This paper presents a novel framework for the symbolic bounds analysis of pointers, array indices, and accessed memory regions. Our framework formulates each analysis problem as a system of inequality constraints between symbolic bound polynomials. It then reduces the constraint system to a linear program. The solution to the linear program provides symbolic lower and upper bounds for the values of pointer and array index variables and for the regions of memory that each statement and procedure accesses. This approach eliminates fundamental problems associated with applying standard xed-point approaches to symbolic analysis problems. Experimental results from our implemented compiler show that the analysis can solve several important problems, including static race detection, automatic parallelization, static detection of array bounds violations, elimination of array bounds checks, and reduction of the number of bits used to store computed values.

This article presents a new analysis technique, commutativity analysis, for automatically parallelizing computations that manipulate dynamic, pointer-based data structures. Commutativity analysis views the computation as composed of operations on objects. It then analyzes the program at this granularity to discover when operations commute (i.e., generate the same final result regardless of the order in which they execute). If all of the operations required to perform a given computation commute, the compiler can automatically generate parallel code. We have implemented a prototype compilation system that uses commutativity analysis as its primary analysis technique

Divide and conquer algorithms are a good match for modern parallel machines: they tend to have large amounts of inherent parallelism and they work well with caches and deep memory hierarchies. But these algorithms pose challenging problems for parallelizing compilers. They are usually coded as recursive procedures and often use pointers into dynamically allocated memory blocks and pointer arithmetic. All of these features are incompatible with the analysis algorithms in traditional parallelizing compilers. This paper presents the design and implementation of a compiler that is designed to parallelize divide and conquer algorithms whose subproblems access disjoint regions of dynamically allocated arrays. The foundation of the compiler is a flow-sensitive, context-sensitive, and interprocedural pointer analysis algorithm. A range of symbolic analysis algorithms build on the pointer analysis information to extract symbolic bounds for the memory regions accessed by (potentially recursive) procedures that use pointers and pointer arithmetic. The symbolic bounds information allows the compiler to find procedure calls that can execute in parallel without violating the data dependences. The compiler generates code that executes these calls in parallel. We have used the compiler to parallelize several programs that use divide and conquer algorithms. Our results show that the programs perform well and exhibit good speedup. 1

This paper presents the results of the Cedar Hand-Parallelization Experiment, conducted from 1989 through 1992 within the Center for Supercomputing Research and Development (CSRD) at the University of Illinois. In this experiment we manually transformed the Perfect Benchmarks R fl into parallel program versions. In doing so, we used techniques that may be automated in an optimizing compiler. We then ran these programs on the Cedar multiprocessor (built at CSRD during the 1980s) and measured the speed improvement due to each technique.

The elimination of induction variables and the parallelization of reductions in FORTRAN programs have been shown to be integral to performance improvement on parallel computers [7, 8]. As part of the Polaris project [5], compiler passes that recognize these idioms have been implemented and evaluated. Developing these techniques to the point necessary to achieve significant speedups on real applications has prompted solutions to problems that have not been addressed in previous reports on idiom recognition techniques. These include analysis techniques capable of disproving zero-trip loops, symbolic handling facilities to compute closed forms of recurrences, and interfaces to other compilation passes such as the data-dependence test. In comparison, the recognition phase of solving induction variables, which has received most attention so far, has in fact turned out to be relatively straightforward. This paper provides an overview of techniques described in more detail in [12].

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Because most of the execution time of a program is typically spend in loops, loop optimization is the main target of optimizing and restructuring compilers. An accurate determination of induction variables and dependencies in loops is of paramount importance to many loop optimization and parallelization techniques, such as generalized loop strength reduction, loop parallelization by induction variable substitution, and loop-invariant expression elimination. In this paper we present a new method for induction variable recognition. Existing methods are either ad-hoc and not powerful enough to recognize some types of induction variables, or existing methods are powerful but not safe. The most powerful method known is the symbolic differencing method as demonstrated by the Parafrase-2 compiler on parallelizing the Perfect Benchmarks (R) . However, symbolic differencing is inherently unsafe and a compiler that uses this method may produce incorrectly transformed programs without issuing a warning. In contrast, our method is safe, simpler to implement in a compiler, better adaptable for controlling loop transformations, and recognizes a larger class of induction variables. 1

. To effectively parallelize real programs, parallelizing compilers need powerful symbolic analysis techniques [13, 6]. In previous work we have introduced an algorithm called range propagation [4] that provides such capabilities. Range propagation has been implemented in Polaris, a parallelizing Fortran compiler being developed at the University of Illinois [7]. Because the algorithm is relatively expensive and several compilation passes make use of it, we have studied opportunities for increasing its efficiency. In this paper we present an algorithm that provides range analysis on-demand. We have implemented this algorithm in Polaris as well, and have measured its effectiveness. 1 Introduction Range propagation was developed for the Polaris parallelizing compiler in response to our observed need of compilation passes to determine and reason about the values and expressions that program variables can take on. The algorithm centers upon the computation and manipulation of ranges, whic...

With the success of formal verification techniques like equivalence checking and model checking for hardware designs, there has been growing interest in applying such techniques for formal analysis and automatic verification of software programs. This paper provides a brief tutorial on model checking of C programs. The essential approach is to model the semantics of C programs in the form of finite state systems by using suitable abstractions. The use of abstractions is key, both for modeling programs as finite state systems and for reducing the model sizes in order to manage verification complexity. We provide illustrative details of a verification platform called F-SOFT, which provides a range of abstractions for modeling software, and uses customized SAT-based and BDD-based model checking techniques targeted for software.

The elimination of induction variables and the parallelization of reductions in FORTRAN programs has been shown to be integral to performance improvement on parallel computers [9, 10]. As part of the Polaris project, compiler passes that recognize these idioms have been implemented and evaluated. Developing these techniques to the point necessary for achieving significant speedups on real applications has prompted solutions to problems that have not been addressed in previous reports. These include analysis capabilities to disprove zero-trip loops, symbolic handling facilities to compute closed forms of recurrences, and interfaces to other compilation passes, such as the datadependence test. In comparison, the analysis phase of induction variables, which has received most attention so far, has turned out to be relatively straightforward. 1 Introduction The parallelization of loops requires resolution of many types of data dependences ([2], [5], [17]). In particular, cross-iteration de...