History-based Schemes and Implicit Path Enumeration

The Implicit Path Enumeration Technique is often used to compute the WCET of control-intensive programs. This method does not consider execution paths as ordered sequences of basic blocks but instead as sets of basic blocks with their respective execution counts. This way of describing an execution path is adequate to compute its execution time, provided that safe individual WCETs for the blocks are known. Implicit path enumeration has also been used to analyze hardware schemes like instructions caches or branch predictors the behavior of which depends on the execution history. However, implicit paths do not completely capture the execution history since they do not express the order in which the basic blocks are executed. Then the estimated longest path might not be feasible and the estimated WCET might be overly pessimistic. This problem has been raised for cache analysis. In this paper, we show that it arises more acutely for branch prediction and we propose a solution to tighten the estimation of the misprediction counts.