Random Degrees of Unbiased Branches

In our previous published research we discovered some very difficult to predict branches, called unbiased branches that have a “random” dynamical behavior. We developed some improved state of the art branch predictors to predict successfully unbiased branches. Even these powerful predictors obtained very modest average prediction accuracies on the unbiased branches while their global average prediction accuracies are high. These unbiased branches still restrict the ceiling of dynamic branch prediction and therefore accurately predicting unbiased branches remains an open problem. Starting from this technical challenge, we tried to understand in more depth what randomness is. Based on a hybrid mathematical and computer science approach we mainly developed some degrees of random associated to a branch in order to understand deeply what an unbiased branch is. These metrics are program’s Kolmogorov complexity, compression rate, discrete entropy and HMM prediction’s accuracy, that are useful for characterizing strings of symbols and particularly, our unbiased branches’ behavior. All these random degree metrics could effectively help the computer architect to better understand branches’ predictability, and also if the branch predictor should be improved related to the unbiased branches.