Accessand Alignment ofDatainan Array Processor

This paperdiscusses thedesign ofaprimary memory systemforanarrayprocessor whichallows parallel, conflict-free access tovarious slices ofdata(e.g., rows, columns, diagonals, etc.), andsubsequent alignment ofthesedataforprocessing. Memory access requirements foranarray processor arediscussed ingeneral termsandasetofcommonrequirements aredefined. Theability to meettheserequirements isshowntodependonthenumberofin- dependent memoryunits andonthemapping ofthedatainthese memories. Next, theneedtoalign these dataforprocessing isdemon- strated andvarious alignment requirements aredefined. Hardware whichcanperform this alignment function isdiscussed, e.g., permu- tation, indexing, switching orsorting networks, -andanetwork (the omeganetwork) basedonStone's shuffle-exchange operation (11 is presented. Construction ofthis network isdescribed andmanyofits useful properties areproven. Finally, asanexample ofthese ideas, an array processor isshownwhichallows conflict-free access andalign- mentofrows,columns, diagonals, backward diagonals, andsquare blocks inroworcolumn majororder, aswell ascertain other special operations. IndexTerms-Alignment network, array processor, array storage, conflict-free acess, dataalignment, indexing network, omeganetwork, parallel processing, permutation network, shuffle-exchange network, storage mapping, switching network.