Extent Analysis of Data

Data parallelism means operating on distributed tables, data elds, in parallel. An abstract model of data parallelism treats data elds as functions explicitly restricted to a nite set. Data parallel functional languages based on this view vill reach a very high level of abstraction. In this report we consider two static analyses that, when successful, give information about the extent of a recursively deened data eld. This information can be used to preallocate the data elds and map then eeciently to distributed memory, and to aid the static scheduling of operations. The analyses are cast in the framework of abstract interpretation: a forward analaysis propagates restrictions on inputs to restrictions on outputs, and a backward analysis propagates restrictions the other way. Fixpoint iteration can sometimes be used to solve the equations that arise, and we devise some cases where this is possible.