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Symbolic Analysis for Parallelizing Compilers
, 1994
"... Symbolic Domain The objects in our abstract symbolic domain are canonical symbolic expressions. A canonical symbolic expression is a lexicographically ordered sequence of symbolic terms. Each symbolic term is in turn a pair of an integer coefficient and a sequence of pairs of pointers to program va ..."
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Cited by 105 (4 self)
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Symbolic Domain The objects in our abstract symbolic domain are canonical symbolic expressions. A canonical symbolic expression is a lexicographically ordered sequence of symbolic terms. Each symbolic term is in turn a pair of an integer coefficient and a sequence of pairs of pointers to program variables in the program symbol table and their exponents. The latter sequence is also lexicographically ordered. For example, the abstract value of the symbolic expression 2ij+3jk in an environment that i is bound to (1; (( " i ; 1))), j is bound to (1; (( " j ; 1))), and k is bound to (1; (( " k ; 1))) is ((2; (( " i ; 1); ( " j ; 1))); (3; (( " j ; 1); ( " k ; 1)))). In our framework, environment is the abstract analogous of state concept; an environment is a function from program variables to abstract symbolic values. Each environment e associates a canonical symbolic value e x for each variable x 2 V ; it is said that x is bound to e x. An environment might be represented by...
Determining Average Program Execution Times and their Variance
, 1989
"... This paper presents a general framework for determining average program execution times and their variance, based on the program's interval structure and control dependence graph. Average execution times and variance values are computed using frequency information from an optimized counterbased exe ..."
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Cited by 87 (0 self)
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This paper presents a general framework for determining average program execution times and their variance, based on the program's interval structure and control dependence graph. Average execution times and variance values are computed using frequency information from an optimized counterbased execution profile of the program. 1 Introduction It is important for a compiler to obtain estimates of execution times for subcomputations of an input program, if it is to attempt optimizations related to overhead values in the target architecture. In earlier work [SH86a, SH86b, Sar87, Sar89], we used estimates of execution times to facilitate the automatic partitioning and scheduling of programs written in the singleassignment language, Sisal, for parallel execution on multiprocessors. In this paper, we present a general framework for estimating average execution times in a program. This approach is based on the interval structure [ASU86] and the control dependence relation [FOW87], both of w...
Termination of polynomial programs
 In VMCAI’2005: Verification, Model Checking, and Abstract Interpretation, volume 3385 of LNCS
, 2005
"... Abstract. We present a technique to prove termination of multipath polynomial programs, an expressive class of loops that enables practical code abstraction and analysis. The technique is based on finite differences of expressions over transition systems. Although no complete method exists for deter ..."
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Cited by 52 (4 self)
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Abstract. We present a technique to prove termination of multipath polynomial programs, an expressive class of loops that enables practical code abstraction and analysis. The technique is based on finite differences of expressions over transition systems. Although no complete method exists for determining termination for this class of loops, we show that our technique is useful in practice. We demonstrate that our prototype implementation for C source code readily scales to large software projects, proving termination for a high percentage of targeted loops. 1 Introduction Guaranteed termination of program loops is necessary for many applications,especially those for which unexpected behavior can be catastrophic. Even for applications that are not considered "safety critical, " applying automatic methodsfor proving loop termination would certainly do no harm. Additionally, proving general temporal properties of infinite state programs requires terminationproofs, for which automatic methods are welcome [4, 7, 10]. We present a method of nonlinear termination analysis for imperative loopswith multiple paths, polynomial guards, and polynomial assignments. The method is nonlinear, first, because the guards and assignments need not be linear and, second, because it can prove the termination of terminating loops that do not have linear ranking functions. The method is sound, but not complete.Indeed, we show that no complete method for this class of programs exists. In practical programs, however, our method proves termination of a high percentageof the targeted loops at low computation cost, and hence is useful.
Complexity Analysis for a Lazy HigherOrder Language
 In Proceedings of the 3rd European Symposium on Programming
, 1990
"... This paper is concerned with the timeanalysis of functional programs. Techniques which enable us to reason formally about a program's execution costs have had relatively little attention in the study of functional programming. We concentrate here on the construction of equations which compute t ..."
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Cited by 47 (2 self)
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This paper is concerned with the timeanalysis of functional programs. Techniques which enable us to reason formally about a program's execution costs have had relatively little attention in the study of functional programming. We concentrate here on the construction of equations which compute the timecomplexity of expressions in a lazy higherorder language. The problem with higherorder functions is that complexity is dependent on the cost of applying functional parameters. Structures called costclosures are introduced to allow us to model both functional parameters and the cost of their application. The problem with laziness is that complexity is dependent on context. Projections are used to characterise the context in which an expression is evaluated, and costequations are parameterised by this contextdescription to give a compositional timeanalysis. Using this form of context information we introduce two types of timeequation: sufficienttime equations and nece...
Static caching for incremental computation
 ACM Trans. Program. Lang. Syst
, 1998
"... A systematic approach is given for deriving incremental programs that exploit caching. The cacheandprune method presented in the article consists of three stages: (I) the original program is extended to cache the results of all its intermediate subcomputations as well as the nal result, (II) the e ..."
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Cited by 47 (19 self)
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A systematic approach is given for deriving incremental programs that exploit caching. The cacheandprune method presented in the article consists of three stages: (I) the original program is extended to cache the results of all its intermediate subcomputations as well as the nal result, (II) the extended program is incrementalized so that computation on a new input can use all intermediate results on an old input, and (III) unused results cached by the extended program and maintained by the incremental program are pruned away, l e a ving a pruned extended program that caches only useful intermediate results and a pruned incremental program that uses and maintains only the useful results. All three stages utilize static analyses and semanticspreserving transformations. Stages I and III are simple, clean, and fully automatable. The overall method has a kind of optimality with respect to the techniques used in Stage II. The method can be applied straightforwardly to provide a systematic approach to program improvement via caching.
Static dependent costs for estimating execution time
 In Proc. of the 1994 ACM Conference on LISP and functional programming
, 1994
"... We present the first system for estimating and using datadependent expression execution times in a language with firstclass procedures and imperative constructs. Thepresence of firstclass procedures and imperative constructs makes cost estimation a global problem that can benefit from type informa ..."
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Cited by 46 (0 self)
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We present the first system for estimating and using datadependent expression execution times in a language with firstclass procedures and imperative constructs. Thepresence of firstclass procedures and imperative constructs makes cost estimation a global problem that can benefit from type information. We estimate expression costs with the aid of an algebraic type reconstruction system that assigns every procedure atype that includes a static dependent cost. A static dependent cost describes the execution time of a procedure in terms of its inputs. In particular, a procedure’s static dependent cost can depend on the size of input data structures and the cost of input firstclass procedures. Our cost system produces symbolic cost expressions that contain free variables describing the size and cost of the procedure’s inputs. At runtime, a cost estimate is dynamically computed from the statically determined cost expression and runtime cost and size information. We present experimental results that validate our cost system onthreecompilers and architectures. We experimentally demonstrate the utility of cost estimates in making dynamic parallelization decisions. In our experience, dynamic parallelization meets or exceeds the parallel performance of any fixed number of processors. 1
Deriving incremental programs
, 1993
"... A systematic approach i s g i v en for deriving incremental programs from nonincremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domainspeci c knowledge, centered around e ective utilization of cachin ..."
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Cited by 39 (21 self)
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A systematic approach i s g i v en for deriving incremental programs from nonincremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domainspeci c knowledge, centered around e ective utilization of caching, in order to provide a degree of incrementality not otherwise achievable by a generic incremental evaluator. 1
A Naïve Time Analysis and its Theory of Cost Equivalence
 Journal of Logic and Computation
, 1995
"... Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nons ..."
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Cited by 39 (7 self)
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Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nonstrict functional programs with lazy lists. One limitation of this basic calculus is that the ordinary equational reasoning on functional programs is not valid. In order to buy back some of these equational properties we develop a nonstandard operational equivalence relation called cost equivalence, by considering the number of computation steps as an `observable' component of the evaluation process. We define this relation by analogy with Park's definition of bisimulation in CCS. This formulation allows us to show that cost equivalence is a contextual congruence (and thus is substitutive with respect to the basic calculus) and provides useful proof techniques for establishing costequivalen...
Automatic Accurate TimeBound Analysis for HighLevel Languages
 In Proceedings of the ACM SIGPLAN 1998 Workshop on Languages, Compilers, and Tools for Embedded Systems, volume 1474 of Lecture Notes in Computer Science
, 1998
"... This paper describes a general approach for automatic and accurate timebound analysis. The approach consists of transformations for building timebound functions in the presence of partially known input structures, symbolic evaluation of the timebound function based on input parameters, optimizati ..."
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Cited by 38 (9 self)
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This paper describes a general approach for automatic and accurate timebound analysis. The approach consists of transformations for building timebound functions in the presence of partially known input structures, symbolic evaluation of the timebound function based on input parameters, optimizations to make the overall analysis efficient as well as accurate, and measurements of primitive parameters, all at the sourcelanguage level. We have implemented this approach and performed a number of experiments for analyzing Scheme programs. The measured worstcase times are closely bounded by the calculated bounds. 1 Introduction Analysis of program running time is important for realtime systems, interactive environments, compiler optimizations, performance evaluation, and many other computer applications. It has been extensively studied in many fields of computer science: algorithms [20, 12, 13, 41], programming languages [38, 21, 30, 33], and systems [35, 28, 32, 31]. It is particularl...
Symbolic Analysis: A Basis for Parallelization, Optimization, and Scheduling of Programs
 In Proceedings of the Sixth Workshop on Languages and Compilers for Parallel Computing
, 1993
"... This paper presents an abstract interpretation framework for parallelizing compilers. Within this framework, symbolic analysis is used to solve various flow analysis problems in a unified way. Symbolic analysis also serves as a basis for code generation optimizations and a tool for derivation of com ..."
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Cited by 36 (0 self)
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This paper presents an abstract interpretation framework for parallelizing compilers. Within this framework, symbolic analysis is used to solve various flow analysis problems in a unified way. Symbolic analysis also serves as a basis for code generation optimizations and a tool for derivation of computation cost estimates. A loop scheduling strategy that utilizes symbolic timing information is also presented. 1 Introduction Empirical results indicate that existing parallelizing compilers cause insignificant improvements on the performance of many real application programs [9, 5]. The speedups obtained by manual transformation of these applications [9] show the potential for significantly advancing parallelizing compiler technology. The poor performance of current restructuring compilers can be attributed to two causes: imprecise analysis and inappropriate performancewise transformations. The causes are not completely independent; namely, imprecise information results in inappropriate...