Abstract

Citation

Researchers should cite this work as follows:

• Beckmann, N. (2023). 2015-Beckmann-Sanchez-Cache Calculus-Modeling Caches through Differential Equations. SIMIODE, QUBES Educational Resources. doi:10.25334/VPFJ-Z408

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Description

Beckmann, Nathan and  Daniel Sanchez.  2015. Cache Calculus: Modeling Caches through Differential Equations. Computer Science and Artifical Intelligence Laboratory, MIT.

See https://people.csail.mit.edu/sanchez/papers/2016.cachecalc.cal.pdf.  Access 28 March 2023.

Abstract: —Caches are critical to performance, yet their behavior is hard to understand and model. In particular, prior work does not provide closed-form solutions of cache performance, i.e. simple expressions for the miss rate of a specific access pattern. Existing cache models instead use numerical methods that, unlike closed-form solutions, are computationally expensive and yield limited insight. We present cache calculus, a technique that models cache behavior as a system of ordinary differential equations, letting standard calculus techniques find simple and accurate solutions of cache performance for common access patterns.

Keywords: cache, differential equation, model, discrete, difference equation