Generalizing parametric timing analysis

Abstract

In the design of real-time and embedded systems, it is important to establish a bound on the worst-case execution time (WCET) of programs to assure via schedulability analysis that deadlines are not missed. Static WCET analysis is performed by a timing analysis tool. This paper describes novel improvements to such a tool, allowing parametric timing analysis to be performed. Parametric timing analyzers receive an upper bound on the number of loop iterations in terms of an expression which is used to create a parametric formula. This parametric formula is later evaluated to determine the WCET based on input values only known at runtime. Effecting a transformation from a numeric to a parametric timing analyzer requires two innovations: 1) a summation solver capable of summation non-constant expressions and 2) a polynomial data structure which can replace integers as the basis for all calculations. Both additions permit other methods of analysis (e.g. caching, pipeline, constraint) to occur simultaneously. Combining these techniques allows our tool to statically bound the WCET for a larger class of benchmarks.