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Probabilistic Alias Analysis for Parallel Programming in SSA Forms.Pdf Probabilistic Alias Analysis for Parallel Programming in SSA Forms Mohamed A. El-Zawawy1 and Mohammad N. Alanazi2 1;2College of Computer and Information Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU) Riyadh, Kingdom of Saudi Arabia 1Department of Mathematics, Faculty of Science Cairo University Giza 12613, Egypt Email1: [email protected] Email2: [email protected] Abstract— Static alias analysis of different type of pro- to achieve tasks like code specialization and data specula- gramming languages has been drawing researcher attention. tion. In other words information calculated by most alias However most of the results of existing techniques for alias analysis techniques do not help compilers to do aggressive analysis are not precise enough compared to needs of optimizations. More specifically, possibly-alias relationships modern compilers. Probabilistic versions of these results, is not rich enough to inform the comfier about the possibility in which result elements are associated with occurrence that constraints for the executions. Hence compilers are probabilities, are required in optimizations techniques of somehow forced to follow a conservative way and assume modern compilers. the conditions validity for all execution paths [1], [2], [3]. This paper presents a new probabilistic approach for alias A dominant programming technique of parallelism for analysis of parallel programs. The treated parallelism model large-scale machines equipped with distributed-memories is that of SPMD where in SPMD, a program is executed is the single program, multiple data (SPMD) model. In using a fixed number of program threads running on dis- SPMD, a program is executed using a fixed number of tributed machines on different data. The analyzed programs program threads running on distributed machines on differ- are assumed to be in the static single assignment (SSA) ent data [4]. SPMD can be executed on low-overhead and form which is a program representation form facilitating simple dynamic systems and is convenient for expressing program analysis. The proposed technique has the form parallelism concepts. This parallelism model is used by of simply-strictured system of inference rules. This enables message-sending architectures such as MPI. SPMD is also using the system in applications like Proof-Carrying Code adapted by languages whose address spaces are globally (PPC) which is a general technique for proving the safety partitioned (PGAS) such as UPC, Co-Array Fortran, and characteristics of modern programs. Titanium. Specific deadlocks can be prevented using the SPDM model which can also be used to achieve probabilistic Keywords: Probabilistic Analysis, Alias Analysis, Parallel Pro- data races and specific program optimizations [5], [6]. gramming, SSA Forms. Static single assignment (SSA) [7], [8] is a program repre- sentation form facilitating program analysis. SSA forms are 1. Introduction important for software re-engineering and compiler construc- Considerable efforts of research have been devoted to tion. Program analysis needs data-flow information about achieve the static alias analysis of different type of pro- points of the program being analyzed. Such information is gramming languages. Algorithms for calculating alias rela- necessary for program compilation and re-engineering and tionships for all program points exist for basic programming is conveniently collected by SSA. For program variables, techniques. Classically, alias relationships fall in two groups: some analyses need to know assignment statements that definitely-alias relationships and possibly-alias relationships. could have assigned the used variable content. In Static The former is typically true for all possible execution paths single assignment (SSA) form exactly one variable definition and the later might typically be true for some of the possible corresponds to a variable use. This is only possible if execution paths. However the information calculated by most the algorithm building the SSA form is allowed to insert existing algorithms for alias analysis is not precise enough auxiliary definitions if it is possible for different definitions compared to the needs of modern compilers. This is so as to get into a specific program point. modern compilers need finer alias-information to be able A general technique for proving the safety characteristics of modern programs is Proof-Carrying Code (PCC) [9], However communications between the distributed machines [10]. PCC proofs are needed and typically constructed using is allowed in a predefined contexts. For example a command logics annotated with inference rules that are language- running on machine 1 may request machine 3 to evaluate a specific. The proofs ensures safety in case there are no bugs specific expression using data of machine 3 and to return in the inference rules. One type of Proof-Carrying Code the result to machine 1. is Foundational Proof-Carrying Code (FPCC) which uses The syntax of the langauge used to present the new prob- theories of mathematical logic. The small trusted base of abilistic alias analysis technique is shown in Figure 1. We FPCCs and the fact that they are not tied to any specific call the langauge mode SSA-DisLang for ease of reference. systems make them more secure and robust. A program in SSA-DisLang consists of a sequence of state- This paper presents a new technique for probabilistic ments where statements are of wide diversity. Statements use alias analysis of parallel programs. The technique has the (distributed) expressions, DExpr. The machines to run SSA- form of simply-strictured system of inference rules. The DisLang programs are typically organized in a hierarchy. information calculated by the proposed technique are precise The distributed expressions include the following: enough compared to information needed by modern compil- • malloc() : allocates a dynamic array in memory and ers for compilations, re-engineering, aggressive-optimization return its base address. processes. The proposed technique is designed to work • run (e; m): evaluates the distributed expression e on on the common and robust data-flow representation; SSA machine m and return the result. forms of parallel programs. The use of inference systems • reform(alis m; int m) e : casts the location denoted by in the proposed technique makes it straightforward for our the distributed expression e as an integer rather than a technique to produce justifications needed by Foundational pointer to a memory location on machine m. Proof-Carrying Code (FPCCs). The proofs have the form of • reform (int mj; int mi)) e : casts the location denoted inference rules derivations that are efficiently transferable. by the distributed expression e as a pointer a memory The parallelism model treated in this paper is that of single location on machine mi rather than as a pointer to a program, multiple data (SPMD) in which the same program memory location on machine mj. is executed on different machines on different sets of data. Our proposed technique assumes that the given program, that is to be be analyzed for its probabilistic alias competent, Motivation has the static single assignments form. Therefore the input The paper is motivated by need for a precise probabilistic program would contain annotations (added by any efficient alias analysis for SPMD programs running on a hierarchy SSA such as algorithm [11]). The program annotations will of distributed machines. The required technique is supposed have the form of new statements added to the original to associate each analysis result with a correctness proof (in program. Therefore statements of SSA-DisLang include the the form of type derivations) to be used in proof-carrying following: code applications. • l := e : this is a classical assignment command. How- Contributions ever the design of the langauge allows using this command to assign a value evaluated at a machine The contribution of the paper is a new approach for to a location on a different machine of the machines probabilistic alias analysis of SPMD programs running on hierarchy. SSA forms of programs and producing justifications with • run (S; m): allows evaluates a specific command S analysis results. on a specific machine m regardless of the executing Paper Outline machine. This command is necessary when some com- mands are convenient only to run on data of certain The outline of this paper is as follows. Section 2 presents machine of the hierarchy. The command is also used the langauge model, SSA-DisLang, of the paper. This section when security is a concern as S would not have access also presents an informal semantics to the langauge con- to all machines. structs. The main content of Section 2 is the new technique • xi := f(xj; xk): this command is to be added by the of the probabilistic alias analysis of SPMD programs. Sec- supposed SSA algorithm and it semantics is that vari- tion 4 concludes the paper and suggests directions for future able xi were created specifically for avoiding multiple work. assignments to variable x. The range of this definition if form definition of variable xj to that of variable xk. 2. Probabilistic Alias analysis for SPMD • xi := md(xj): this is the second sort of annotations This section presents a new technique for probabilistic SSA-DisLang programs. The semantics of this statement alias analysis of parallel programs. The parallelism model is that it is highly likely that variable xi is used to used here is that of SPMD where the same program is define variable xj. Recall that our main technique of the executed on distrusted machines havering different data. paper cares about possibility of assignments to occur in x 2 lVar; iop 2 Iop; bop 2 Bop; and m 2 M ⊆ M l 2 Loc ::= x j l ! y j [l]: e 2 DExpr ::= l j e1 iop e2 j &l j malloc() j run (e; m) j reform(alis m; int m) e j reform (int mj ; int mi)) e: S 2 Stmts ::= l := e j run (S; m) j S1; S2 j xi := f(xj ; xk) j xi := md(xj ) j mu(xj ) j if e then St else Sf j while e do St: Fig.
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