Access Ordering Algorithms for an Interleaved Memory

Superscalar processors are well suited for meeting the demands of scientific computing, given sufficient memory bandwidth. Employing parallel memory modules increases the bandwidth available; however , storage schemes devised to reduce module conflict for vector computers are not suitable for scalar computation. Access ordering is a compilation technique that increases effective bandwidth by reordering references to exploit the underlying memory system. Ordering algorithms are derived in this report for a sequentially interleaved memory architecture. Memory system parameters: word size page size page-hit read cycle time page-hit write cycle time page-miss overhead uniform-access read cycle time uniform-access write cycle time Stream parameters: stream start address (vector accessed) stride of access data size mode of access number of data items referenced per functional iteration MAP notation: access to the next element of stream access from for a given access sequence iteration set of all streams in a given MAP number of streams in number of different vectors referenced by streams in depth of loop unrolling Performance measures: average time per access processor-memory bandwidth w p T p/ r T p/ w T p/ m T u/ r T u/ w v s d m σ a i t i a i k k th t i S N S V S b T avg BW iv General properties of stream : number of accesses per loop iteration intermix factor Properties of stream for a sequentially interleaved architecture: number of modules referenced set of modules referenced module stride maximum number of accesses serviced at any module for a given iteration Modeling functions: average number of data items per word average number of data items per page average per iteration page miss count average per iteration page miss count for intermixed write stream average per iteration page miss count for wrap-around adjacent read stream effect of intermixing on average page miss count of write stream effect of wrap-around adjacency on page miss count of read stream t i ε i