Data Dependence and Data-Flow Analysis of Arrays

The power of any compiler is derived from, and also limited by, its program analyzers. Finding the right abstraction for program analysis is crucial in the development of compiler technology. For the abstraction to be useful, it must include sufficient information to support the code optimizations and transformations. In addition, it must be tractable to extract the information from at least a large enough set of programs. Data dependence, distance vectors and direction vectors are important data abstractions that have been proven useful for parallelization and loop transformations, and they are applicable to a large set of programs. The parallelizing compiler research frontier is currently pushing the limits of traditional data dependence analysis. For example, evaluation of today’s compiler technology suggests that reuse of data arrays in programs greatly reduces the opportunities for parallelism. Many more loops can be parallelized by privatizing the work arrays, that is, assigning a separate copy of the array to each processor. The information needed to support such an optimization is not just memory disambiguation, that is, if two references can refer to the same location. To determine if each iteration can have its own copy of the array, we need data-flow analysis on individual array elements. Another important research topic is code generation for distributed memory machines. The compiler is responsible for maintaining the coherence of data across processors. Generating efficient distributed memory code requires exact data-flow relationships between accesses to individual array locations. This paper proposes several analysis techniques that are useful for higher level optimizations. As we develop new data dependence abstractions, it is useful to relate the different abstractions in a uniform mathematical framework. We show that the various existing data dependence abstractions can be viewed as simply different approximations to the same dependence problem. For example, we say that two references are dependent as long as one dynamic pair of the instances of the two references can refer to the same location. Dependence levels, direction vectors and distance vectors provide more accurate approximations. We can define the approximations precisely using the mathematical concept of equivalence classes. Simple data dependence is a lower limit of the approximation in that all pairs of instances are said to belong to the same single equivalence class. The upper