Deriving Limits of Branch Prediction with the Fano Inequality

Information theory provides tools and techniques to measure the fundamental limits of predictability. Apart from this formal basis, researchers have attempted to construct so-called ‘optimal’ predictors in order to conduct limits studies for different aspects of program predictability (such as branch outcomes and method return values). This paper reports on two case studies for branch prediction limits. The first study duplicates an earlier analysis of the branch predictability of the Quicksort algorithm by Mudge et al [15]. Whereas they design an optimal predictor for the algorithm, we use information theory and arrive at the same result with considerably less effort. The second study is the information theoretic analysis of the Championship Branch Prediction traces. Our analysis establishes the limits