On the mathematics of caching

  • Authors:
  • Richard Enbody;Mark W. Brehob

  • Affiliations:
  • -;-

  • Venue:
  • On the mathematics of caching
  • Year:
  • 2003

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Abstract

Computer circuits get faster at a much more rapid rate than memory. In order for historical computer performance gains to continue, memory latency and bandwidth need to continue to improve. The most common way to provide this performance is to use small, but very fast, memory devices to store the most commonly used data called caches. Cache performance relies upon locality: the predictable way in which caches tend to access memory elements that have accessed in the past or near those previous accesses. Of fundamental importance to improving a complex device is understanding how that device functions. This work contributes to that understanding in two ways. First, it expands upon an old and mostly unused model of locality called ‘stack distance’ and shows how that locality interacts with various types of caches including victim and skew caches. Second, a negative result is provided showing that it is computationally intractable to find an optimal schedule for most non-standard caches. This result means that a very useful tool for cache evaluation is not available when working with these non-standard caches. It also means that those working on finding a tractable optimal algorithm for these caches can stop—they will not succeed.