Time and Parallel Processor Bounds for Fortran-Like Loops

The main goal of this paper is to show that a large number of processors can be used effectively to speed up simple Fortran-like loops consisting of assignment statements. A practical method is given by which one can check whether or not a statement is dependent upon another. The dependence structure of the whole loop may be of different types. For each type, a set of time and processor upper bounds is given. We also show how a loop can sometimes be transformed to change its dependence structure. Finally, we give a result on the possible splitting up of a given recurrence system into a number of smaller subsystems. These results can be used to modify and sometimes improve the bounds for the loops as demanded by special circumstances.