The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0-Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worst-case exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...

Precise and efficient dependence tests are essential to the effectiveness of a parallelizing compiler. This paper proposes a dependence testing scheme based on classifying pairs of subscripted variable references. Exact yet fast dependence tests are presented for certain classes of array references, as well as empirical results showing that these references dominate scientific Fortran codes. These dependence tests are being implemented at Rice University in both PFC, a parallelizing compiler, and ParaScope, a parallel programming environment.

this paper we present a practical technique for detecting a broader class of linear induction variables than is usually recognized, as well as several other sequence forms, including periodic, polynomial, geometric, monotonic, and wrap-around variables. Our method is based on Factored Use-Def (FUD) chains, a demand-driven representation of the popular Static Single Assignment form. In this form, strongly connected components of the associated SSA graph correspond to sequences in the source program: we describe a simple yet efficient algorithm for detecting and classifying these sequences. We have implemented this algorithm in Nascent, our restructuring Fortran 90+ compiler, and we present some results showing the effectiveness of our approach.

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...

Standard array data dependence techniques can only reason about linear constraints. There has also been work on analyzing some dependences involving polynomial constraints. Analyzing array data dependences in real-world programs requires handling many "unanalyzable" terms: subscript arrays, run-time tests, function calls. The standard approach to analyzing such programs has been to omit and ignore any constraints that cannot be reasoned about. This is unsound when reasoning about value-based dependences and whether privatization is legal. Also, this prevents us from determining the conditions that must be true to disprove the dependence. These conditions could be checked by a run-time test or verified by a programmer or aggressive, demand-driven interprocedural analysis. We describe a solution to these problems. Our solution makes our system sound and more accurate for analyzing value-based dependences and derives conditions that can be used to disprove dependences. We also give some p...

Many analyses and transformations in a parallelizing compiler can benefit from the abilityto compare arbitrary symbolic expressions. In this paper, we describe how one can compare expressions by using symbolic ranges of variables. A range is a lower and upper bound on a variable. We will also describe how these ranges can be efficiently computed from the program text. Symbolic range propagation has been implemented in Polaris, a parallelizing compiler being developed at the University of Illinois, and is used for symbolic dependence testing, detection of zero-trip loops, determining array sections possibly referenced by an access, and loop iteration-count estimation.

Compiling for efficient execution on advanced computer architectures requires extensive program analysis and transformation. Most compilers limit their analysis to simple phenomena within single procedures, limiting effective optimization of modular codes and making the programmer's job harder. We present methods for analyzing array side effects and for comparing nonconstant values computed in the same and different procedures. Regular sections, described by rectangular bounds and stride, prove as effective in describing array side effects in Linpack as more complicated summary techniques. On a set of six programs, regular section analysis of array side effects gives 0 to 39 percent reductions in array dependences at call sites, with 10 to 25 percent increases in analysis time. Symbolic analysis is essential to data dependence testing, array section analysis, and other high-level program manipulations. We give methods for building symb...

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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.

It is the goal of the Polaris project to develop a new parallelizing compiler that will overcome limitations of current compilers. While current parallelizing compilers may succeed on small kernels, they often fail to extract any meaningful parallelism from large applications. After a study of application codes, it was concluded that by adding a few new techniques to current compilers, automatic parallelization becomes possible. The techniques needed are interprocedural analysis, scalar and array privatization, symbolic dependence analysis, and advanced induction and reduction recognition and elimination, along with run-time techniques to allow data dependent behavior.