On minimizing materializations of array-valued temporaries

We consider the analysis and optimization of code utilizing operations and functions operating on entire arrays. Models are developed for studying the minimization of the number of materializations of array-valued temporaries in basic blocks, each consisting of a sequence of assignment statements involving array-valued variables. We derive lower bounds on the number of materializations required, and develop several algorithms minimizing the number of materializations, subject to a simple constraint on allowable statement rearrangement. In contrast, we also show that when statement rearrangement is unconstrained, minimizing the number of materializations becomes NP-complete, even for very simple basic blocks.