Abstract

Data parallelism means operating on distributed tables, data fields, in parallel. An abstract model of data parallelism treats data fields as functions explicitly restricted to a finite 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 defined data field. This information can be used to preallocate the data fields and map then efficiently 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.

Citations