A Declarative Compositional Timing Analysis for Multicores Using the Latency-Rate Abstraction

Abstract

This paper presents a functional model for timing analysis by abstract interpretation, used for estimation of worst-case execution times (WCET) in multicore architectures using a denotational semantics. The objective aims at surpassing the intrinsic computational complexity of timing analysis of multiple processing units sharing common resources. For this purpose, we propose a novel application of latency-rate ($\mathcal{LR}$) servers, phrased in terms of abstract interpretation, to achieve timing compositionality on requests to shared resources. The soundness of the approach is proven with respect to a calculational fixpoint semantics for multicores that is able to express all possible ways in which a shared resource can be accessed. Experimental results show that the loss in precision introduced by the $\mathcal{LR}$ server model is about 10% on average and is fairly compensated by the gain in analysis time, which is above 99%. The system is implemented in Haskell, taking advantages of the declarative features of the language for a simpler and more robust specification of the underlying concepts.