159,858 research outputs found
Certifying floating-point implementations using Gappa
High confidence in floating-point programs requires proving numerical
properties of final and intermediate values. One may need to guarantee that a
value stays within some range, or that the error relative to some ideal value
is well bounded. Such work may require several lines of proof for each line of
code, and will usually be broken by the smallest change to the code (e.g. for
maintenance or optimization purpose). Certifying these programs by hand is
therefore very tedious and error-prone. This article discusses the use of the
Gappa proof assistant in this context. Gappa has two main advantages over
previous approaches: Its input format is very close to the actual C code to
validate, and it automates error evaluation and propagation using interval
arithmetic. Besides, it can be used to incrementally prove complex mathematical
properties pertaining to the C code. Yet it does not require any specific
knowledge about automatic theorem proving, and thus is accessible to a wide
community. Moreover, Gappa may generate a formal proof of the results that can
be checked independently by a lower-level proof assistant like Coq, hence
providing an even higher confidence in the certification of the numerical code.
The article demonstrates the use of this tool on a real-size example, an
elementary function with correctly rounded output
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
Efficient symbolic computation of approximated small-signal characteristics of analog integrated circuits
A symbolic analysis tool is presented that generates simplified symbolic expressions for the small-signal characteristics of large analog integrated circuits. The expressions are approximated while they are computed, so that only those terms are generated which remain in the final expression. This principle causes drastic savings in CPU time and memory, compared with previous symbolic analysis tools. In this way, the maximum size of circuits that can be analyzed, is largely increased. By taking into account a range for the value of a circuit parameter rather than one single number, the generated expressions are also more generally valid. Mismatch handling is explicitly taken into account in the algorithm. The capabilities of the new tool are illustrated with several experimental result
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Functional Relationships between Kinetic, Flow, and Geometrical Parameters in a High-Temperature Chemical Microreactor.
Computational fluid dynamics (CFD) simulations and isothermal approximation were applied for the interpretation of experimental measurements of the C10H7Br pyrolysis efficiency in the high-temperature microreactor and of the pressure drop in the flow tube of the reactor. Applying isothermal approximation allows the derivation of analytical relationships between the kinetic, gas flow, and geometrical parameters of the microreactor, which, along with CFD simulations, accurately predict the experimental observations. On the basis of the obtained analytical relationships, a clear strategy for measuring rate coefficients of (pseudo) first-order bimolecular and unimolecular reactions using the microreactor was proposed. The pressure- and temperature-dependent rate coefficients for the C10H7Br pyrolysis calculated using variable reaction coordinate transition state theory were invoked to interpret the experimental data on the pyrolysis efficiency
Surface roughness effect on ultracold neutron interaction with a wall and implications for computer simulations
We review the diffuse scattering and the loss coefficient in ultracold
neutron reflection from slightly rough surfaces, report a surprising reduction
in loss coefficient due to roughness, and discuss the possibility of transition
from quantum treatment to ray optics. The results are used in a computer
simulation of neutron storage in a recent neutron lifetime experiment that
re-ported a large discrepancy of neutron lifetime with the current particle
data value. Our partial re-analysis suggests the possibility of systematic
effects that were not included in this publication.Comment: 39 pages, 9 figures; additional calculations include
Estimating anisotropy parameters and traveltimes in the tau-p domain
The presence of anisotropy influences many aspects of
seismic wave propagation and has therefore implications
for conventional processing schemes. To estimate the
anisotropy, we need both forward modelling and inversion
tools. Exact forward modelling in anisotropic media
is generally done by raytracing. However, we present a
new and fast method, using the tau-p transform, to calculate
exact P and SV reflection moveout curves in stratified,
laterally homogeneous, anisotropic media which
requires no ray tracing. Results are exact even if the
SV-waves display cusps. In addition, we show how the
same method can be used for parameter estimation.
Since inversion for anisotropic parameters is very
nonunique, we develop expressions requiring only a reduced
number of parameters. Nevertheless, predictions
using these expressions are more accurate than Taylor
series expansions and are also able to handle cusps in
the SV traveltime curves. In addition, layer stripping is
a linear process. Therefore, both effective (average) and
local (interval) estimates can be obtained
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