Knowing the Worst-Case Execution Time (WCET) of a program is necessary when designing and verifying real-time systems. The WCET depends both on the program ow (like loop iterations and function calls), and on hardware factors like caches and pipelines.

Embedded systems often have real-time constraints. Traditional timing analysis statically determines the maximum execution time of a task or a program in a real-time system. These systems typically depend on the worst-case execution time of tasks in order to make static scheduling decisions so that tasks can meet their deadlines. Static determination of worst-case execution times imposes numerous restrictions on real-time programs, which include that the maximum number of iterations of each loop must be known statically. These restrictions can significantly limit the class of programs that would be suitable for a real-time embedded system. This paper describes work-in-progress that uses static timing analysis to aid in making dynamic scheduling decisions. For instance, different algorithms with varying levels of accuracy may be selected based on the algorithm’s predicted worst-case execution time and the time allotted for the task. We represent the worstcase execution time of a function or a loop as a formula, where the unknown values affecting the execution time are parameterized. This parametric timing analysis produces formulas that can then be quickly evaluated at run-time so dynamic scheduling decisions can be made with little overhead. Benefits of this work include expanding the class of applications that can be used in a real-time system, improving the accuracy of dynamic scheduling decisions, and more effective utilization of system resources. 1.

AbstractResource-constrained devices are becoming ubiquitous. Examples include cell phones, palm pilots, and digital ther-mostats. It can be difficult to fit required functionality into such a device without sacrificing the simplicity and clarityof the software. Increasingly complex embedded systems require extensive brute-force testing, making development andmaintenance costly. This is particularly true for system components that are written in assembly language. Static check-ing has the potential of alleviating these problems, but until now there has been little tool support for programming at theassembly level.

This paper describes an inter-procedural technique for computing symbolic bounds on the number of statements a procedure executes in terms of its scalar inputs and user-defined quantitative functions of input data-structures. Such computational complexity bounds for even simple programs are usually disjunctive, non-linear, and involve numerical properties of heaps. We address the challenges of generating these bounds using two novel ideas. We introduce a proof methodology based on multiple counter instrumentation (each counter can be initialized and incremented at potentially multiple program locations) that allows a given linear invariant generation tool to compute linear bounds individually on these counter variables. The bounds on these counters are then composed together to generate total bounds that are non-linear and disjunctive. We also give an algorithm for automating this proof

Symbolic complexity bounds help programmers understand the performance characteristics of their implementations. Existing work provides techniques for statically determining bounds of procedures with simple control-flow. However, procedures with nested loops or multiple paths through a single loop are challenging. In this paper we describe two techniques, control-flow refinement and progress invariants, that together enable estimation of precise bounds for procedures with nested and multi-path loops. Control-flow refinement transforms a multi-path loop into a semantically equivalent code fragment with simpler loops by making the structure of path interleaving explicit. We show that this enables non-disjunctive invariant generation tools to find a bound on many procedures for which previous techniques were unable to prove termination. Progress invariants characterize relationships between

While caches have become invaluable for higher-end architectures due to their ability to hide, in part, the gap between processor speed and memory access times, caches (and particularly data caches) limit the timing predictability for data accesses that may reside in memory or in cache. This is a significant problem for real-time systems. The objective our work is to provide accurate predictions of data cache behavior of scalar and non-scalar references whose reference patterns are known at compile time. Such knowledge about cache behavior provides the basis for significant improvements in bounding the worst-case execution time (WCET) of real-time programs, particularly for hardto-analyze data caches. We exploit the power of the Cache Miss Equations (CME) framework but lift a number of limitations of traditional CME to generalize the analysis to more arbitrary programs. We further devised a transformation, coined “forced ” loop fusion, which facilitates the analysis across sequential loops. Our contributions result in exact data cache reference patterns — in contrast to approximate cache miss behavior of prior work. Experimental results indicate improvements on the accuracy of worst-case data cache behavior up to two orders of magnitude over the original approach. In fact, our results closely bound and sometimes even exactly match those obtained by trace-driven simulation for worst-case inputs. The resulting WCET bounds of timing analysis confirm these findings in terms of providing tight bounds. Overall, our contributions lift analytical approaches to predict data cache behavior to a level suitable for efficient static timing analysis and, subsequently, real-time schedulability of tasks with predictable WCET. 1.

Estimating the Worst-case Execution Time (WCET) of real-time embedded software is an important problem. WCET is defined as the upper bound b on the execution time of a program P on a processor X such that for any input the execution time of P on X is guaranteed to not exceed b. Such WCET estimates are crucial for schedulability analysis of real-time systems. In this paper, we present Chronos, a static analysis tool for generating WCET estimates of C programs. It performs detailed micro-architectural modeling to capture the timing effects of the underlying processor platform. Consequently, we can provide safe but tight WCET estimate of a given C program running on a complex modern processor. Chronos is an opensource distribution specifically suited to the needs of the research community. We support processor models captured by the popular SimpleScalar architectural simulator rather than targeting specific commercial processors. This makes Chronos flexible, extensible and easily accessible to the researcher.

Abstract. This paper describes a precise numerical abstract domain for use in timing analysis. The numerical abstract domain is parameterized by a linear abstract domain and is constructed by means of two domain lifting operations. One domain lifting operation is based on the principle of expression abstraction (which involves defining a set of expressions and specifying their semantics using a collection of directed inference rules) and has a more general applicability. It lifts any given abstract domain to include reasoning about a given set of expressions whose semantics is abstracted using a set of axioms. The other domain lifting operation domain via introduction of max expressions. We present experimental results demonstrating the potential of the new numerical abstract domain to discover a wide variety of timing bounds (including polynomial, disjunctive, logarithmic, exponential, etc.) for small C programs. 1

Parametric worst-case execution time (WCET) bounds are critical in removing restrictions, such as known loop bounds, on algorithms for important applications such as scheduling for real-time embedded systems. Current parametric approaches have difficulties with loop nests that include non-rectangular loops, zero-trip loops, and/or loops with non-unit strides. This paper presents a novel approach to parametric WCET estimation based on numeric/symbolic manipulation of polynomial representations for the timing of rectangular and non-rectangular loop nests including those with zero-trip loops, non-unit strides, and multiple critical paths.

TUBOUND is a conceptually new tool for the worst-case execution time (WCET) analysis of programs. A distinctive feature of TUBOUND is the seamless integration of a WCET analysis component and of a compiler in a uniform tool. TUBOUND enables the programmer to provide hints improving the precision of the WCET computation on the high-level program source code, while preserving the advantages of using an optimizing compiler and the accuracy of a WCET analysis performed on the low-level machine code. This way, TUBOUND ideally serves the needs of both the programmer and the WCET analysis by providing them the interface on the very abstraction level that is most appropriate and convenient to them. In this paper we present the system architecture of TUBOUND, discuss the internal work-flow of the tool, and report on first measurements using benchmarks from Mälardalen University. TUBOUND took also part in the WCET Tool Challenge 2008.