dept. of Computer Science, University of Maryland, College Park, November 1994.

The New Framework for Loop Nest Optimization in GCC.. - Pop, Cohen, Jouvelot, .. (Correct)