Piecewise Linear Schedules For Recurrence Equations

The scheduling problem for a system of &ne recurrence equaitions (SARE) has been studied by many researchers. The emphasis has been on an important class of timing functions called linear or afine schedules. For many SAREs, linear schedules may not exist, although the SARE is computable. It will be shown that it is possible to find joiecewise linear schedules (PLS) for many practical algorithms expressed in terms of SAREs. PLS have different slopes for different variables in the algorithm. For each variable, the computation domain is partitioned into finitely many “pieces” in which the schedule is different for each subdomain. The main focus of this paper is to introduce PLS and develop a synthesis procedure to find PLS for the given SARE.