A data processor system includes a local memory, a processor core, and an extent monitor. The local memory stores a block of data at a task memory location that is exclusive to a particular task during a duration of time. The processor core accesses the task memory location of the local memory during the execution of the particular task, and modifies to the block of data stored in the task memory location. The extent monitor monitors a write operation the processor core to the local memory to determine a first most-extreme address of the task memory location modified by the execution of the particular task during the duration of time. The processor core also executes a write back instruction to write back to a shared memory location less than the entire block of data based upon the most-extreme address.