Implications of program phase behavior on timing analysis

Knowledge about program worst case execution time (WCET) is essential in validating real-time systems and helps in effective scheduling. One popular approach used in industry is to measure execution time of program components on the target architecture and combine them using static analysis of the program. Measurements need to be taken in the least intrusive way in order to avoid affecting accuracy of estimated WCET. Several programs exhibit phase behavior, wherein program dynamic execution is observed to be composed of phases. Each phase being distinct from the other, exhibits homogeneous behavior with respect to cycles per instruction (CPI), data cache misses etc. In this paper, we show that phase behavior has important implications on timing analysis. We make use of the homogeneity of a phase to reduce instrumentation overhead at the same time ensuring that accuracy of WCET is not largely affected. We propose a model for estimating WCET using static worst case instruction counts of individual phases and a function of measured average CPI. We describe a WCET analyzer built on this model which targets two different architectures. The WCET analyzer is observed to give safe estimates for most benchmarks considered in this paper. The tightness of the WCET estimates are observed to be improved for most benchmarks compared to Chronos, a well known static WCET analyzer.

Estimation of Probabilistic Bounds on Phase CPI and Relevance in WCET Analysis

Estimating program worst case execution time(WCET) accurately and efficiently is a challenging task. Several programs exhibit phase behavior wherein cycles per instruction (CPI) varies in phases during execution. Recent work has suggested the use of phases in such programs to estimate WCET with minimal instrumentation. However the suggested model uses a function of mean CPI that has no probabilistic guarantees. We propose to use Chebyshev's inequality that can be applied to any arbitrary distribution of CPI samples, to probabilistically bound CPI of a phase. Applying Chebyshev's inequality to phases that exhibit high CPI variation leads to pessimistic upper bounds. We propose a mechanism that refines such phases into sub-phases based on program counter(PC) signatures collected using profiling and also allows the user to control variance of CPI within a sub-phase. We describe a WCET analyzer built on these lines and evaluate it with standard WCET and embedded benchmark suites on two different architectures for three chosen probabilities, p={0.9, 0.95 and 0.99}. For p= 0.99, refinement based on PC signatures alone, reduces average pessimism of WCET estimate by 36%(77%) on Arch1 (Arch2). Compared to Chronos, an open source static WCET analyzer, the average improvement in estimates obtained by refinement is 5%(125%) on Arch1 (Arch2). On limiting variance of CPI within a sub-phase to {50%, 10%, 5% and 1%} of its original value, average accuracy of WCET estimate improves further to {9%, 11%, 12% and 13%} respectively, on Arch1. On Arch2, average accuracy of WCET improves to 159% when CPI variance is limited to 50% of its original value and improvement is marginal beyond that point.