Data-centric transformations on non-integer iteration spaces

Data-centric transformations have been used in recent years to improve locality for several classes of applications. However, the existing work has applied these transformations for integer iteration spaces, i.e., the iteration spaces involving loop variables that take integer values between specified lower and upper bounds. In many applications, a loop could involve a loop variable which takes values from a sequence or set of real numbers, strings, or any other data type. We refer to such iteration spaces as non-integer iteration spaces. This paper focuses on the problem of applying data-centric transformations on applications with non-integer iteration spaces. We first present a general algorithm that uses a hash table. Then, we show how in many cases, we can exploit the repetitive nature of the dataset to avoid the overhead associated with such a table. Our algorithms have been implemented as part of a compiler for the XML query language XQuery, which supports processing over virtual XML. Our system also parallelizes the processing. We present experimental results from several applications to demonstrate the effectiveness of our transformations and parallel performance.