Toward Compact Abstractions For Processor Pipelines

Hard real-time systems require programs to react on time. Static timing analysis derives timing guarantees by analyzing the behavior of programs running on the underlying execution platform. Efficient abstractions have been found for the analysis of caches. Unfortunately, this is not the case for the analysis of processor pipelines. Pipeline analysis typically uses an expensive powerset domain of concrete pipeline states. Therefore, pipeline analysis is the most complex part of timing analysis. We propose a compact abstract domain for pipeline analysis. This pipeline analysis determines the minimal progress of instructions in the program through the pipeline.We give a concrete semantics for an in-order pipeline, which forms the basis for an abstract semantics. On the way, we found out that in-order pipelines are not guaranteed to be free of timing anomalies, i.e. local worst decisions do not lead to the global worst case. We prove this by giving an example. A major problem is how to find an abstract semantics that guarantees progress on the abstract side. It turns out that monotonicity on the partial progress order is sufficient to guarantee this.