A computer processing system method and apparatus having a processor employing an operating system (O/S) multi-task control between multiple user programs and which ensures that the programs do not interfere with each other, said computing processing system having a branch multiple page size prediction mechanism which predicts a page size along with a branch direction and a branch target of a branch for instructions of a processing pipeline, having a branch target buffer (BTB) predicting the branch target, said branch prediction mechanism storing recently used instructions close to the processor in a local cache, and having a translation look-aside buffer TLB mechanism which tracks the translation of the most recent pages and supports multiple page sizes.