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As the ratio between the rate of computation and rate with which data can beretrieved from various layers of memory continues to deteriorate, a questionarises: Will the current best algorithms for computing matrix-matrixmultiplication on future CPUs continue to be (near) optimal? This paperprovides compelling analytical and empirical evidence that the answer is "no".The analytical results guide us to a new family of algorithms of which thecurrent state-of-the-art "Goto's algorithm" is but one member. The empiricalresults, on architectures that were custom built to reduce the amount ofbandwidth to main memory, show that under different circumstances, differentand particular members of the family become more superior. Thus, this familywill likely start playing a prominent role going forward.

The MOMMS Family of Matrix Multiplication Algorithms