M.N. Wegman and F.K. Zadeck. Constant propagation with conditional branches. In ACM Symposium on Principles of Programming Languages, 1985. 34  Home/Search   Document Not in Database   Summary   Related Articles   Check

....intraprocedural express lane transformation. The range analysis we use allows the upper bound of a range to be increased once before it widens the upper bound to (MaxVal 1) Lower bounds are treated similarly. Our range analysis is similar to Wegman and Zadeck s conditional constant propagation [14] in that (1) it simultaneously performs dead code analysis and (2) it uses conditional branches to refine the data flow facts. The value 99 was arrived at experimentally; duplicating more paths does not cause a greater benefit for range analysis, but it does cause a significant increase in ....

M.N. Wegman and F.K. Zadeck. Constant propagation with conditional branches. In POPL85.

....handler number 3 is executed in a context where lx necessarily is One v, the switch it performs is useless and line 16 can be simpli ed into 3 . This elimination of useless tests[4] is usually performed at a lower level by combining dead code elimination[9] and conditional constant propagation[21, 6]. Finally, after all optimizations, there remains one redundant switch in produced code, in trap handler number 2 (line 12) As a result, vectors (Cons (v1, v2) Nil) are mapped to 2 by testing ly twice. One should notice that this is precisely the test that would get duplicated by compilation to ....

Wegman, M., and Zadeck, F. K. Constant propagation with conditional branches. In Conference Record of the 12th Annual ACM Symposium on Principles of Programming Languages (New Orleans, LS, Jan. 1985), B. K. Reid, Ed., ACM Press, pp. 291-299.

....combine analyses without manually specifying their interaction The answers to these questions impact the structure of optimizing compilers in a fundamental way. We investigate these questions by relating two avours of imperative program improvement often called pessimism and optimism (e.g. WZ91,CC95] to ideas from algebra and coalgebra. We consider a restricted subset of program improvements that t the following model: the improvement decides some relation (for example, def use, congruence, must alias) and then transforms the program based on this relation. Within this model we ....

....call this approach iterating improvement passes. if false then return x y false if y then return 2 Fig. 1: Two programs to illustrate a phase ordering problem. 1.2 Combining improvements Surprisingly, iterating improvement passes is not always the optimal solution. Wegman and Zadeck [WZ91] describe a combination of unreachable code elimination with constant propagation called conditional constant propagation (CCP) CCP achieves results strictly better than iterating the two passes separately. Consider the program code: loop : if x = 0 then else goto loop Neither ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-210, April 1991.

....tests, ranging from Banerjee s GCD test[2] to Pugh s Omega test[13] which allow the data flow analysis required for copy propagation to be made more accurate for array accesses. An extension to constant propagation that takes conditional branches into account is given by Wegman and Zadeck[18], but it is limited to branch conditions that evaluate to a constant true or false. To the best of our knowledge, our work is the first attempt to automate copy propagation and constant propagation for programs with arrays by treating each instance of each statement separately, and thus allowing ....

M. Wegman and K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

....can be negative. 3.2 Bitwidth Analysis We use a flow sensitive interprocedural bitwidth analysis to find constant values, unused and constant fields, and to reduce field sizes where possible. Our dataflow framework uses Wegman and Zadeck s Sparse Conditional Constant (SCC) propagation algorithm [19] as a basis. We then extend their analysis interprocedurally, add coverage of Java language features, and extend the value lattice to handle bitwidths. Since almost all types in Java are signed (with the exception of the 16 bit char) we must be able to describe bitwidths of both negative and ....

....closure of this map over the call graph to determine a safe set of methods which the constructor may call before a definite initialization of f. As long as control flow may not pass to a method not in the safe set before f is written, then f is definitely initialized. On the SCC lattice of [19], 0 5 = but see footnote 7) When performing bitwidth analysis, definitely initialized fields are allowed to start at in the dataflow lattice. All other fields must start at value 0, which will make it impossible for the field to represent a non zero constant value. The results of ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-- 210, April 1991.

....framework is based on control flow graphs that have two types of nodes: calculation nodes, whose affect on the flow of control is limited, and conditional branches. Static knowledge of values of controlling expressions enables such optimizations as elimination of redundant conditional branches [WZ], elimination of unreachable code, and removal of conditional branches from some execution paths [Sk] Two novel optimizations enabled by the analysis are presented in this paper. These optimizations eliminate conditional branches from some of execution paths. One of them involves code ....

....are an example [LR] The environments are designed to capture relevant program properties while remaining compact. Note that most predicate symbols in procedural languages are either equivalence relations or linear orderings. The analysis presented here subsumes conditional constant propagation [WZ] and number interval propagation with widening (widening is embedded into meet ) CC, Bo] Usually, properties of program variables are the subject of data flow analyses. Our analysis takes advantage of tracking properties of all program expressions (and possibly others) Transfer functions ....

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M.N. Wegman, F.K. Zadeck. Constant Propagation with Conditional Branches. ACM Transactions on Programming Languages and Systems, v. 13, 1991, #2, 181-210.

....to accomplish both loop invariant code motion and common subexpression elimination [33, 35, 23] Our compiler performs global reassociation and global renaming prior to running lcm [5] 2. Sparse conditional constant propagation (sccp) has been applied to identify and fold compile time constants [47]. This discovers a large class of constant values and makes them textually obvious. We approximate the property of invariance with a pair of properties that are easier to test. After both lcm and sccp have been applied, the algorithm considers a value to be a region constant if its value is a ....

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. In Conference Record of the Twelfth Annual ACM Symposium on Principles of Programming Languages, pages 291--299, New Orleans, Louisiana, Jan. 1985. 18

....3.2 proves that variables are renamed correctly to satisfy properties 2.1, 2.2 and 2.3. 3.1. 3 Pruning SSI form The SSI algorithm can be run using any conservative approximation to the liveness information (including the function MaybeLive(v; n) true) if unused code elimination We follow [19] in distinguishing unreachable code elimination, which removes code that can never be executed, from unused code elimination, which deletes sections of code whose results are never used. Both are often called dead code elimination in the literature. 100 1000 10000 100000 10 100 1000 10000 ....

....not on algorithmic worst bounds complexity, but on empirical evidence. This reasoning is not unjusti ed; Knuth [13] showed in 1974 that human generated programs almost without exception show properties favorable to analysis; in particular shallow maximum loop nesting depth. Wegman and Zadeck [19] clearly make this distinction by noting that: In theory the size [of the SSA form representation] can be O(EV ) but empirical evidence indicates that the work required to compute the SSA graph is linear in the program size. Our worst case space complexity bounds for SSI form are identical ....

[Article contains additional citation context not shown here]

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-210, April 1991.

....in CPS is more costly than necessary. Hence, instead of using Kelsey s CPSbased approach, we prefer to formalise the mapping of programs from SSA to ANF (in Section 2) we do so more formally than Appel [2] Section 3 exploits the correspondence of SSA and ANF by rephrasing Wegman and Zadeck s [22] sparse conditional constants algorithm, which performs constant propagation and unreachable code elimination. In the following, we call Wegman and Zadeck s original SSA based algorithm Scc ssa and call our new ANF based algorithm Scc anf . We present Scc anf in a notation that has a well de ned ....

....rigorously de ned. We establish that Scc anf is conservative; i.e. that the variables marked as constant are indeed constant (Section 4) However, we do not actually prove that Scc anf and Scc ssa implement the same analysis. In fact, this would be hard to achieve due to Wegman and Zadeck s [22] rather informal presentation. We do, however, present formal statements about the soundness of our mapping of SSA programs to ANF programs and about the soundness of Scc anf . We like to regard the results in this paper as a step towards reaping the well established bene ts of typed, functional ....

[Article contains additional citation context not shown here]

Wegman, M. N. and F. K. Zadeck, Constant propagation with conditional branches, ACM Transactions on Programming Languages and Systems 13 (1991), pp. 181-210. 15

....in our analysis. 3.2 Bitwidth Analysis We use a flow sensitive interprocedural bitwidth analysis to find constant values, unused and constant fields, and to reduce field sizes where possible. Our dataflow framework uses Wegman and Zadeck s Sparse Conditional Constant (SCC) propagation algorithm [17] as a basis. We then extend their analysis interprocedurally, add coverage of Java language features, and extend the value lattice to handle bitwidth. Since almost all types in Java are signed (with the exception of the 16 bit char) we must be able to describe bitwidths of # # # # # # # # ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

....type of quadruple, and a flowgraph of the SSA format quadruple list was input to the optimization routines. 4.2. 3 Conditional Constant Propagation Wegman and Zadeck s Sparse Conditional Constant (SCC) algorithm was used to find constant expressions, constant conditions, and unreachable code [WZ91] Figure 3 shows the optimization extent possible. The output of the SCC algorithm is an association of variables to one of f ; c; g, where marks a variable that is never defined, c indicates a constant value, and i 1 1 j 1 i 1 Theta 4 = j 1 4 if (j 1 1 2) i 4 OE(i 2 ; i ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and

....an iloc to iloc transformation designed to improve the code in some way. In the experiments for this paper, the following 10 program transformations were used: 1. Constant propagation (cprop) This pass is an implementation of Wegman and Zadeck s sparse conditional constant propagation technique [22]. We run cprop with an option ( m) that disables conversion of multiplies into shifts and adds. That conversion forestalls some subsequent optimizations and increases code size. We also enable the option ( f) that performs propagation on symbolic constants. 2. Dead Code Elimination (dead) Our ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM 13(2):181--210, April 1991.

....restrictions as possible, which will typically require substantial changes to the runtime system. 3. 1 Bitwidth analysis Our bitwidth analysis is an inter procedural extension of that described in [3] It is based on Wegman and Zadeck s Sparse Conditional Constant (SCC) propagation algorithm [11], with extensions to a bitwidth lattice. Since almost all types in Java are signed (with the exception of the 16 bit char) we must handle both negative and positive numbers. We rst extend the basic three level value lattice of Wegman and Zadeck to allow the classi cation of negative, positive, ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-210, April 1991.

....in [8] are instructive, but the optimization techniques presented there are not applicable: speed is not an issue for efficient hardware we want the most precise analysis possible. The necessary analysis has much in common with the Wegman and Zadeck s Sparse Conditional Constant optimization [16], where the constants being propagated can be imagined as constant pointers to class instances. Cliff Click s work on combining optimizations is instructive [7] the best extended type analysis is possible only in conjunction with standard constant propagation and dead code analysis. The algorithm ....

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, Apr. 1991. 5

....380 36,959 681.2M gs 1,142 68,590 48.2M Figure 13: Program characteristics etc) are given in terms of intermediate code instructions. The compiler s optimizer includes the following passes: global value driven code motion [4] operator strength reduction [5] conditional constant propagation [21], copy propagation, local value numbering, global dead code elimination [10] useless control flow removal, and global register allocation [3] For this study we deliberately avoided using optimization passes that would increase code size, such as inlining and loop unrolling. The register ....

M. Wegman and K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-- 210, April 1991.

....is, arguably, the strongest global technique fordetecting redundant scalar values. It finds all the redundancies discovered by the Alpern Wegman Zadeck algorithm [2] It finds a broad class of algebraic identities. It discovers all the constants found by the sparse simple constant algorithm [34]. Sccvn has been implemented in a number of compilers. The sccvn algorithm extends Simpson s dominator based technique (dvnt)toaglobal scope [7, 30] It abstracts cycles out in the control flow graph (cfg)anditerates over each cycle s internal structure to find a fixed point solution for that ....

....from Mediabench [22] 4 from SPEC2000 CPU integer benchmarks [32] The benchmarks and the statistics of the compiled Iloc intermediate form for the applications are listed in Table 1. The applications are first translated from C into Iloc,and asequence of sparse conditional constant propagation [34], dead code elimination, control flow restructuring (to remove empty and unreachable basic blocks) copy coalescing passes are appliedtotheIloc.Afterthat,wholeprogram pointer analysis is run to get the annotated Iloc with point to and function ref and mod information. The v0 and v1 pass works on ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transact i ons on Programming Languages and Systems, 13(2):181--210, 1991.

....closure of this map over the call graph to determine a safe set of methods which the constructor may call before a definite initialization of f. As long as control flow may not pass to a method not in the safe set before f is written, then f is definitely initialized. On the SCC lattice of [22], 0 # 5 = # (but see footnote 8) static field bits alloc ed Benchmark before after space saved compress 7591 5430 3.0 jess 13349 10634 30.1 raytrace 7467 5296 0.9 db 6777 4983 0.3 javac 11560 8161 5.4 mpegaudio 6777 4983 1.5 mtrt 7467 5296 0.9 jack 8356 6037 17.2 Table 2: ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

....an iloc to iloc transformation designed to improve the code in some way. In the experiments for this paper, the following 10 program transformations were used: 1. Constant propagation (cprop) This pass is an implementation of Wegman and Zadeck s sparse conditional constant propagation technique [22]. We run cprop with an option ( m) that disables conversion of multiplies into shifts and adds. That conversion forestalls some subsequent optimizations and increases code size. We also enable the option ( f) that performs propagation on symbolic constants. 2. Dead Code Elimination (dead) Our ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM 13(2):181--210, April 1991.

....to emulate the data flow of programs leads to a high level specification for constant propagation which is directly executable. There are many algorithms for constant propagation, most of them use a graph representation such as control flow graphs with the static single assignment (SSA) property [21], or even the gated single assignment property [17] Special # assignments are introduced to provide the representation of a program with unique variable definitions. The most used algorithm for constant propagation is the Sparse conditional constant propagation (SCC) 21,17,14,2] SCC is an ....

....(SSA) property [21] or even the gated single assignment property [17] Special # assignments are introduced to provide the representation of a program with unique variable definitions. The most used algorithm for constant propagation is the Sparse conditional constant propagation (SCC) [21,17,14,2]. SCC is an optimistic algorithm which avoids to consider unreachable code and continues the propagation of constant values in the branches of conditionals statements. These algorithm properties are also present in our specification. Another approach uses system dependence graphs (SDG) to ....

Wegman, M. and F. Zadeck, Constant propagation with conditional branches, ACM Transactions on Programming Languages and Systems 13 (1991), pp. 181--210.

....intermediatecode level, and all results (code space, dynamic instruction count, etc) are given in terms of intermediatecode instructions. The compiler s optimizer includes the following passes: global value driven code motion [4] operator strength reduction [5] conditional constant propagation [21], copy propagation, local value numbering, global dead code elimination [10] useless control flow removal, and global register allocation [3] For this study we deliberately avoided using optimization passes that would increase code size, such as in instructions Program Funcs static dynamic ....

M. Wegman and K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-- 210, April 1991.

....to sophisticated and extensive optimization to approach the full potential of modern computer architectures. Many powerful optimizations rely on static analysis of the source code. Examples of such static analysis include: live variable analysis [7] various forms of constant propagation [10,20], and aliasing analysis [4] All of these static analyses may be realized as instances of flow analysis problems. They share the following general framework [10] 1. A model of the program defines points where information is to be determined, as well as how control may flow between those points ....

Wegman, M. and F. Zadeck. "Constant Propagation with Conditional Branches," ACM TOPLAS 13, 2, April, 1991, pp. 181-210.

....1(b) at the right. Our goal is now to specialize each copy of the scope 0 with respect to (i) the (hot) value of its key ; and (ii) the values of the invariant portion of the heap. The specialization is carried out with the Wegman Zadeck Sparse Conditional Constant Propagation (SCCP) [31] algorithm. Thanks to its sparsity and linear time efficiency, SCCP is a good fit for runtime specialization. At the same time, despite its simplicity, SCCP serves as a rather powerful on line specializer: First, by evaluating conditionals (some of which may be run time constants) SCCP ignores an ....

....work over a lattice containing concrete addresses, not only integers. To specialize 0 with respect to the invariant memory locations, we need to modify how SCCP evaluates loads (which in our setting are getfield and getarray bytecodes) SCCP processes instructions with the routine VisitInstr [31]. We extend it as shown below: if (I is r = load p ) LatticeVal(p) if ( is not a constant) or 1. else if (sp.IsInvariant( 2. LoadMemory( 3. LatticeVal(r) 4. add D Q F to GuardedLocations The effect of the extension (lines 1 3) is that when the ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

....as well as other live ranges. Briggs uses SSA in his implementation of rematerialization [5] By examining the defining instruction for each value, he recognizes never killed values and prop agates this information through the SSA graph. Sparse simple constant algorithm by Wegman and Zadeck [52] is used to propagate never killed information. 4.3.1 The FBR Algorithm The FBR algorithm is described in Figure 4.7. The basic framework of FBR is very similar to FBS. We first perform the splitting step and partition the live range Ll into two live ranges Lll and Ll2. We then check all live ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with con- ditional branches. TOPLAS, 13(2):181 210, April 1991. 216

....what live ranges in a program are rematerializable. Briggs [3] suggests that each live range should be decomposed into its component values, according to the structure of the SSA [15] graph. To discover rematerializable values, a simple forward propagation algorithm similar to constant propagation [51] can be used. In Briggs scheme, the following values are considered to be rematerializable: All constants, All address arithmetic expressions that depend only on constants and dedi cated registers such as the frame pointer and a global data pointer. Loads from constant offset in the stack ....

M. Wegman and K. Zadeck. Constant propagation with conditional branches. ACM Trans. on Programming Languages and Systems, 13(2):181 210, April 1991.

....combine analyses without manually specifying their interaction The answers to these questions impact the structure of optimizing compilers in a fundamental way. We investigate these questions by relating two flavours of imperative program improvement often called pessimism and optimism (e.g. WZ91,CC95] to ideas from algebra and coalgebra. We consider a restricted subset of program improvements that fit the following model: the improvement decides some relation (for example, def use, congruence, must alias) and then transforms the program based on this relation. Within this model we ....

....improvement passes. if false then 2 return x Program 2 false if y then return 2 return 1 Fig. 1: Two programs to illustrate a phase ordering problem. 1.2 Combining improvements Surprisingly, iterating improvement passes is not always the optimal solution. Wegman and Zadeck [WZ91] describe a combination of unreachable code elimination with constant propagation called conditional constant propagation (CCP) CCP achieves results strictly better than iterating the two passes separately. Consider the program code: loop : if x = 0 then else goto loop Neither ....

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

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M.N. Wegman and F.K. Zadeck. Constant propagation with conditional branches. In ACM Symposium on Principles of Programming Languages, 1985. 34

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Wegman, M., and Zadeck, F. Constant propagation with conditional branches. ACM Trans. Program. Lang. Syst. 13, 2 (Apr. 1990), 181--210.

No context found.

Wegman, M., and Zadeck, F. Constant propagation with conditional branches. ACM Trans. Program. Lang. Syst. 13, 2 (Apr. 1990), 181--210.

No context found.

M. Wegman and F. Zadeck, "Constant propagation with conditional branches," ACM Transactions on Programming Languages, Vol. 13, No. 2, pp. 181-210, 1991.

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Wegman, Mark N., and F. Kenneth Zadeck. 1991. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems 13(2):181--210.

No context found.

Wegman, M. N., and Zadeck, F. K. Constant propagation with conditional branches. In Conference Record, Twelfth Annual ACM Symposium on Principles of Programming Languages (Jan. 1985), pp. 291--299.

No context found.

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, Apr 1991.

No context found.

M. N. Wegman and K. Zadeck. Constant propagation with conditional branches. Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM 13(2):181-210, April 1991.

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Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991. 104

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Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. In Conference Record of the Twelfth Annual ACM Symposium on Principles of Programming Languages, pages 291--299, New Orleans, Louisiana, January 1985.

No context found.

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

Wegman, M.N., Zadeck, F.K.: Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems 13 (1991) 181-210

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M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, 1991.

No context found.

M. N. Wegman and F. K. Zadeck. Constant Propagation with Conditional Branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, Apr. 1991.

No context found.

Mark N. Wegman and Kenneth Zadeck. Constant Propagation with Conditional Branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

M. Wegman and F.K. Zadeck. Constant propagation with conditional branches. In ACM Transactions on Programming Languages and Systems 13(2), April 1991.

No context found.

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. In 12th Annual ACM Symposium on Principles of Programming Languages, POPL 1985.

No context found.

M. N. Wegman and K. Zadeck. Constant Propagation with Conditional Branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-210, Apr. 1991.

No context found.

Mark N. Wegman and F. Kenneth Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181--210, April 1991.

No context found.

M. N. Wegman and F. K. Zadeck, "Constant Propagation with Conditional Branches", ACM Transactions on Programming Languages and Systems, Vol. 13, No. 2, April 1991, pp. 181--210.

No context found.

M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2):181-210, 1991.

No context found.

M. Wegman and F. K. Zadeck, `Constant propagation with conditional branches', Conference Record of the 12th Annual ACM Symposium on Principles of Programming Languages, January 1985, pp. 291--299.

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