Open Access Journal of Applied Science and Technology(OAJAST)

College of Nanotechnology, Science, and Engineering, University at Albany, SUNY, USA

Publications

• Research Article   
  Machine Shape and Hierarchical Blocking: A Mathematics of Arrays Formalization, with an Open Problem in Hierarchical Shape Occupancy
  Author(s): Lenore M. Mullin*
  
  A companion empirical study found that dense matrix multiplication block sizes calibrated on Apple M1 Pro correspond to two cache-fit formulas that mispredict badly on a different chip’s known cache sizes. This paper formalizes the question that finding raises. We extend the Mathematics of Arrays (MoA) framework’s array-shape derivation operator to a new operator that derives a hierarchical, multi-level blocking and prefetch schedule from a machine’s shape: an ordered sequence of cache-level capacities, bandwidths, and occupancy fractions. This operator recovers the calibrated values on every one of three real machines tested to date as a special case, reducing each machine’s unknowns to a small number of level-specific occupancy fractions. We then state precisely, without claiming to resolve, the paper’s central open problem: whether those fractions are .. Read More»
  

  Abstract HTML PDF