10,459 research outputs found
Hardware-Independent Proofs of Numerical Programs
On recent architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding error of each floating-point computation whatever the environment. This approach is implemented in the Frama-C platform for static analysis of C code. Small case studies using this approach are entirely and automatically prove
Hardware-independent proofs of numerical programs
International audienceOn recent architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding error of each floating-point computation whatever the environment. This approach is implemented in the Frama-C platform for static analysis of C code. Small case studies using this approach are entirely and automatically proved
Modular Verification of Interrupt-Driven Software
Interrupts have been widely used in safety-critical computer systems to
handle outside stimuli and interact with the hardware, but reasoning about
interrupt-driven software remains a difficult task. Although a number of static
verification techniques have been proposed for interrupt-driven software, they
often rely on constructing a monolithic verification model. Furthermore, they
do not precisely capture the complete execution semantics of interrupts such as
nested invocations of interrupt handlers. To overcome these limitations, we
propose an abstract interpretation framework for static verification of
interrupt-driven software that first analyzes each interrupt handler in
isolation as if it were a sequential program, and then propagates the result to
other interrupt handlers. This iterative process continues until results from
all interrupt handlers reach a fixed point. Since our method never constructs
the global model, it avoids the up-front blowup in model construction that
hampers existing, non-modular, verification techniques. We have evaluated our
method on 35 interrupt-driven applications with a total of 22,541 lines of
code. Our results show the method is able to quickly and more accurately
analyze the behavior of interrupts.Comment: preprint of the ASE 2017 pape
Certifying cost annotations in compilers
We discuss the problem of building a compiler which can lift in a provably
correct way pieces of information on the execution cost of the object code to
cost annotations on the source code. To this end, we need a clear and flexible
picture of: (i) the meaning of cost annotations, (ii) the method to prove them
sound and precise, and (iii) the way such proofs can be composed. We propose a
so-called labelling approach to these three questions. As a first step, we
examine its application to a toy compiler. This formal study suggests that the
labelling approach has good compositionality and scalability properties. In
order to provide further evidence for this claim, we report our successful
experience in implementing and testing the labelling approach on top of a
prototype compiler written in OCAML for (a large fragment of) the C language
Interval Slopes as Numerical Abstract Domain for Floating-Point Variables
The design of embedded control systems is mainly done with model-based tools
such as Matlab/Simulink. Numerical simulation is the central technique of
development and verification of such tools. Floating-point arithmetic, that is
well-known to only provide approximated results, is omnipresent in this
activity. In order to validate the behaviors of numerical simulations using
abstract interpretation-based static analysis, we present, theoretically and
with experiments, a new partially relational abstract domain dedicated to
floating-point variables. It comes from interval expansion of non-linear
functions using slopes and it is able to mimic all the behaviors of the
floating-point arithmetic. Hence it is adapted to prove the absence of run-time
errors or to analyze the numerical precision of embedded control systems
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